• Course Code: 01:640:488
• Semester(s) Offered: Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Probability (Math 477)

COURSE DESCRIPTION

This course provides a thorough grounding in property - casualty actuarial mathematics with a strong leaning towards practical applications in the insurance world.

COURSE OBJECTIVES

The student should be able to explain concepts, recognize notation and solve problems in actuarial mathematics. This course together with Mathematics of Life Contingent Risk Models I covers the majority of the material required by the Society of Actuaries for exam FAM (Fundamentals of Actuarial Mathematics).

The following topics will be covered:

• Insurance and Reinsurance Coverages
• Severity, Frequency, and Aggregate Models of Losses
• Parametric and Non-Parametric Estimation
• Introduction to Credibility Theory
• Pricing and Reserving for Short-Term Insurance Coverages

Please note that the "Semester(s) Offered" entry does not guarantee that the course will always be offered in that semester. Please consult the online Schedule of Courses to verify whether a course will be offered in an upcoming semester.

• Course Code: 01:640:490
• Semester(s) Offered: Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 485 or B+ or better in Math 477

General Information

The goal of this course is to develop, implement, and present small-group research projects on topics in mathematical finance. The first half of the course will be devoted to learning relevant background material including Brownian motion, Ito calculus, the Feynman-Kacs PDE (connecting probability to PDEs for pricing derivatives), and the Hamilton-Jacobi-Bellman PDE (connecting probability to PDEs to describe optimal investment problems).

The course themes will vary from semester to semester. Some possible themes include universal basic income welfare models in a financial equilibrium, financial modeling with jumps, the rise and use of trading platform apps, using backward stochastic differential equations for financial optimization problems, market microstructure, modeling of mortgages, and sports betting.

Throughout the first half of the course, the mathematical setting for the theme will be covered in enough detail to be a launching pad for the research projects. Each group's specific research project topic will be based on the broader theme and will be generated in collaboration with the instructor and the group. The second half of the course will be devoted to implementing and executing the research projects. The students will present their work to the class in the final two weeks of the semester.

Prerequisites

• 01:640:485.
• Alternatively, 01:640:477 with grade of B+ or A.

To register using the alternative prerequisites, fill out this form.

Textbook

We will not follow a specific textbook, so you are encouraged to take notes in class.  Supplementary material will be posted to our course's Canvas site.

• Course Code: 01:640:489
• Semester(s) Offered: Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 485 (or B+ or better in Math 477) and Intro Programming (CS 107 or CS 111 or 14:332:252)

General Information

The course starts with Monte Carlo (MC) simulation (in particular, simulation of stochastic differential equations, SDEs) followed by finite difference (FD) methods for PDEs. Applications include fixed income models (Vasicek and CIR), stochastic volatility models (Heston, Stein and Stein, and Bates) and credit derivatives (credit default swaps (CDS) and basket derivatives). A large part of lectures will be devoted to create Matlab code.

Prerequisites

• 01:640:485 and either 01:198:107 or 01:198:111.
• Alternatively, 01:640:485 and 14:332:252.
• Alternatively, 01:640:477 with grade of B+ or A and any one of 01:198:107, 01:198:111, or 14:332:252

To register using alternative prerequisites, fill out this form.

Textbook

We will not follow a specific text so you are asked to take notes in class (if you miss class, ask fellow students for a copy). 

• Course Code: 01:640:130
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 3
• SAS Core Certified: QQ, QR
• Counts toward math major/minor?: No
• Prerequisites: Math 111 or Math 115 or placement

General Information

Math 130 is a calculus course intended for RBS students and some Economics majors. Each section meets twice a week for 80 minutes. Class meetings will be made up of a lecture followed by either a groupwork assignment or quiz. There is no separate recitation.

This course fulfills both the Quantitative Information (QQ) and Mathematical or Formal Reasoning (QR) learning goals of the SAS Core Curriculum.

This is a terminal course and cannot be used as a prerequisite for Calculus 2.

Catalog listing:

01:640:130 Business Calculus (3)

Math 130 provides an introduction to calculus, covering exponential and logarithmic functions, limits and continuity, the derivative and tangent lines, applications of the derivative, and basic integration. Examples will be drawn from business and economics, including market equilibrium, maximizing profit, elasticity, and marginal analysis.

Prerequisites: Math 111 or Math 112 or Math 115 or appropriate performance on the placement test in mathematics.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

• Course Code: 01:640:158
• Semester(s) Offered: Fall, Spring
• Credits: 1
• Counts toward math major/minor?: No
• Prerequisites: This is a support course for students currently taking Math 152

General Information (Catalog listing)

01:640:158 Calculus II for Mathematical and Physical Sciences Practicum (1)
Application of algorithms studied in 01:640:152 to problems.
Corequisite: 01:640:152.

This class gives a review of topics that are covered in Math 151 and not in Math 135 (or less heavily). For example, inverse trigonometry, Riemann sums, and vertical integration (dy vs dx). It is intended to help those students more likely to struggle in Math 152 to pass the class successfully. There are ten 80 minute meetings twice a week for the first five weeks of the semester.

Who should take this course?

Students in Math 152 that are good candidates for Math 158 are students who:

• took Math 135,
• received a low grade in Math 151,
• earned a 4 on the AP Calculus AB exam,
• took Calculus I at another school, or
• feel they may be at risk to do poorly in Math 152.

Course Overview

Course Format: There are ten 80 minute meetings twice a week for the first five weeks of the semester.

Grading: The grade will be based on workshops, quizzes, homework, attendance, and participation. There are no exams in this class.

Questions: Students with questions about the course should email Paul Ellis at prellis at rutgers dot edu.

Schedule of Sections: 

 01:640:158 Schedule of Sections

• Course Code: 01:640:157
• Semester(s) Offered: Fall, Spring
• Credits: 1
• Counts toward math major/minor?: No
• Prerequisites: This is a support course for students currently taking Math 151

General Information (Catalog listing)

01:640:157 Calculus I for Mathematical and Physical Sciences Practicum (1)
Application of algorithms studied in 01:640:151 to problems.
Corequisite: 01:640:151.

This class gives a review of precalculus material and discusses proper math notation and vocabulary. It is intended to help those students more likely to struggle in Math 151 to pass the class successfully.

Who should take this course?

Students in Math 151 that are good candidates for Math 157 are students who:

• have a low CLS placement score,
• received a low grade in precalculus, or
• feel they may be at risk to do poorly in Math 151.

Course Overview

Course Format: There are ten 80 minute meetings twice a week for the first five weeks of the semester.

Grading: The grade will be based on quizzes, homework, attendance, and participation. There are no exams in this class.

Questions: Students with questions about the course should email Paul Ellis at prellis at rutgers dot edu.

Enrollment

Students interested in registering for this course can register for any open section.

Problem: Some students are unable to register themselves due to a prerequisite issue. This can be overridden by a dean or advisor. While their enrollment is being sorted out, these students should attend the first class meeting of their preferred section of Math 157.

Schedule of Sections:

 01:640:157 Schedule of Sections

• Course Code: 01:640:125
• Semester(s) Offered: Fall, Spring
• Credits: 2
• Counts toward math major/minor?: No
• Prerequisites: None. Typically taken in parallel with a Precalculus or Calc I course.

Chair:  Michael Beals

Members:  Janos Komlos, Jian Song

The formal requirements for students in the honors track are divided into three main groups of courses:

• 100-200 level courses. There are five required courses: Calculus I (151), Calculus II (152), Multivariable Calculus (251 or 291), Differential Equations (252 or 292), and Linear Algebra (250, or covered via 291-292). Many honors students will receive AP credit for one or more of the calculus classes.  Honors track students should take honors sections of the calculus courses. Honors track students should, if possible, choose one of the MATLAB sections of 250.
• The seminar requirement
• Courses at the 300 level or higher. Students are required to take 9 upper level courses. As described below, each student's program of study must be approved by the honors track committee.

A major part of the program is the requirement to take two rigorous semesters of Real Analysis (411-412, though 501-502 may be substituted with permission) and Algebra (451-452, though 551-552 may be substituted with permission). Honors track students will normally aim to take one (or, with permission, both) of the sequences 411-412 and 451-452 during their junior year. Also, on rare occasions, a student may take one of these sequences in their sophomore year. Students will receive individual advice from their advisors and the honors track committee about when to take these.

Students should prepare for these sequences during their 2nd year  The standard preparation is to take 300H, the honors section of 300, in the fall.  (Students who begin with 291 in their 1st year may consider taking 300H in the spring of their 1st year, along with 292.)  This course is designed to prepare students for all subsequent honors courses.  It is followed by the freshman/sophomore honors seminar 196 in the spring of the 2nd year, as well as 311H or 350H (or both).  Typically, 311H is prerequisite for 411-412, and 350H (or 351-352) is prerequisite for 451-452.

The appropriate course plan for a student depends on a number of factors, and each student should discuss their plans with the chair of the honors committee, and/or their honors track advisor if that person is other than the committee chair.

Students should also normally take a semester of complex analysis (403 or 503) and a semester of probability (477). Students planning to go to graduate school should also normally take Topology (441) since it is a prerequisite for many graduate classes.

The honors track is designed so that students will be prepared to take some of graduate courses in mathematics in their senior year. Taking some graduate courses (suitably chosen) is generally encouraged, though not required for the program.

The honors track is designed so that students will be prepared to take some of graduate courses in mathematics in their senior year. Taking some graduate courses (suitably chosen) is generally encouraged, though not required for the program.

Preparing and your Plan of Study During the semester following their acceptance into the honors track, the student and their honors track advisor would prepare a tentative plan of study.  It outlines the courses the student will take as part of the honors track. Of course, it is generally impossible to make a full plan since the courses a student will take may depend on what they learn from their current courses. So the initial plan can be somewhat vague about the future, and revised as needed, subject to committee approval.  The plan of study can be fairly informal. After preparing it and reviewing it with your advisor you should email it to the chair of the honors committee. Here is a suggested format.

• Your name
• Your expected graduation year
• Your major(s) (Mathematics or Mathematics +…)
• Your plans/goals beyond Rutgers (e.g. graduate school in Math or some other field, employment in some field)
• A list of all courses in Mathematics at the 300 level or higher that you have taken already (including the semester the course was taken and instructor)
• A list of Mathematics courses you plan to take with the given semester. This list may not be final. Your plan for the coming semester should be close to final. For subsequent semesters the plan will be less final, in which case you may want to include some possibilities you are considering (with a few sentences of explanation, if needed).
• Any courses in other departments with significant mathematical content that you think may be relevant.

• Course Code: 01:640:492
• Semester(s) Offered: Spring
• Credits: 1
• Counts toward math major/minor?: Honors track only
• Prerequisites: Special permission only. Topics and prerequisites vary.

Undergraduate Mathematics Seminar: Reading, presentation, and discussion of mathematical topics.

This is a one-credit honors-level seminar. The topics, and prerequisites, vary from semester to semester. Typically, the seminar focuses on a subject area in mathematics that is outside the usual undergraduate curriculum, and participants take turns lecturing.

Admission to the Junior-Senior Honors Seminar is by special permission. To apply, use the online special permission form for honors courses. Students in the mathematics honors track are automatically admitted; other students are admitted based on course record and recommendations by mathematics faculty. Students in the seminar are expected to participate actively by contributing to discussions, making presentations in the seminar, and collaborating with other students in preparing talks.

While almost all participants in the seminar are juniors or seniors, applications from exceptionally qualified freshman and sophomores are considered.

Questions may be sent to one of the Department of Mathematics honors advisors at .

Textbook and Syllabus

Textbook, syllabus, and content change each time the seminar is offered. See the individual course descriptions, or the current textbook list

Spring 2025 - Prof. Dima Sinapova

Textbooks: Jech, Set Theory, the Millenium Edition

We will cover topics from set theory, in particular combinatorial properties of infinite objects. Some of the concepts include introductory cardinal arithmetic, infinite trees, the Suslin hypothesis, regularity properties of the real numbers, the axiom of determinacy.

I will give the first couple of lectures, and then students will take turns presenting. We will be following various chapters in Jech, Set Theory. No prior knowledge of set theory is required.

Admission to the course is by application through the online special permission for honors courses form.

Spring 2021 - Prof Xiaojun Huang

In this one semester seminar course, we will read part of the materials from a very nice small book by S. Krantz: Complex Analysis, the Geometric Viewpoint, the Carus Mathematical Monographs (Number 23).  This viewpoint starts with a classical paper by Ahlfors (An extension of Schwarz's lemma, Trans of the AMS 43(1938), 359-364).  We will discuss  the connection between some classical subjects in one complex variable with those in differential geometry. The prerequisite or corequisite for this course is Math 403, or permission of the instructor.

Notes

This seminar satisfies an honors track requirement.

There is also a U-seminar, for first or second year students.

This course is offered each Spring Semester.
Information will be available during the registration period, through the Honors Track or the Undergraduate Office.

Schedule of Sections

 01:640:492 Schedule of Sections

Previous semesters:

• Spring 2017 Prof. Kontorovich, Number theory, group theory and Ramanujan graphs
• Spring 2016 Prof. Kiessling, Less is more -- the beauty of minimal design
• Spring 2015. Prof. Kahn Surprising mathematical applications of linear algebra.
• Spring 2014 Prof. Beheshti, Mathematical General Relativity.
• Spring 2013
• Spring 2012
• Spring 2011 Profs. Goodman and Wilson The Geometry of finite reflection groups Finite Reflection Groups
• Spring 2010, Prof. Borisov
  Representation Theory
• Spring 2009, Prof. Hoelscher
  Matrix Groups: where Geometry meets Algebra
• Spring 2008, Prof. Carlen
  Inequalities
  
• Spring 2007, Prof. Woodward
  Elementary Number Theory, Group Theory, and Ramanujan Graphs
• Spring 2006, Prof. Beck
  Discrepancy Theory: Uniformity versus Irregularity
• Spring 2005, Profs. Tunnell and Woodward
  Modern Number Theory
• Spring 2004, Profs. Goodman and Sahi
  Fourier Analysis on Finite Groups

• Course Code: 01:640:196
• Semester(s) Offered: Spring
• Credits: 1
• Counts toward math major/minor?: Honors track only
• Prerequisites: Special permission only. Students should have completed at least Calc II.

Undergraduate Mathematics Seminar: Reading, presentation, and discussion of mathematical topics.

This one-credit honors-level seminar is designed for first- and second-year students who are considering studies in advanced mathematics. There is also a Junior-Senior Honors Seminar. These seminars satisfy requirements of the Honors Track in Mathematics.

The First and Second Year Honors Seminar provides a glimpse into the world of mathematics that lies beyond elementary calculus. It aims to be informal, lively, and challenging.

There are no problem sets or exams in the course. Students are expected to participate actively by making presentations in the seminar, collaborating with other students in preparing talks, and contributing to discussions. Occasionally, we have guest speakers (professors and graduate students).

Admission to the First and Second Year Honors Seminar is by special permission. To apply, use the online special permission form for honors courses.

Questions may be addressed to Professors Janos Komlos and Michael Beals (Honors Committee chair).

Textbook and Syllabus

The Spring 2025 textbook is "Conjecture and Proof" by Miklós Laczkovich and is available on the AMS website: https://bookstore.ams.org/clrm-15

Notes

This seminar satisfies an honors track requirement.

This course is offered each Spring Semester.
Information will be available during the registration period, through the Honors Committee or the Undergraduate Office.

Schedule of Sections:

01:640:196 Schedule of Sections

• Course Code: 01:640:491
• Semester(s) Offered: Fall
• Credits: 1
• Counts toward math major/minor?: Honors track only
• Prerequisites: Special permission only. Students should have completed at least Calc II.

This is a one credit seminar in mathematical problem solving.  It is aimed at undergraduate students who enjoy solving mathematical problems in a variety of areas, and want to strengthen their creative mathematical skills, and their skills at doing mathematical proofs.

A secondary goal of this seminar is to help interested students prepare for the William Lowell Putnam Undergraduate Mathematics Competition , which is an annual national mathematics competition held every December. Any full-time undergraduate who does not yet have a college degree is eligible to participate in the exam. (However, you are free to participate in the seminar without taking the exam, and vice versa.)

The meetings of the seminar will be a mixture of presentations by the instructors, group discussions of problems, and student presentations of solutions/ideas.

The seminar qualifies as an honors seminar for the honors track. It does not count as one of the required 300-400 level courses for the major or minor.

Students who have taken the seminar previously may not register for it, but are very welcome to attend.

All students taking the seminar are expected to:

• Attend regularly.
• Participate actively in group problem solving.
• Present problem solutions (or partial solutions) to the class.
• Work on some of the assigned problems and turn in a carefully written solution for at least one problem per week.
• Read assigned material prior to class.

Students taking the seminar for honors track credit may have additional requirements consisting either of doing additional problems or doing more extensive class presentations.

Some Appetizers:

• When you multiply the numbers 1, 2, 3, ..., 400, how many trailing 0's does the answer have?
• Suppose you have a finite collection of points on the plane, such that whenever you draw a line through any 2 of them, that line passes through a 3rd point. Must all the points be collinear?
• Is the 50000th Fibonacci number odd or even?
• Can the product of 2 consecutive integers be a perfect square?
• Suppose you have n red points and n blue points in the plane. Can you pair up the red points with the blue points (each red point is paired with one blue point) so that all the line segments between the pairs are nonintersecting?

This course is offered during the Fall semester.

Schedule of Sections

Archive

• Fall 2008
• Fall 2006

• Semester(s) Offered: Occasional
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Topics and prerequisites vary.

General Information

Content varies widely.

In Fall 2026, there will be two sections of Math 495:

• Section 01: AI Tools for Mathematics
  Instructor: Prof. Carbone <>
  Course Description: see Syllabus
  Prerequisites: Background in proof-based mathematics, 640:300 Intro Math Reasoning or equivalent is required. Graduate students in CS and ECE may receive an exemption with instructor permission. Programming experience will be beneficial but is not essential. 
  If you have taken Math 300 but are missing some of the official prerequisites listed in Webreg (Math 250 and Calc IV = Math 244/252), please fill out the Prerequisite Override Form for assistance with registration.
  
  
• Section 02: Multilinear Algebra and Tensor Networks
  Instructor: Prof. Echeverria <>
  Course Description: see Syllabus
  Prerequisites: Math 251 and Math 250, but Webreg lists Calc IV = Math 244/252 and Math 250 as the prerequisites. If you are missing Calc IV but have taken the true prerequisites (Math 251 and Math 250), please fill out the Prerequisite Override Form for assistance with registration.

In Spring 2026, there were three sections of Math 495:

• Section 01: AI Tools for Mathematics
  Course Description: see Syllabus
  Prerequisites: Background in proof-based mathematics, 640:300 Intro Math Reasoning is strongly recommended. Programming experience will be beneficial but is not essential.
  
  
• Section 02: Combinatorial Game Theory
  

  Course Description: A combinatorial game is ordinarily a two-player game with no hidden information, ending when there are no possible moves remaining. These games have a tendency to break down into smaller pieces, which can be analyzed independently. Dots and Boxes is perhaps a familiar example; one core objective of this course is to seek awesomeness at Dots and Boxes. Combinatorial Game Theory has also been applied to Go, but that is way beyond the scope of this course.

  This course will cover both impartial games (in which both players have the same options) such as Nim, and partizan games, such as Hackenbush. A balance will be sought between deep dives on specific games (such as Sprouts or Hey! That's My Fish!) and general theory. The space of combinatorial games has a rich structure, with many surprising connections.

  (Please note that this topic is essentially disjoint from "game theory", as studied by von Neumann, Nash, etc. No one will earn a Nobel prize based on knowledge from this course.)

  Prerequisites: Math 300 or Math 428 or Math 454, but the website will list 244 and 250 as the prerequisites. In such case, please fill out the Prerequisite Override Form for assistance with registration.
  
  
• Section 03: Introduction to Topological Data Analysis
  Course Description: see Syllabus
  Prerequisites: Math 251 and Math 250, but the website will list 244 and 250 as the prerequisites. In such case, please fill out the Prerequisite Override Form for assistance with registration.
  
  

In Fall 2025, there were three sections of Math 495:

• Section 01: AI Tools in Mathematics
  Course Description: see Syllabus
  Prerequisites: Background in proof-based mathematics, 640:300 Intro Math Reasoning is strongly recommended. Programming experience will be beneficial but is not essential.
  
  
• Section 02: Tensor Networks as a bridge between Neural Networks and Quantum Physics
  Course Description: see Syllabus
  Prerequisites: Linear Algebra (Math 250) is the only prerequisite for this course, 
  
  
• Section 03: An Introduction to Machine Learning
  Course Description: see Syllabus
  Prerequisites: A course in Linear Algebra
  
  

In Spring 2025, there were two sections of Math 495:

• Section 01: A Mathematical Invitation To Machine Learning
  Course Description: This mathematics course covers topics related to machine learning. Some of these are multivariable calculus applications in neural networks, linear regression, principal component analysis and support vector machines. Emphasis will be on the mathematics aspects and connections.
  Textbooks: The pre-print versions of both textbooks are freely available for download for personal use. The primary textbook: "Mathematics For Machine Learning" by Deisenroth, Faisal, Ong. (Cambridge University Press). Secondary textbook: "Foundations of Data Science" by Blum, Hopcroft, Kannan. (Cambridge University Press).
  Pre-requisites: Math 152 or equivalent. Further courses such as linear algebra, multivariable calculus, probability or statistics, are a plus. Prior exposure to machine learning is not required. (If you have completed Math 152 but not the official prerequisite courses Math 244/252 and Math 250, fill out the Prerequisite Override Form for assistance with registration.)
  
  
• Section 02: From Gravitational Waves to Supersonic Flows: An Introduction to Hyperbolic PDEs
  Course Description: The sonic boom of jets, the rippling of ocean waves, and even the gravitational waves detected by astronomers are all described by Hyperbolic Partial Differential Equations (PDEs). This course offers an introduction to the mathematical theory of hyperbolic PDEs, focusing on simplified models in fluid dynamics and linear wave propagation. While the emphasis will be on mathematical rigor, no prior knowledge of PDEs will be assumed.
  Textbook: Hyperbolic Partial Differential Equations, Serge Alinhac.
  Pre-requisites: Multivariable calculus (Math 251), elementary ODE theory (Math 244/252), intro linear algebra (Math 250).
  Assignments: Final presentation on a topic of the students' choosing (a list of suggested topics will be provided). Optional weekly homework will be available for extra credit.
   

In Spring 2024, there were two sections of 495:

• Section 01: Proofs from THE BOOK
  Prerequisites - Math 300
  Syllabus
• Section 02: Mathematical Adventures in One-Dimensional Physics
  Prerequisites - (244 or 252 or 292) (ODEs) and (250 or 291) (Lin. Alg.)
  Syllabus

See the archives for details.

Archives

• Spring 2009: Connections Seminar, Prof. Cohen
• Spring 2008: Connections Seminar, Prof. Retakh
• Fall 2007 Financial Mathematics, Professor Rodriguez.
• Spring 2007
• Fall 2006 (Financial Mathematics)

Schedule of Sections:

 01:640:495 Schedule of Sections

• Course Code: 01:640:486
• Semester(s) Offered: Fall
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 285 and Probability (Math 477 or Stat 381)

General Information (Catalog listing)

Survival models, life tables. Valuation of benefits, premiums, policy values of standard, single life insurance products. Covers part of the syllabus for Exam MLC of the Society of Actuaries.

Prerequisites:

• Introduction To Interest Theory For Actuarial Science - 01:640:285 
• Mathematical Theory of Probability - 01:640:477 or Theory of Probability 01:960:381

Textbook: 

Textbook:  For current textbook please refer to our Master Textbook List page

Offered in the fall. Required for the actuarial specialization.

Schedule of Sections:

01:640:486 Schedule of Sections

• Course Code: 01:640:487
• Semester(s) Offered: Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: C or better in Math 486

Course description (Catalog):

01:640:487 Mathematics of Life Contingent Risk Models II

Continuation of Mathematics of Life Contingent Risk Models I. Policy values, multiple state models, pension mathematics, effect of interest rate risk, emerging costs of traditional life insurance.

Covers part of the syllabus for Exam MLC of the Society of Actuaries.

Prerequisite: 01:640:486. Grade of C or better required in prerequisite course.

Offered in the spring only.

Schedule of Sections:

01:640:487 Schedule of Sections

• Course Code: 01:640:350
• Semester(s) Offered: Fall, Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250 and Calc III and a C or better in Math 300

General Information

Math 350 is a proof-based continuation of Math 250, covering abstract vector spaces and linear transformations, diagonalization, Jordan canonical form, and inner product spaces. Math 350 is one of two courses most mathematics majors may take to satisfy the upper-level algebra requirement. The other is Math 351.

The focus of Math 350 is axiomatic linear algebra, starting from the abstract notions of vector space and of linear transformation. Students will be expected to write precise proofs, building on their proof-writing experience from Math 300. From this abstract viewpoint, linear algebra will be developed far beyond Math 250, with new insight and new applications.

The honors section of Math 350 covers the same topics as the non-honors sections, but in significantly greater depth. Enrollment in the honors section requires the approval of the Honors Advisor.

Prerequisites

• Math 250, Introductory Linear Algebra
• and a C or better in Math 300, Mathematical Reasoning
• and Math 251, or Math 291, Multivariable Calculus

Enrollment in the honors section requires the approval of the Honors Advisor.

Textbook

For current textbook please refer to our Master Textbook List page

General Syllabus

Topics, in approximate sequence:

• Review of the basic ideas and techniques of Math 250
• Abstract vector spaces
• Subspaces; span of subsets; linear independence
• Bases and dimension
• Linear transformations; matrix representation
• Composition of linear transformations; invertibility
• Change-of-coordinate matrices (change of basis)
• Theoretical aspects of systems of linear equations
• Determinants and their properties
• Eigenvalues and eigenvectors; the characteristic polynomial
• Diagonalizability
• Invariant subspaces; the Cayley-Hamilton Theorem
• Jordan canonical form
• Real and complex inner product spaces
• Normal and self-adjoint matrices; unitary and orthogonal matrices

Instructors have some flexibility in deciding which proofs to treat.

As time allows, with the instructor’s discretion, some subset of the following topics may also be covered: Dual spaces, Direct sums of subspaces, Minimal polynomial, Rational canonical form, Normal and self-adjoint operators, Bilinear and quadratic forms, Applications of the theory.

Schedule of Sections:

01:640:350 Schedule of Sections

• Course Code: 01:640:351
• Semester(s) Offered: Fall, Spring
• Credits: 4
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250 and Calc III and a C or better in Math 300

General Information

Math 351 is one of two courses most mathematics majors may take to satisfy the algebra requirement. The other is Math 350.
Math 351 was originally part of a two-course sequence, Math 351-352. The continuation, Math 352, is no longer offered.

Catalog Description

01:640:351-352 Introduction to Abstract Algebra I, II (4,3)
Abstract algrebraic systems, including groups, rings, fields, polynomials, and some Galois theory.
Prerequisites: CALC3; 01:640:250; and a C or better in 300 or permission of department.

Textbook

For current textbook please refer to our Master Textbook List page

Topics, in approximate order

Division
Primes and unique factorization
Congruence
Modular arithmetic
Rings
Properties of rings
Isomorphisms and homomorphisms
Division in F[x]
Irreducibles and unique factorization
Roots and reducibility
Congruence in F[x]
Congruence and Ideals
Ring isomorphism theorems, prime and maximal ideals
Groups
Properties of groups
Subgroups
Group isomorphisms and homomorphisms
Symmetric and alternating groups
Lagrange’s Theorem
Conjugacy classes
Normal subgroups
Quotient groups
Center and commutator subgroups
Group isomorphism theorems
Simplicity of alternating groups
Classification of finite abelian groups

Sample Course Page

https://rutgers.instructure.com/courses/38827 

Course History

Schedule of Sections:

• Course Code: 01:640:354
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250

General Information (Catalog Listing)

01:640:354 Linear Optimization(3)
Linear programming problems, the simplex method, duality theory, sensitivity analysis, introduction to integer programming, the transportation problem, network flows, and other applications.
Prerequisite: 01:640:250. Credit not given for both this course and 01:640:453 or 01:711:453.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Syllabus

Sample Syllabus from Spring 2006

Office Hours

The TA's for this course will host online office hours on the website Discourse Technologies.

Previous semesters:

• Spring 2010, Section 01
• Spring 2010, Section 05
• Summer 2009

Schedule of Sections:

01:640:354 Schedule of Sections

• Course Code: 01:640:356
• Semester(s) Offered: Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 300 and Calc III

General Information (Catalog Description)

Priorities of the natural numbers, congruences, disophantine equations, and elementary arithmetical functions.

Prerequisite: CALC3 and Math 300 or permission of the department.

Math 300 (Mathematical Reasoning) or a very good background in mathematical proof is required. Students with a strong record in their mathematics courses who have not taken Math 300, but wish to take Number Theory, should request a prerequisite override from the Head Advisor ().

• Suggested Textbook
• Suggested Syllabus
• Sections Taught This Semester
• Previous Semesters

Suggested Textbook

Instructors in 356 sometimes use a different text and follow a different syllabus than the one shown.

Textbook:  For current textbook please refer to our Master Textbook List page

Suggested Syllabus

A suggested syllabus follows. However, anything posted on a page for the current semester supersedes this syllabus.

One midterm exam and a final exam seem appropriate for this course. A selection of the optional topics in the middle of the table may be inserted if the earlier material is completed before an exam can be given. Topics listed for lecture 14 should not be introduced before the midterm exam. This syllabus allows two weeks at the end of the course for additional topics. Such topics should be dictated by the interest of the class.

Schedule of Sections:

Previous Semesters

• Fall 2016 : Prof. Tunnell
• Fall 2013 : Doron Zeilberger
• Summer 2011 : Jerrold Tunnell
• Fall 2010 : Anders Buch
• Summer 2010 : Thom Tyrrell
• Fall 2009 : Prof. Weibel
• Summer 2009 : L. Medina
• Fall 2008 : Prof. Munshi
• Summer 2008 : Michael Weingart
• Fall 2007 : Prof. Sahi
• Fall 2006 : Prof. Sills (T Th 1:40-3 PM, SEC-217)
• Fall 2001 : Prof. Miller
• Summer 2000 : One section taught by David Nacin. A lecture schedule is available.
• Fall 1998 : Prof. Bumby (One section.)

• Course Code: 01:640:357
• Semester(s) Offered: Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250 and Calc III

Course Description:

This is a course aiming for undergraduate students majoring in math and engineering who are interested in understanding the importance of linear algebra and its application to problems within and outside mathematics. The basic concepts and results of linear algebra (vector spaces, linear transformations, matrices, determinants, eigenvalues and eigenvectors, orthogonality and diagonalization) will be reviewed. The course will cover the following topics: least square approximation, discrete Fourier transformation, numerical computations with matrices, graphs and networks, and image compression. Possible additional topics include: finite element method, systems of ordinary differential equations and linear programming.

The instructor may set MatLab assignments at their discretion.

Prerequisites:

Math 250 Introductory Linear Algebra and Math 251 Multivariable Calculus. 

Textbook:

For current textbook please refer to our Master Textbook List page

Published version of the textbook available in Spring 2016 from  World Scientific Publishing

Other Resources

• Survey of course topics by Roe Goodman
  Discrete Fourier and Wavelet Transforms: Mathematical Microscopes for Signal Processing
• Fast Fourier Transform links
• Wikipedia page on Wavelets
• An article on Image Compression and the JPEG 2000 algorithm based on the CDF Wavelet transform (which is studied in this course).
• An article on Discrete Wavelet Transformations and Undergraduate Education by C. Beneteau and P. J. Van Fleet (from Notices of the American Mathematical Society, May 2011) that outlines all the mathematical topics covered in the course with many interesting examples of image processing.
• The MIT Open CourseWare page of Gibert Strang's course Wavelets and Filter Banks.
• Wavelet books and link

Other Recommended Books (not required for course)

A. Jensen and A. la Cour-Harbo, Ripples in Mathematics: The Discrete Wavelet Transform
S. Allen Broughton and Kurt Bryan, Discrete Fourier Analysis and Wavelets
James S. Walker, A Primer on Wavelets and Their Scientific Applications (Second Edition)

Topics

Geometry of Linear Equations, Gaussian Elimination
Matrix Multiplication, LU Decomposition
Row Operations, Inverses and Transposes
Vector Spaces and Subspaces, Kernel and Range of Matrices
Linear Independence, Basis, Dimension
Solving Ax=b
Graphs and Networks
Linear Transformations
Orthogonal Vectors and Subspaces
Orthogonal Projection
Least Square Method
Gram-Schmidt Procedure, QR Decomposition
Fast Fourier Transform
Determinants and Their Properties
Applications of Determinants, Eigenvalues
Diagonalization of Matrices
Matrix Powers and Difference Equations
Matrix Exponentials and Differential Equations, Similarity Transformations
Minima, Maxima, and Saddle Points
Positive Definite Matrices
Singular Value Decomposition
Minimum Principles, Finite Element Method
Matrix Norms and Condition Number
Iterative Methods to Solve Ax=b

Sample Course Materials

• General information and grading policy
• Course Syllabus
• Homework Problems

Sample MATLAB Assignments

• Project 1: Digital Signals and Vector Graphics  (pdf format)
• Project 2: Convolution and Discrete Fourier Transform  (pdf format)
• Project 3: Haar Wavelet Transform  (pdf format)
• Project 4: Implementation of Wavelet Transforms (pdf format)
• Project 5: Image Analysis by Wavelet Transforms (pdf format)

For Project 2 you will use the Finite Fourier transform graphic user interface.
Matlab m-file. Here is the link to download this m-file:  fftgui

For Projects 4 and 5 you will use the Uvi_Wave collection of Matlab m-files for wavelet transforms (developed at the University of Vigo, Spain). Here is the link to download these m-files:  Uvi_Wave zip file (unzip the file to use the package)

Using Matlab

Note: You can run Matlab on your own computer (without buying the program) by using the Rutgers X-application server.

• Click on this apps server link.
• Log in to the apps server using the connect button at the upper right-hand corner of the screen and your Rutgers NetID.
• From the Main Menu at the lower left corner of the apps server toolbar, click on Education and then on Matlab
• From the Main Menu click on Internet and then on Firefox Web Browser to access the Uvi_Wave files from the math 357 course web page.
• Copy the fftgui.m file and the whole unzipped Uvi_Wave directory into a directory that your create on the X-apps server. Then set the Matlab path to this directory.

Course History

Taught by Prof. R. Goodman 2005-2008 and 2010-2014, Prof. V. Retakh 2009 and 2016, Dr. M. Thibault 2015.

Schedule of Sections:

01:640:357 Schedule of Sections

• Course Code: 01:640:361
• Semester(s) Offered: Fall
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 300 and either Math 250 or Calc 3

General Information

Catalogue listing for SET THEORY (3):
Introduction to set theory. The set-theoretic foundactions of mathematics, including the construction of the real number system, countable and uncountable sets, cardinal numers, and ordinals, the axiom of choice.
Prerequisite: 01:640:300 and either 01:640:250 or CALC3, or permission of department

Note: This course makes extensive use of the proof writing skills students develop in Math 300. Students who need further pratice with these skills are adviced to take Math 311 before taking Math 361, if possible

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

This course is taught every Fall term.

Schedule of Sections

Previous semesters:

• Fall 2010, Prof. Cherlin
• Fall 2009, Prof. Cherlin
• Fall 2008. Prof. Deloro
• Fall 2007. Prof. Weibel: MW 4th period (1:40-3 PM) in BECK 201 (Livingston campus)
• Fall 2006: Prof. Schleimer

• Course Code: 01:640:373
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Calc IV

• Catalog Description
• 373 versus 374
• 640:373 versus 198:323
• Prerequisites
• Programming
• Sections Taught This Semester
• Previous Semester Resources

Catalog Description

01:640:373-374. NUMERICAL ANALYSIS I,II (3,3)
Prerequisites: CALC4 and familiarity with a computer language. Credit not given for both these courses and 01:198:323,324.
Textbook: Numerical Analysis / Burden & Faires / Cengage / 978-1305253667 / 10th Edition / 2015

An analysis of numerical methods for the solution of linear and nonlinear equations, approximation of functions, numerical differentiation and integration, and the numerical solution of initial and boundary value problems for ordinary differential equations.

373 versus 374

The catalog description treats this a single two semester course with no fixed division of topics between the two parts. This allows some flexibility in organizing the course to follow the presentation in the textbook. One approach is to put things dealing with functions of one variable in the first semester, with multivariable methods in the second semester. In particular, techniques of numerical linear algebra are more likely to appear in the second semester, and the solution of differential equations in the first. The page for the current course should be consulted for a syllabus.

640:373 versus 198:323

The needs of the subject tends to blur the distinction between Mathematics and Computer Science. It is not unusual for the same textbook to be used in the two courses. Neither course is a collection of Numerical Recipes, although it is likely that programming considerations and questions of machine implementation would be more at home in a Computer Science course, while questions of the existence of solutions or the theoretical basis for error estimates are more suitable for a Mathematics course.

Prerequisites

Since the numerical solution of differential equations is a major topic in Math 373, prior exposure to the topic in a CALC4 course is essential. That course uses linear algebra, which is also used in other topics contained in Math 373 such as interpolation. The brief treatment of linear algebra in Math 244 will probably suffice for Math 373, but a course equivalent of Math 250 is strongly recommended for Math 374. Some prior programming experience is desirable, but not essential.

Programming

Part of the course involves computer implementation of the algorithms discussed, and therefore some prior programming experience is desirable, although not essential. The computer assignments will be fairly short, and although a computer language is not taught in the course, a description of Matlab commands that can be used to write the programs and examples of their use will be provided on the course webpage.

Schedule of Sections

Previous semester resources

• Summer 2010: O. Ilinca
• Summer 2009: N. Trainor
• Spring 2009: Prof. Irvine
• Fall 2008: Prof. Falk
• Spring 2008: Prof. Irvine
• Fall 2007 Professor Lee
• Summer 2007, T. Thanatipanonda.
• Spring 2007 (Prof. Vogelius).
• Spring 2004 (Prof. Tunnell).
• Fall 2003
• Fall 2000
• Spring 2000

• Course Code: 01:640:325
• Semester(s) Offered: Fall
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Calc IV

General Information
Interdisciplinary course, intended primarily for juniors and seniors majoring in mathematics, physics, or philosophy, dealing with what can be concluded from quantum mechanics about the nature of reality.

Prerequisites: CALC4 or permission of instructor (As far as mathematics is concerned, students need a working knowledge of complex numbers, eigenvalues of matrices, and partial derivatives. Prior knowledge in physics is not required but helpful.)

Contents: It has been claimed that quantum mechanics entails the most radical consequences about the world and our knowledge of it, such as the existence of parallel universes, faster-than-light action-at-a-distance, limitations to what we can know, that reality itself can be paradoxical, or that electrons become real only when observed. On the other hand, it has been claimed that quantum mechanics, in its orthodox formulation, is "unprofessional" (J. Bell), "incoherent" (A. Einstein), "incomprehensible" (R. Feynman), and "insane" (E. Schrodinger). We will investigate these claims, their basis and merits. The course will involve advanced mathematics, as appropriate for a serious discussion of quantum mechanics, but will not focus on technical methods of problem-solving.

Topics will include most of the following: The Schrodinger equation, the Born rule, self-adjoint matrices, axioms of the quantum formalism, the double-slit experiment, non-locality, the paradox of Schrodinger's cat, the quantum measurement problem, Heisenberg's uncertainty relation, interpretations of quantum mechanics (Copenhagen, Bohm's trajectories, Everett's many worlds, spontaneous collapse theories, quantum logic, perhaps others), views of Bohr and Einstein, no-hidden-variables theorems, and identical particles.

Text: J. Bell: Speakable and unspeakable in quantum mechanics, Cambridge University Press.

Learning goals: To understand the rules of quantum mechanics; to understand several important views of how the quantum world works; to be familiar with the surprising phenomena and paradoxes of quantum mechanics.

This course is normally in Fall semesters.

Schedule of Sections:

 01:640:325 Schedule of Sections

• Course Code: 01:640:403
• Semester(s) Offered: Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Calc IV

Course description:

A first course in the theory of differentiable functions of one complex variable. Topics include line integrals, Cauchy's theorem and its applications, Taylor and Laurent expansions, singularities, and conformal mapping.
Prerequisite: CALC4

Textbook:  For current textbook please refer to our Master Textbook List page

Previous semesters:

• Spring 2025: Prof. Anders Buch
• Spring 2020: Prof. Doron Zeilberger

• Course Code: 01:640:411
• Semester(s) Offered: Fall
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Special permission only. Typically students have already taken Math 311.

General Information (Catalog Listing)

01:640:411-412 Mathematical Analysis I,II (3,3)
Rigorous analysis of the differential and integral calculus of one and several variables.
Prerequisites: Permission of department and instructor. For students preparing for graduate study in the mathematical sciences.

This course forms part of the Honors Track sequence. Special permission is required for admission to Math 411. Requests for admission are evaluated based on the student's prior achievements, level of interest, and potential for success in the course.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Math 411-412 is a year long sequence.

Schedule of Sections

Previous semesters:

• Fall 2012. Prof. Speer
• Fall 2009. Prof. Speer
• Fall 2008. Prof. Greenfield
• Fall 2007 Prof. Teixeira
• Fall 2006. Prof. Speer

• Course Code: 01:640:412
• Semester(s) Offered: Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 411

General Information (Catalog Listing)

01:640:411-412 Mathematical Analysis I,II (3,3)
Rigorous analysis of the differential and integral calculus of one and several variables.
Prerequisites: Permission of department and instructor. For students preparing for graduate study in the mathematical sciences.

Math 412 is part of the Honors Track sequence. It is intended to be taken immediately after Math 411. Students enrolled in Math 411 during the Fall semester should be able to preregister for Math 412 in the Spring without assistance. All other students should contact the Honors Advisor <>.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Math 411-412 is a year long sequence.

Schedule of Sections

Previous semesters:

• Spring 2009: Prof. Speer
• Spring 2008: Prof. E. Teixeira
• Spring 2007: Prof. Bahri

• Course Code: 01:640:421
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Calc IV. No credit for both Math 421 and Math 423. This version of the class is aimed at engineers and physics majors.

• General Information
• Textbook
• Sample Syllabus
• Sections Taught This Semester
• Archive
• Notes for Instructors 

General Information (Catalog Listing)

01:640:421. Advanced Calculus for Engineering (3)
Primarily for mechanical engineering majors. Prerequisite: CALC4.
Credit not given for both this course and 01:640:423.
Covers Laplace transforms, numerical solution of ordinary differential equations, Fourier series, and separation of variables method applied to the linear partial differential equations of mathematical physics (heat, wave, and Laplace's equation).

Notes: CALC4 (Differential Equations) means Math 244, 252, or 292.
Math 423 is Elementary Partial Differential Equations. It covers similar material to Math 421, but is aimed at students majoring in Mathematics or Physics, rather than Engineering students.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Syllabus

Individual sections may vary, but chapters 4, 12 and 13 should be covered in detail, supplemented with a treatment of linearity including a review of Vector Calculus from Part 2. If time permits, Chapter 14 will introduce boundary value problems in non-rectangular coordinate systems.

Sample syllabus

Schedule of Sections

Archive:

• Fall 2010
• Spring 2006: Professor Bumby's section
• Fall 2005: Professor Greenfield's section (HW, Syllabus)
• Spring 2004: Komorova and Greenfield.
• Fall term 2003. List of sections. No individual section pages were produced.
• Fall term 2002. Details from Fall 2002, three sections, with web pages for two.
• Spring term 2001. Details from Spring 2001, two sections.
• Spring term 1999. Previous course page based on a syllabus provided by Dr. R. Doran.
• Spring term 1996. Some differences from the syllabus here are due to an earlier edition of the textbook being used at that time

Notes for Instructors

Comments and corrections by Peter Landweber for the 3rd edition of the text. (Similar to the 4th.)

A selection of recommended homework problems, from the 3rd edition.

• Course Code: 01:640:423
• Semester(s) Offered: Fall, Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Calc IV. No credit for both Math 421 and Math 423. This version of the class is aimed at math majors.

Catalog Description

01:640:423. Elementary Partial Differerntial Equations (3)
Prerequisite: CALC4. Credit not given for both this course and 01:640:421.
Linear partial differential equations of mathematical physics (heat, wave, and Laplace's equation), separation of variables, Fourier series.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Math 421 vs Math 423: A comparison

These two courses are only superficially similar: 421 series to introduce techniques needed by the Mechanical Engineering program while 423 is an introduction to the mathematics of partial differential equations.

Prerequisities

Calculus through a course in Ordinary Differential Equations.

Schedule of Sections

Previous semester resources

Use the drop-down menu above to see who has taught the course since 2006. Some prior course pages are archived below.

• Fall 2008
• Fall 2007
• Fall 2006
• Fall 2003
• Spring 2002
• Fall 2001
• Spring 2001

• Course Code: 01:640:428
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250 and Calc III

General Information (Catalog listing)

01:640:428 Graph Theory (3)
Colorability, connectedness, tournaments, eulerian and hamiltonian paths, orientability, and other topics from the theory of finite linear graphs, with an emphasis on applications chosen from social, biological, computer science, and physical problems.
Prerequisites: CALC3 and 01:640:250.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Syllabus

Syllabus may vary.

Schedule of Sections:

01:640:428 Schedule of Sections

Previous semesters:

• Fall 2010 Prof. Weibel
• Summer 2010: Wesley Pegden
• Summer 2009: Prof. Beck
• Fall 2008: Prof. Butler
• Summer '08. A. Thanatipanonda
• Fall 2007. Prof. Ocone
• Summer 2007. Liviu Ilinca
• Fall 2006. Prof. Beck. (Used a different text: Brualdi)
• Fall 2005 (Schleimer)
• Fall 2004 (Maclagan)
• Fall 2003 (Zeilberger)
• Fall 1997 (Weibel

• Course Code: 01:640:432
• Semester(s) Offered: Spring (frequently)
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 311. Material from prior courses (Math 250 and Calc III) will also be essential.

General Information

Differential geometry is the study of geometric properties of curves, surfaces, and their higher dimensional analogues using the methods of calculus. It has a long and rich history, and, in addition to its intrinsic mathematical value and important connections with various other branches of mathematics, it has many applications in various physical sciences, e.g., solid mechanics, computer tomography, or general relativity. Differential geometry is a vast subject. A comprehensive introduction would require prerequisites in several related subjects, and would take at least two or three semesters of courses. In this elementary introductory course we develop much of the language and many of the basic concepts of differential geometry in the simpler context of curves and surfaces in ordinary 3 dimensional Euclidean space. Our aim is to build both a solid mathematical understanding of the fundamental notions of differential geometry and sufficient visual and geometric intuition of the subject. We hope that this course is of interest to students from a variety of math, science and engineering backgrounds, and that after completing this course, the students will be in a position to (i) apply their knowledge and skills in this course to their related subjects, (ii) be ready to study more advanced topics such as global properties of curves and surfaces, geometry of abstract manifolds, tensor analysis, and general relativity.

Prerequisites:

The officially listed prerequisite is 01:640:311. But equally essential prerequisites from prior courses are Multivariable Calculus and Linear Algebra. Most notions of differential geometry are formulated with the help of Multivariable Calculus and Linear Algebra.
01:640:311, which itself requires Multivariable Calculus and Linear Algebra as prerequisites, is an important prerequisite because it helps students build mathematical maturity and gain the ability to understand, formulate and present precise mathematical concepts and proofs.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Sample Syllabus

Syllabus, Spring 2008. (for the DoCarmo text). Now obsolete.

This course is taught in the Spring semester.

Schedule of Sections

Previous semesters

• Spring 2009. Prof. Nussbaum
• Spring 2008. Prof. Han

• Course Code: 01:640:435
• Semester(s) Offered: Fall (frequently)
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250 and Calc III and Math 300

General Information (Catalog listing)

01:640:435 Geometry (3)
Various geometries, including projective and non-Euclidean geometries, and geometric axiom systems.
Prerequisites: CALC3, 01:640:250, and 300, or permission of department.

Prerequisites

Most notions of differential geometry are formulated with the help of Multivariable Calculus and Linear Algebra. Math 300 is an important prerequisite because it helps students build mathematical maturity and gain the ability to understand, formulate and present precise mathematical concepts and proofs. Additional exposure to proofs in courses like Math 311 and Math 350 is also helpful.

Textbook

For current textbook please refer to our Master Textbook List page

Sample Syllabus

Prof. Tunnell (2019)

This course is taught during the Fall semester.

Schedule of Sections:

01:640:435 Schedule of Sections

Previous semesters:

• Fall 2008. Prof. Han
• Fall 2007, Sec. 01. Prof. Carbone, Sec. 02. Prof. Gonzalez
• Fall 2006, Sec. 1. Prof. Han
• Fall 2006, Sec. 02. Prof. X. Huang
• Fall 2005, Section 1, Prof. Han
• Fall 2004, Section 1, Prof. Han
• Fall 2002, Section 1, Prof. Han

• Course Code: 01:640:437
• Semester(s) Offered: Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250 and Calc III

Course Description

This course will present an overview of the development of mathematics from ancient civilizations to the beginning of the 19th century. Selected topics from the history of mathematics in China, India, Europe, and the Islamic world, including number systems, Euclidean geometry, algebra, combinatorics, and calculus. Recurrent themes include calculation of areas and volumes, finding zeros of polynomials, progressive enlargement of number systems, and changing concepts of rigorous proof.

Prerequisites: Math 250 and Calc III (Math 251 or Math 291)

This course may include oral or written presentations of selected topics by students. However, it does not satisfy writing requirements for the SAS core curriculum.

Textbook

For current textbook, please refer to our Master Textbook List page

Previous Semesters

• Spring 2026: Kiessling
• Spring 2025: Retakh
• Fall 2021: Zeilberger

• Course Code: 01:640:441
• Semester(s) Offered: Fall
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Calc IV and Analysis (Math 311 or Math 411)

General Information (Catalog listing)

01:640:441-442 Introductory Topology I,II (3,3)
Math 441: Introduction to topology with emphasis on the foundations of analysis; Euclidean spaces, metric spaces, topological spaces, and their properties; applications to analysis. Math 442: Basic concepts of algebraic topology, including the fundamental group, plane curves, homotopy, and a brief introduction to homology.
Prerequisites: CALC4 and Math 311 (Analysis I) or permission of department.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Syllabus

See the 2004 syllabus for a general idea, but be prepared for considerable variation in emphasis from one year to the next.

This course is offered during the Fall semester.

Schedule of Sections:

01:640:441 Schedule of Sections

Previous semesters:

• Fall 2019: Prof. Weibel
• Fall 2018: Prof. Tarasca
• Fall 2017: Prof. Nussbaum
• Fall 2016: Prof. Rong
• Fall 2010. Prof. Saks
• Fall 2008. Prof. Speer
• Fall 2007. Prof. Bahri; Followed in Spring 2008 by Math 442, taught by Prof. Bahri.
• Spring 2007. Prof. Chanillo.
• Fall 2005. Prof. Sahi
• Fall 2004. Prof. Luo

• Course Code: 01:640:442
• Semester(s) Offered: Spring (frequently)
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 441

General Information (Catalog listing)

01:640:441-442 Introductory Topology I,II (3,3)
Math 441: Introduction to topology with emphasis on the foundations of analysis; Euclidean spaces, metric spaces, topological spaces, and their properties; applications to analysis. Math 442: Basic concepts of algebraic topology, including the fundamental group, plane curves, homotopy, and a brief introduction to homology.
Prerequisites: CALC4 and Math 311 (Analysis I) or permission of department.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Syllabus

See the syllabus from 2020 for a general idea, but be prepared for considerable variation in emphasis from one year to the next.

Schedule of Sections:

01:640:442 Schedule of Sections

Previous semesters:

• Spring 2020. Prof. Weibel
• Fall 2010. Prof. Saks
• Fall 2008. Prof. Speer
• Fall 2007. Prof. Bahri; Followed in Spring 2008 by Math 442, taught by Prof. Bahri.
• Spring 2007. Prof. Chanillo.
• Fall 2005. Prof. Sahi
• Fall 2004. Prof. Luo

• Course Code: 01:640:451
• Semester(s) Offered: Fall
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Special permission only. Typically students have already taken Math 350 or Math 351.

General Information (Catalog listing)

01:640:451-452 Abstract Algebra I,II (3,3)
Rigorous study of abstract algebraic systems including groups, rings, and fields.
Prerequisites: Permission of department and instructor. For students preparing for graduate study in the mathematical sciences.

This course forms part of the Honors Track sequence. Special permission is required for admission to Math 451. Requests for admission are evaluated based on the student's prior achievements, level of interest, and potential for success in the course.

Required Textbook

Michael Artin; Algebra (second edition); Prentice-Hall, 2011 (560 pp.); (ISBN: 0-13-241377-9; ISBN13: 9780132413770).
See also the  Master Textbook List page.

Short Description

Groups: axiomatic formulation, subgroups, isomorphisms, cosets, quotient groups
Symmetry: actions of groups on sets and vector spaces
Theory of groups: groups of finite order, Sylow theorems, free groups, generators and relations
Representations of groups: representing groups via linear transformations

Topics, in approximate order

Groups and subgroups
Group homomorphisms and isomorphisms
Cosets and Lagrange’s theorem
Conjugation and normal subgroups
Quotient groups
Group actions
Groups of isometries
Groups of permutations
The orbit-stabilizer theorem
Groups of finite order
Sylow theorems
Free groups, generators and relations
Group representations
Characters
The regular representation

As time allows, with the instructor’s discretion, some additional topics may also be covered, such as the following:
Finite groups of Lie type, finite simple groups, classifying abelian groups, linear groups.

Sample Syllabus

Spring 2013

Schedule of Sections

Previous semesters

• Course Code: 01:640:452
• Semester(s) Offered: Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 451

General Information (Catalog listing)

01:640:451-452 Abstract Algebra I,II (3,3)
Rigorous study of abstract algebraic systems including groups, rings, and fields.
Prerequisites: Permission of department and instructor. For students preparing for graduate study in the mathematical sciences.

Math 452 is part of the Honors Track sequence. It is intended to be taken immediately after Math 451. Students enrolled in Math 451 during the Fall semester should be able to preregister for Math 452 in the Spring without assistance. All other students should contact the Honors Advisor <>.

Required Textbook

Michael Artin; Algebra (second edition); Prentice-Hall, 2011 (560 pp.); (ISBN: 0-13-241377-9; ISBN13: 9780132413770).
See also the Master Textbook List page.

Short Description

Review of vector spaces, linear transformations and matrices, including Jordan canonical form.
Factoring in commutative rings: principal ideal domains, unique factorization domains; examples.
Modules; free modules; diagonalizing integer matrices; application to the structure of finitelygenerated abelian groups.
Modules over polynomial rings; application to rational canonical form for linear operators.

Topics, in approximate order

Review of vector spaces, linear transformations, matrices and Jordan canonical form
Rings
Commutative rings
Homomorphisms and ideals
Quotient rings, product rings
Rings of fractions
Maximal ideals
Factoring in commutative rings
Principal ideal domains
Unique factorization domains
Modules
Free modules
Noetherian rings
Structure of abelian groups
Application to linear operators, rational canonical form

 As time allows, with the instructor’s discretion, some additional topics may also be covered, such as the following:
Quadratic number fields, fields and Galois theory, non-commutative rings, algebras.

Sample Syllabus

Spring 2013

Schedule of Sections

Previous semesters

• Course Code: 01:640:454
• Semester(s) Offered: Fall, Summer
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250 and Calc II

General Information (Catalog listing)

01:640:454 Combinatorics (3)
Existence and enumeration of designs and patterns such as codes, graphs, and block designs, and extremal problems related to such objects. Emphasis on applications to computer, biological, physical, and social problems.
Prerequisites: CALC2 and 01:640:250.

Textbook

Textbook varies

Textbook:  For current textbook please refer to our Master Textbook List page

Syllabus set by Instructor

Sample syllabus: Fall 2021 Prof. Weibel

Taught in Summer and Fall semesters.

Schedule of Sections:

01:640:454 Schedule of Sections

Previous semesters:

• Fall 2011: Prof. Weibel (Roberts/Tesman)
• Fall 2010: Prof. Beck.
• Fall 2009: Prof. Beck.
• Summer 2009: Paul Raff (Roberts/Tesman)
• Fall 2008: Prof. Beck (Roberts/Tesman)
• Summer 2008, Paul Ellis (Roberts/Tesman)
• Fall 2007, Prof. Bumby (Roberts/Tesman)
• Summer 2007, Michael Weingart (Roberts/Tesman)
• Fall 2006, Prof. Beck. Using Brualdi
• Fall 2005, Prof. Cherlin. Using Roberts/Tesman

• Course Code: 01:640:461
• Semester(s) Offered: Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 300 and Calc III

General Information (Catalog listing)

Intuitive and formal development of the sentential and predicate calculus. Special emphasis given to questions of consistency, completeness, and independence. Formal systems; incompleteness and undecidability; theorems of Gödel. Exploration of which properties of structures can be defined in the first-order language.
Prerequisite: CALC3 and either 01:640:300 or permission of department

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Sample Syllabus

Variable: Spring 2007

This course is taught each Spring semester.

Schedule of Sections

Archives

For Instructors

Previous semesters:

• Spring 2009. A. Deloro
• Spring 2008. Sam Coskey
• Spring 2007. Prof. Thomas

• Course Code: 01:640:477
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Calc III

• General Information
• Textbook
• Special Accommodations
• Academic Integrity
• Sample Syllabus
• Related Sites
• Sections Taught this Semester
• Previous Semesters

General Information

Prerequisites: CALC III -- third-semester, multiple-variable calculus, which is Math 251 at Rutgers-NB -- is an unwaivable prerequisite. A working knowledge of multiple integrals and partial derivatives is essential for the course.

Restrictions on Credit: A student can receive credit for at most one of the courses

• 01:640:477
• 01:198:206
• 01:960:381
• 14:332:226

(despite the fact that Math 477 covers considerably more material than Comp Sci 206).

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Special Accommodations

Students with disabilities requesting accommodations must follow the procedures outlined at https://ods.rutgers.edu/students/applying-for-services

Academic Integrity

All Rutgers students are expected to be familiar with and abide by the academic integrity policy. Violations of the policy are taken very seriously.

Sample Syllabus

Prof. Salamon (2022)
Prof. Speer (2010).

Related Sites

• Mathematical Finance at Rutgers
• Actuarial Club
• Probability Theory (Wikipedia)

Schedule of Sections:

01:640:477 Schedule of Sections

Previous semesters

• Course Code: 01:640:478
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250 and Calc III and Probability (Math 477 or Stat 381)

General Information (Catalog listing)

01:640:478 Markov chains for discrete-time models, Poisson processes, Markov chains for continuous-time models, queuing theory, renewal processes.

Prerequisites:

• 01:640:250
• Either 01:640:477, or both 01:640:251 and 01:960:381

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Syllabus

The syllabus is available from the instructor.

Schedule of Sections

Previous Semesters

• Spring 2008: Prof. Gundy
• Spring 2008: Prof. Petrie
• Spring 2007: Prof. Petrie

• Course Code: 01:640:481
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250 and Probability (Math 477 or Stat 381)

General Information

Topics: Fundamental principles of mathematical statistics, sampling distributions, estimation, testing hypotheses, correlation analysis, regression, analysis of variance, nonparametric methods.

Prerequisites: 01:640:250 and either 01:640:477 or both 01:640:251 and 01:960:381. Credit not given for both this course and 01:960:382.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Instructor Information and Grading Policy

Fall 2009

Sample Syllabus

Fall 2009

Schedule of Sections

 Previous semesters

• Spring 2009: Prof. Goodman.
• Fall 2008. Professor Balaban
• Spring 2008. Prof. Ocone
• Fall 2007. Prof. M. Zieve
• Spring 2007. Prof. M. Kiessling
• Spring 2006. Prof. A. Sills

• Course Code: 01:640:485
• Semester(s) Offered: Fall
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250 and Calc IV and Probability (Math 477 or Stat 381 or 14:332:226)

General Information (Catalog listing)

Study of the mathematical theory and financial concepts used to model and analyze financial derivatives. Topics include martingales, Brownian motion, and stochastic differentials, with applications to discrete and continuous time stochastic models of asset prices, option pricing, the Black-Scholes pricing model, and hedging.

Prerequisites:

• Intro Linear Algebra (01:640:250)
• Differential Equations (01:640:244, 252, or 292)
• Probability (01:640:477, 01:960:381, or 14:332:226)

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

{rucourse course = "01:640:485" semester = "92017"}

Schedule of Sections

01:640:485 Schedule of Sections

Previous semesters

• Fall 2008. Prof. Rodriguez
• Ran as Math 495 prior to Fall 2008

• Course Code: 01:640:348
• Semester(s) Offered: Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250 and one of Math 300, Math 356, or Math 477

General Information (Catalog listing)

01:640:348 Cryptography

Applications of algebra and number theory to cryptography (encryption/decryption) and cryptanalysis (attacking encrypted messages). Topics include congruences, finite fields, finding large primes, pseudoprimes, and primality testing, as well as the Vigenere and Hill ciphers, the Data Encryption Standard, probabilistic, and trapdoor attacks on encrypted messages, and public key ciphers. 

Prerequisites: 01:640:250 Linear Algebra; one of 01:640:300, 356, or 477, or permission of department.
This is an introduction to modern cryptology: making and breaking ciphers.

Topics to be covered include: Symmetric ciphers and how to break them, including DES and AES, Public Key/Private Key Ciphers and their weaknesses. The appropriate mathematical background will also be covered.

Textbook:  For current textbook please refer to our Master Textbook List page

Schedule of Sections

Previous Semesters:

• Spring 2017: Sec 01 Prof. Garnett
• Spring 2016: Sec 01 Prof. Radziwill
• Spring 2015: Sec 01 Prof. Kontorovich
• Spring 2014: Sec 01 Prof. Saraf
• Spring 2013: Sec 01 Prof. Miller
• Spring 2012: Sec 01 Prof. Tunnell
• Spring 2011: Sec 01 Prof. Miller
• Spring 2009: Sec 01 Prof. Munshi
• Spring 2008: Sec 01. Prof. Weibel
• Spring 2007: Sec 01 Prof. Munshi
• Spring 2006: Sec 01 Prof. Miller
• Spring 2005: Sec 01 Prof. Tunnell
• Spring 2004: Sec 01 Prof. Weibel
• Fun facts from 2004

Fun Facts from 2004

In May 2004, the US found out that Ahmed Chalabi had told Iran that the United States had broken the Iranian intelligence service's secret communications code. How? The Iranians didn't believe it, and cabled a report to Teheran using the broken cipher - which the US decrypted!

Fun Facts about Mersenne primes:

In 1644, a French monk named Marin Mersenne studied numbers of the form N=2^p-1, where p is prime, and published a list of 11 such numbers he claimed were prime numbers. Such prime numbers are called Mersenne primes. (He got two wrong.) The first few Mersenne primes (p=2,3,5,7) are 3,7,31,127, and p=11 gives the non-prime 2047=23*89 (as was discovered in 1536 by Hudalricus Regius).
Not all numbers of the form 2^p-1 are prime, as Regius' example 2047 (p=11) shows. The next few primes for which 2^p-1 is not prime are p=23 and p=37 (discovered by Fermat in 1640), and p=29 (discovered by Euler in 1738). By the end of World War II, all 12 of the Mersenne primes with p<258 had been completely checked by hand.

Of course, after this point all calculations have been carried out by computers. For more details, see the Mersenne prime website. Over the next 50 years, the number of known Mersenne primes grew to 34, with the largest having almost 100,000 digits. Each Mersenne prime N=2^p-1 has p log₁₀(2) digits.

Starting in 1995, the Electronic Frontier Foundation (EFF) offered a $50,000 prize for the first known prime with over 10 million digits. If a Mersenne prime won its prime p would have to be over 33 million. The race was on.

As part of this race, the 40th Mersenne prime was discovered in 2003 by a 26-year-old graduate student in chemical engineering, Michael Shafer. The number is 2^p-1 with p=20,996,011, and is 6,320,430 digits long. At the time, it was only known to be the largest among all 40 known Mersenne primes. It took seven years (until July 2010) to confirm that this is the 40th Mersenne prime (i.e., there are only 39 smaller ones).

The race to win the EFF prize came down the wire in Summer 2008, as the 45th and 46th known Mersenne primes were discovered in within 2 weeks of each other by the UCLA Math Department (who won the prize) and an Electrical Engineer in Germany, respectively. The 45th known has 13 million digits and p=43,112,609; it is larger that the 46th known, which has only 11 million digits.

More recently, the 47th known Mersenne prime was discovered in April 2009 by a Norwegian named Odd Magner Stridmo, with p=42,643,801. Surprisingly, it is slightly smaller (by 141,000 digits) than the 45th Mersenne prime. For more information, check out the Mersenne prime.

Schedule of Sections:

01:640:348 Schedule of Sections

• Course Code: 01:640:338
• Semester(s) Offered: Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250, Calc III, and Probability (Math 477 or CS 206 or Stat 381)

General Information

Please see the current semester's course page for syllabus.

Catalog description:

Models for biological processes based on discrete mathematics (graphs, combinatorics) and probabilistics and optimization methods, such as Markov chains and Markov fields, Monte-Carlo simulation, maximum-likelihood estimation, entropy and information. Applications selected from epidemiology, inheritance and genetic drift, combinatorics and sequence alignment of nucleic acids, energy optimization in protein structure prediction, topology of biological molecules.

The prerequisites are Linear Algebra, Math 640:250, Calculus III, Math 640:251, and Probability, either Math 640:477 or Comp. Sci. 198:206 or Statistics 960:381).

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Online Course Text

Previous Semesters

• Spring 2010. Prof. Ocone
• Spring 2009. Prof. Ocone
• Spring 2008. Prof. Sontag
• Spring 2007. Prof. Ocone
• Spring 2006. Prof. Ocone
• Spring 2005. Prof. Sontag
• Spring 2004. Prof. Ocone
• Spring 2003. Prof. Ocone
• Spring 2002. Prof. Sontag
• Spring 2001. (Old version, see 336)  Profs. Sontag, Sussmann

Schedule of Sections:

01:640:338 Schedule of Classes

• Course Code: 01:640:336
• Semester(s) Offered: Fall
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250 and Calc IV

General Information

Math 336 was introduced as a separate course in the Fall 2001 semester. Previously, this content was available as one option in Math 338. The catalog description of the course is as follows.

01:640:336. DYNAMICAL MODELS IN BIOLOGY (3)
Models for biological processes based on ordinary and partial differential equations. Topics selected from models of population growth, predator-prey dynamics, biological oscillators, reaction-diffusion systems, pattern formation, neuronal and blood flow physiology, neural networks, biomechanics. 
Prerequisites: CALC4 and 01:640:250.

The most recent semester covered the following topics: review of modeling with ordinary differential equations, steady-states, nullclines, linearization, linear ODE's, and stability, with illustrations from chemostats, drug infusion, epidemics, and chemical kinetics; singular perturbations and Michelis-Menten enzyme dynamics; bifurcations and switching behavior; activator-inhibitor systems; limit cycles and Poincare-Bendixon theory; relaxation oscillations; transport equation and travelling waves; chemotaxis: gradients; attraction and repulsion; diffussions and their relation to random walks.

The Course Announcement gives information on prerequisites, credit restrictions, and relation to the Biomathematics major.

Previous semesters:

• Fall 2013
• Fall 2008: Prof. Ocone
• Fall 2007: Section 01. Prof. Mischaikow
• Fall 2006: Prof. Eduardo Sontag
• Fall 2003: Dr. Patrick De Leenheer.
• A version taught as Math 338, Spring 2001.

Taught in the Fall Term. 

Schedule of Sections

• Course Code: 01:640:321
• Semester(s) Offered: Fall
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Calc IV

General Information (Catalog Listing)

01:640:321 Introduction to Applied Mathematics (3)
Mathematical models of mechanical vibrations, population dynamics, and traffic flow, involving ordinary differential equations and nonlinear first-order partial differential equations.

Prerequisite: CALC4.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Schedule of Sections

• Course Code: 01:640:312
• Semester(s) Offered: Spring (frequently)
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 311

Course Description (Catalog Copy)

01:640:312 Introduction to Real Analysis II (3) 
Series of numbers and functions, integration of functions of one variable, pointwise and uniform convergence, differential calculus in several variables, implicit and inverse function theorems.
Prerequisites: Math 311.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Course goals

• Greatly strengthening student's understanding of
  • the results of calculus and the basis for their validity
  • the uses of deductive reasoning
• Increasing the student's ability to
  • understand definitions
  • understand proofs
  • analyze conjectures
  • find counter-examples to false statements
  • construct proofs of true statements
• Enhancing the student's mathematical communication skills
• Provides a solid foundation for honors courses, especially Math 411

Taught Spring Semester

Schedule of Sections:

01:640:312 Schedule of Sections

• Course Code: 01:640:311
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 4
• Counts toward math major/minor?: Yes
• Prerequisites: Calc IV and a C or better in Math 300

Course Description (Catalog Copy)

01:640:311 Introduction to Real Analysis I (4) 
Introduction to language and fundamental concepts of analysis. The real numbers, sequences, limits, continuity, differentiation in one variable.

Prerequisites

• CALC 4 and a C or better in  01:640:300 or permission of department.

Textbook (regular sections)

Textbook:  For current textbook please refer to our Master Textbook List page

311H (Honors Section)

Textbook:  For current textbook please refer to our Master Textbook List page

Course goals and exams

• Strengthening student's understanding of
  • the results of calculus and the basis for their validity
  • the uses of deductive reasoning
• Increasing the student's ability to
  • understand definitions
  • understand proofs
  • analyze conjectures 
  • find counter-examples to false statements,  
  • construct proofs of true statements
• Materials to be covered:  Chapters 0,1,2,3,4 of the text book 
• Instructors make their own midterm and final exams
  
• A link to a brief syllabus, a midterm exam and  a final exam by X. Huang in the Fall semester of 2016:   (math.rutgers.edu/~huangx/math_311_syl.pdf) (math.rutgers.edu/~huangx/math_311_midterm.pdf) (math.rutgers.edu/~huangx/math_311_final.pdf)
  

2017 - Spring webpage

Schedule of Sections:

• Course Code: 01:640:300:H
• Semester(s) Offered: Fall, Spring
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Special permission only

This is a special honors section of Math 300. Math 300 is a course required for all mathematics majors which teaches fundamental skills, especially the reading and writing of mathematical proofs, that are needed for future mathematics courses. The honors section of math 300 covers more material and is significantly more challenging than the normal sections of 300. It is intended for highly motivated students who have demonstrated strong mathematical ability.

One of the main purposes of Math 300 H is to serve qualified students who are interested in joining the Department of Mathematics Honors Track. Students who do well in math 300 H are good candidates for acceptance into the track. However, interest in the honors track is not a requirement for being accepted into 300 H.

Special permission is required for admission to 300 H. When applying for special permission, be sure to include your reasons for applying. Requests for admission to 300 H are evaluated based on the student's prior achievements, level of interest, and potential for success in the course.

Schedule of Sections

• Course Code: 01:640:300
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250 or Calc III or special permission

General Information (Catalog Listing)

01:640:300 Introduction to Mathematical Reasoning (3)
Fundamental abstract concepts common to all branches of mathematics. Special emphasis placed on ability to understand and construct rigorous proofs. Prerequisite: 250 or 251 or 291 or permission of department.

This course is specifically intended to help Mathematics majors prepare for 640:311, 640:350, 640:351 and other proof-oriented courses. 
It is required for any mathematics major who is not already experienced in doing mathematical proofs.

Students need to obtain a C or better in 640:300 in order to be eligible to take 640:311, 640:350, or 640:351.

If you are considering taking this course, please read this cautionary message.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Schedule of Sections:

01:640:300 Schedule of Sections

• Course Code: 01:640:292
• Semester(s) Offered: Spring
• Credits: 4
• Counts toward math major/minor?: Yes
• Prerequisites: Math 291. Students who have taken Math 250 as well as Math 251 may also apply.

Description

01:640:291-292
Honors Calculus III,IV (4,4) Covers the same material as 01:640:251 and 252 in a more thorough and demanding fashion. Prerequisites: Permission of department. Prerequisites for 292: 01:640:291, or permission of the department.

Note: Students may not receive credit for more than one of the fourth-semester calculus courses 01:640:244, 252, or 292.

252 vs. 292

Math 252 is the fourth semester of calculus, following after multivariable calculus in the sequence Math 151, 152, 251. The subject is differential equations and after using one textbook for three terms, the fourth term has a different text.

Math 292 is a course in honors mathematics for students whose primary interest in the course is the mathematics it contains. Theorems may be proved in class and required on examinations.

The course makes use of linear algebra topics that are covered in Math 291 and Math 250.

Prerequisites

The “normal” prerequisites for Math 292 is Math 291. Students who have taken Math 250 as well as Math 251 (in an honors or a regular section) with outstanding results are welcome to apply during registration period. Applications for admission by special permission are available here.

Previous semesters

• Spring 2009.  Prof. Wheeden
• Spring 2008. Sec. 01 Prof. R. Wheeden
• Spring 2007. Sec 01. Prof E. Teixeira
• Spring 2006. Prof. E. Teixeira

Schedule of Sections:

01:640:292 Schedule of Sections

• Course Code: 01:640:291
• Semester(s) Offered: Fall
• Credits: 4
• Counts toward math major/minor?: Yes
• Prerequisites: Special permission only. Most students in Math 291 are incoming freshmen who scored a 5 on the AP Calculus BC exam.

Catalog Description

01:640:291. Honors Calculus III (4) 
Covers the same material as 01:640:251 in a more thorough and demanding fashion.

251 vs. 251H vs. 291.

Math 251 continues the sequence begun with Math 151-152, usually with the same textbook and at the same level of rigor.  The honors sections labeled 251H of Math 251 are (in general) intended for honors students in disciplines other than mathematics and are “more demanding versions of the same course.” By contrast, Math 291 is deliberately intended as a course in honors mathematics for students whose primary interest in the course is the mathematics it contains. The textbook may not be that used in other calculus courses, and the choice of course material is at the instructor's discretion to a greater extent than in other lower-division courses. Theorems may be proved in class and required on examinations, and “many variables” may mean n variables, not just 2 or 3.

Prerequisites

Most students who take Math 291 are incoming freshmen who scored a 5 on the AP Calculus BC exam. For more information, please contact the Head Advisor at <>.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Schedule of Sections:

01:640:291 Schedule of Sections 

• Course Code: 01:640:285
• Semester(s) Offered: Fall
• Credits: 3
• Counts toward math major/minor?: Actuarial track only
• Prerequisites: Calc III

General Information (Catalog Listing)

01:640:285 Introduction to Interest Theory for Actuarial Science (3)

Compound interest rate theory and application to valuation of financial instruments; measurement of interest; present value; equations of value and yield rates; amortization; annuities; bond valuation; duration; immunization.

Prerequisite: 01:640:251.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Schedule of Sections

• Course Code: 01:640:252
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 250 and Calc III

General Resources

Catalog description

• Textbook
• Syllabus
• Supplements
• Current Semester
• Past Semesters

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Syllabus

A suggested syllabus is available. Dr. Sontag's section can find that syllabus and course material's in the course's Sakai website!

Supplements

Available supplements, in a uniform PDF format are collected here. 

• N1 Introduction to first order equations, with an emphasis on modeling.
• RTB1 Euler's method, including error estimate and application to existence and uniqueness of solutions.
• N2 Some comments on bifurcations.
• N3 Some Remarks on Phase Planes.
• N4 Introduction to Matrix Exponentials.
• RTB2 An easily remembered formula for exponentials of matrices with complex eigenvalues.
• BW1 The method of variation of parameters for solving inhomogeneous systems.

Math 252 Syllabus for Third Edition of Blanchard, Devaney and Hall

Students in Section 2, Spring 06, should instead use the syllabus linked from that section's webpage
This syllabus is intended as a general outline of the course. It was originally written by E. Sontag for the first edition of the text and adapted to the second edition by R. Wheeden and to the third edition by E. Sontag (Jan 06). Individual instructors may alter its pace, assign different homework, and add or delete topics. Some variations will be described briefly in the notes following the syllabus. Note: The main difference between the 2nd and 3rd Editions is that old Section 1.8 is now "1.9", and a new section 1.8 has been inserted. In addition, many homework problems have been renumbered, and some new problems have been inserted.

Assignments usually refer to sections of the textbook. A designation such as N4 is a link to a supplementary note.
 

Notes:
a. For numerical assignments, there is a package available in the CD ROM that comes with the book. A strongly suggested alternative is the Java Applet, JOde, which runs on any Java-enabled browser, including those at the University computer labs. Assignments using JOde will be posted to the Section 2, Spring 06 webpage

b. The existence and uniqueness theorem may be applied in abutting regions with continuity across the boundary to allow for piecewise continuous forcing functions.  Projects exploring this have been used in the course.

c. Sections 2.1/2.2 are not really different, and should studied (and possibly lectured upon) simultaneously.  Even 2.3 and 2.4 are not very different, actually.

d. The material on damped harmonic oscillator does not fit well with the topic of section 2.3, and may be deferred until the topic is considered in more detail in chapter 4.

e. Instead of the emphasis on exact trajectories in N3 and related supplements, instructors may introduce isoclines at this point to help guess phase plane portaits in simple cases like saddle points. The aim should be to complement the study of straight line solutions to appear in section 3.2 rather than to insert all of section 5.2 into the syllabus at this point.

f. Note to students: please make sure to review eigenvalues and eigenvectors from your linear algebra notes (which you kept from when you took the course!)

g. Some instructors may wish to skip the notes N4. The matrix exponential, while a useful topic (developed further in notes elaborating on the case of complex eigenvalues) , may be omitted. The time saved could be used to introduce variation of parameters.

h. Instructors may wish to introduce some or all of section 5.1 when discussing sections 3.6 and 3.7. Students should notice that phase planes for linear systems help predict those for nonlinear ones. Section 5.1 is an important part of the course; if it is not introduced in connection with sections 3.6 and 3.7, instructors should be sure to give adequate coverage later.

i. Problem 36(c) is worth looking at - the design of active automobile suspension systems is an area of much current research (at places like Ford, for example) - this question can be taken as an open ended one - be creative, and perhaps introduce nonlinear damping and nonlinear springs!

j. The exercises for 4.4 are to write the steady-state solution of the odd problems 1-9 of section 4.2 in the form   A cos(wt+f).

k. Instructors emphasizing bifurcations should aim to allow more time for chapter 8 in order to include sections 8.3 and possibly also 8.4.  

Schedule of Sections

Past Semester Pages

• Spring 2002
• Spring 2001 (Prof. Han's section)
• Spring 2000

• Course Code: 01:640:251
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 4
• Counts toward math major/minor?: Yes
• Prerequisites: Calc II

General Information:

01:640:251 Multivariable Calculus (4 Credits)  

This course covers multi-variable and vector calculus. Topics include analytic geometry of three dimensions, partial derivatives, optimization techniques, multiple integrals, vectors in Euclidean space, and vector analysis.

Prerequisite: Math 152

Textbook:

Thomas' CALCULUS Early Transcendentals, 15/e,  by Joel Hass, Christopher Heil, and Maurice Weir. Pearson Education. ISBN: 978-0137559756 

MyMathLab access with etext: ISBN: 978-0137560103

MyMathLab access can be purchased directly from Pearson.

Standard Syllabus, and Homework

• Syllabus
• Lecture Topics
• Exam Protocols
• MyLab - Online Homework
• Grading Weights
• Practice exams and review materials
• There is a Canvas course site for each lecture group where all grades, exam reviews, syllabus, etc., are posted. You can access your Canvas course at https://canvas.rutgers.edu/.

Lecture Topics & textbook homework for Math 251 

MyLab - Online Homework

Students are required to purchase access to MyLab Math to complete the online homework, and possibly quizzes and exams. The MyLab assignments are similar to the exercises in the official list of HW exercises. (The official HW exercises are not handed in for grading but instead form a significant, but not exhaustive, portion of your study guide for the course.) Each assignment will have a specific due date set by the professor, and these assignments must be completed online.

How to use MyLab properly:
If you take shortcuts like trying to find answers to MyLab problems from various "homework help" web services without solving all of the problems yourself in their entirety, then your performance on exams will suffer. Instead, use the built-in help tools within MyLab. This online homework exists primarily to give you feedback on your ability to calculate correct answers at early stages of the learning process. The homework is not intended to measure your mastery of the material; only the midterm exams and final exam measure mastery. Without doing well on the exams, it is impossible to pass the course, even with a perfect score on the homework. So be sure to take full advantage of MyLab to get as much feedback as possible on your problem-solving skills.

Getting started with MyLab:

• You will be able to access your MyLab course directly through your Canvas site for Math 251.
• In your Canvas site, navigate to MyLab and Mastering and follow the on-screen instructions to create a Pearson account (or link an existing Pearson account) to your Canvas account.
• You will automatically be enrolled in the MyLab course.
• If you switch to a different section of Math 251, you can enroll in your new section's MyLab course by following these same instructions.

Student support for MyLab:

• System RequirementsMyLab works on a series of pop-up screens. You MUST enable pop-ups when working in MyLab. For help on how to do this, as well as make sure your browser is up to date, use the link above.
• How to Use MyLab on a Mobile Device
  This video shows you how to set up your mobile device with any necessary browser add-ons and apps to use MyLab properly. 
• Pearson Support Database
  Use the above link to search Pearson's database for support topics (e.g., resetting password).
• Contact SupportUse the above link to contact technical support. Fill out the required form and you will be immediately connected to a support agent based on your issue.
• Pearson sales representative: Melissa Blum is our Pearson Sales representative. If you are having technical issues, please first contact Technical Support. If you are still having issues after contacting Technical Support, please email Melissa Blum with the Incident Number you received from working with Technical Support. You must have an Incident Number for Melissa to be able to help.

Other information about MyLab:

• MyLab is an interactive, online homework system. The assignments follow the lecture topics.
• Questions are algorithmically generated to give each student their own random versions of the questions.
• After entering an incorrect answer, students are given helpful feedback and hints. Most exercises will also include learning aids, such as guided solutions and sample problems.
• You have three attempts to get an answer correct. If you use all three attempts, you will be told the correct answer and given a new, random version of the same problem. There is no limit to the number of versions of a particular problem you can be given. So you are strongly encouraged to work on a problem until you get the correct answer. There is no penalty for the number of attempts taken.

Grading Weights

Letter Grade Cutoffs

Solutions to practice exams and additional documents

Extra Problems 251 if you have finished working on the practice exams and additional review material provided by your instructor, you may want to check this list of problems if you want to do additional practice problems. Some of these are more conceptual in nature, so they may be useful to enhance your understanding of the course material. https://www.dropbox.com/scl/fi/zf60bu894t8bvf5j85nwl/extra-problems-251.pdf?rlkey=jb0yvp3962ji90p4wq377wt2c&st=pwazkd3n&dl=0

Practice Exams and Study Guides
https://www.dropbox.com/scl/fo/hbqc979lyn7y7qoa5jlsm/AMaNEKklTcGaaqgTniTgaGs?rlkey=zig2h25nkh2quk23ms0f3c94q&st=g24pfnuf&dl=0

Schedule of Sections:

01:640:251 Schedule of Sections 

• Course Code: 01:640:250
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 3
• Counts toward math major/minor?: Yes
• Prerequisites: Math 112 or Math 115 or placement

General Information (Catalog listing)

Prerequisite: Precalculus (Math 115 or 111-112) or placement into calculus

Systems of linear equations, Gaussian elimination, matrices and determinants, vectors in two- and three-dimensional Euclidean space, vector spaces, introduction to eigenvalues and eigenvectors. Possible additional topics: systems of linear inequalities and systems of differential equations.

Updated description

Systems of linear equations, Gaussian elimination, Vectors in n-space, Span and linear independence of a set of vectors, Linear Transformations, Matrix algebra, Determinants, Vector spaces, Basis and dimension, Coordinate vectors and change of coordinates, Eigenvalues and eigenvectors, Diagonalization of a matrix, Geometry of vectors, Orthogonality, Symmetric matrices.
(current, 2025)

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

The details of the syllabus and the timing of the midterm exams will vary from section to section. Each section of Math 250 has its own midterm exams and final exam. The final exam times are determined from the class meeting times. The room of the final exam may or may not be the usual lecture room! See the Final Exam schedule or the Math Department main website for updated details about final exams, when this information is available.

Course materials for all sections of Math 250

Course materials for Math 250C1, C2, and C3 ---the MATLAB sections

• Click here to access the webpage for the 250C (MATLAB) sections, where the MATLAB assignments can be found.

Suggested examination review materials for all sections of Math 250

Students are expected to follow the Rutgers Standards of Academic Integrity on the assignments, quizzes and exams in the course.

Another Resource for MATLAB

(Note: for the MATLAB Assignments for the MATLAB Sections C1, C2, and C3, please refer to the Math 250C webpage instead)

• Matlab Tutorial (from MIT)

Schedule of Sections:

01:640:250 Schedule of Sections

• Course Code: 01:640:244
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 4
• Counts toward math major/minor?: Yes
• Prerequisites: Calc III

General Information

01:640:244 Differential Equations for Engineering and Physics (4)
First- and second-order ordinary differential equations; introduction to linear algebra and to systems of ordinary differential equations.
Prerequisite: CALC3. Credit restriction CR4.

Course Learning Goals: The specific learning goals for this course can be found on the document here. In addition, this document contains a list of recommended problems from each section of the textbook. These problems cover most of the essential topics that will be discussed during this course. 

Textbook:  The current textbook used for this course is Differential Equations: An Introduction for Engineers. This is a freely available textbook that was written to fit the desired structure and sequencing of this course. The PDF version can be found here: https://sites.rutgers.edu/matthew-charnley/course-materials/differential-equations-an-introduction-for-engineers/. 

Special Accommodations: Students with disabilities requesting accommodations must follow the procedures outlined at https://ods.rutgers.edu/students/applying-for-services

Academic Integrity: All Rutgers students are expected to be familiar with and abide by the academic integrity policy (http://academicintegrity.rutgers.edu/academic-integrity-policy). Violations of the policy are taken very seriously.

Approximate Syllabus, Math 244

All section numbers refer to Charnley, Differential Equations: An Introduction for Engineers, version 0.9.

NOTE: This is a suggested syllabus, which individual instructors may revise.

MATLAB in Math 244

Math 244 uses MATLAB assignments to given an opportunity for students to explore the computational side of differential equations and see how MATLAB can be used to solve and visualize these equations. Assignments and due dates will be decided by individual instructors. In order to complete the assignments, students will need the supplemental MATLAB functions as well as format files that outline the details of each assignment.

All of the information for these assignments are available to current students of Math 244. This is available on your section's Canvas site. There you will find information about when the assignments are due, how to submit them, and extra resources that are available to help with these assignments. The MATLAB On-Ramp can also be helpful for a review/introduction to Matlab if needed.

 Schedule of Sections:

01:640:244 Schedule of Sections 

• Course Code: 01:640:152
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 4
• SAS Core Certified: QQ, QR
• Counts toward math major/minor?: Yes
• Prerequisites: Calc I (Math 135 or Math 151, not Math 130)

Math 152 (Calculus II for Math and Physical Sciences) is a continuation of Math 151, and is part of the three-semester calculus sequence for the mathematical and physical sciences at Rutgers University, New Brunswick. Math 152 covers the integral calculus and its applications, the theory of infinite series and power series, parametric curves, polar coordinates, and complex numbers.

All sections of Math 152 (other than asynchronous online sections) will have two lecture meetings and one workshop meeting per week. The Lecturer presents the course material during the lecture meetings.  The workshop class is a smaller meeting with a Workshop Instructor (WI), where students engage in group work to solve in-depth problems related to the content delivered in the lectures. Workshops typically require students to complete a pre-class assignment, a write-up of their in-class activity results, and a short quiz following the problem-solving session. The workshop problems will form the basis for some of the problems that students will encounter on midterm quizzes and on the final exam.

The required textbook is Thomas' Calculus: Early Transcendentals (15th edition), by Hass, et al. with MyMathLab access code. You may use either the hardcover edition or the eBook; they contain exactly the same material. Both are available through the Rutgers bookstore, and the eBook can be purchased directly through the course canvas page.

• The ISBN for the physical textbook with MyMathLab access is 978-0137559756.
• The ISBN for the eBook with MyMathLab access is 978-0137560103.

Math 152 covers parts of Chapters 5, 6, 8, 10, 11 and 18 of the textbook.  The course sets the following learning goals for each student:

• To use integrals to find volumes, arc lengths, and surfaces of revolution.
• To find antiderivatives using techniques including u-substitution, integration by parts, and trigonometric substitution.
• To determine whether an infinite series converges, and to find and use Taylor series and Taylor polynomials.
• To use derivatives and integrals with parametric equations, and with equations defined in polar coordinates.
• To use polar and exponential forms of a complex number.

A more detailed list of learning goals can be found here.

Typical Lecture Schedule (may vary slightly by semester)

Specific course information, resources, and policies for the current semester are available to course registrants through the Math 152: All Sections Canvas site.

Schedule of Sections:

01:640:152 Schedule of Sections

• Course Code: 01:640:151
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 4
• SAS Core Certified: QQ, QR
• Counts toward math major/minor?: Yes
• Prerequisites: Math 112 or Math 115 or placement

Math 151 (Calculus I for Math and Physical Sciences) is the first semester of the three-semester calculus sequence for the mathematical and physical sciences at Rutgers University, New Brunswick. Math 151 covers differential calculus of the elementary functions of a single real variable: the rational, trigonometric, and exponential functions and their inverses; various applications via the Mean Value Theorem; and an introduction to the integral calculus.

All sections of Math 151 will have two lecture meetings and one workshop meeting per week. The Lecturer presents the course material during the lecture meetings.  The workshop class is a smaller meeting with a Workshop Instructor (WI), where students engage in group work to solve in-depth problems related to the content delivered in the lectures. Workshops typically require students to complete a pre-class assignment, a write-up of their in-class activity results, and a short quiz following the problem-solving session. The workshop problems will form the basis for some of the problems that students will encounter on midterm exams and on the final exam.

Textbook and Online Homework:   The required textbook is Thomas' Calculus: Early Transcendentals (15th edition), by Hass, et al. with MyMathLab access code. Students may use either the hardcover edition or the eBook; they contain the same material. Students must purchase MyMathLab access with their textbook.  Both are available through the Rutgers bookstore.

• The ISBN for the physical textbook with MyMathLab access is 978-0137559756.
• The ISBN for the eBook with MyMathLab access is 978-0137560103.

Math 151 covers Chapters 1-5 of the textbook.  The course sets the following learning goals for each student:

• To acquire the ability to compute limits, derivatives, and integrals of certain algebraic, trigonometric, exponential, and logarithmic functions.
• To achieve understanding of the notions of continuity and differentiability.
• To develop the ability to use first and second derivatives to determine the shape of the graph of a function.
• To acquire practice solving optimization problems using calculus.

A more detailed list of learning goals can be found here.

Specific course information, resources, and policies for the current semester are available to course registrants through the Math 151: All Sections Canvas site.

Schedule of Sections:

01:640:151 Schedule of Sections

• Course Code: 01:640:135
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 4
• SAS Core Certified: QQ, QR
• Counts toward math major/minor?: Yes
• Prerequisites: Math 112 or Math 115 or placement

Course Overview

Schedule of Sections

Math 135 provides an introduction to calculus, covering limits and continuity, the derivative and tangent lines, applications of the derivative, and basic integration. Math 151 is another introductory calculus course. See below for important policies regarding these two sequences.

Who should take the Math 135 sequence?

• Math 135 is intended and required for many majors in the biological and social sciences.
• Some Economics majors may only need Math 135, but others may also need Math 152. Please see an adviser in your major if you are unsure.
• Students in Rutgers Business School are also currently required to pass Math 135 with a grade of C. (All current details can be found on the RBS web site.)
• It is possible to take Math 152 after Math 135, but this is not a recommended sequence.
• Math 136 does not satisfy the prerequisite for Math 251.

Who should take the Math 151 sequence?

• Math 151 is intended and required for many majors in mathematical and physical sciences.
• Students in Rutgers School of Engineering are also currently required to take Math 151. SOE does not accept Math 135 for CALC1 credit. (All current details can be found on the SOE web site.)
• If you will need Math 152, you should take Math 151 instead of Math 135
• If you will need Math 251, you must take Math 152, whose recommended prerequisite is Math 151. Hence if you will need Math 251, you are strongly recommended to take Math 151 instead of Math 135.

Can I take Calculus I a third time?

• As of Fall 2019, students who have failed Calculus I (either 135 or 151) twice can no longer take the course again at Rutgers -- New Brunswick.
• Students who have failed Calculus I twice because of extenuating circumstances can request an exception by submitting an appeal.
• ATTENTION: Due to the COVID-19 crisis, all students from all schools (including SOE and RBS) who have previously failed Calculus I and then have repeated the class in Spring 2020 obtaining an F or NC can apply to the Math Department for permission to one more attempt during Summer 2020 or Fall 2020 without need of any supporting documentation.
• More details can be found on the special permissions page.

• Course Code: 01:640:110
• Semester(s) Offered: Spring (even years)
• Credits: 3
• SAS Core Certified: QQ, QR
• Counts toward math major/minor?: No
• Prerequisites: Math 107

General Information

This course examines algebraic thinking in the context of middle school algebra, with emphasis on mathematical reasoning, conceptual reasoning, and communicating concepts effectively.

This algebra course is designed specifically for future teachers, and is strongly recommended for those pursuing the 15-credit middle school mathematics endorsement. It is also very suitable for future teachers at the elementary level who are strong mathematically (e.g. who have done well in another 100 level mathematics course at Rutgers). The emphasis of the course is on understanding the mathematics conceptually, and articulating the reasoning process. The prerequisite is Math 026:Intermediate Algebra, or equivalent, or Math 107.  Many students take Math 107 before 110, but taking the courses in this sequence is not required. Registration for Math 110 requires a special permission number. Please apply for an SPN via Special Permission for K-8 Teaching Courses. The course is typically offered in the spring semester.

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Syllabus

Consult the instructor.

Schedule of Sections

01:640:110 Schedule of Sections 

• Course Code: 01:640:109
• Semester(s) Offered: Spring (odd years)
• Credits: 3
• SAS Core Certified: QQ, QR
• Counts toward math major/minor?: No
• Prerequisites: Math 026 or Math 107 or placement

General Information

Math content course on geometry and measurement stressing depth of understanding needed for effective middle grade teaching. Justifying procedures and formulas. Multiple points of view in explanations. Geometric objects in two and three dimensions. Transformations, symmetry, congruences, similarity, scaling. Perimeter, area, volume. Error estimates in measurement. Changing units.

This geometry course is designed specifically for future teachers, and is strongly recommended for those pursuing the 15-credit middle school mathematics endorsement. It is also very suitable for future teachers at the elementary level who are strong mathematically (e.g. who have done well in another 100 level mathematics course at Rutgers). The emphasis of the course is on understanding the mathematics conceptually, and articulating the reasoning process.

The prerequisite is Math 026:Intermediate Algebra, or equivalent. Many students take Math 107 before 109, but taking the courses in this sequence is not required.

Registration for Math 109 requires a special permission number. Please apply for an SPN via Special Permission for K-8 Teaching Courses. The course is typically offered in the Fall semester in odd-numbered years

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Schedule of Sections

 01:640:109 Schedule of Sections

• Course Code: 01:640:107
• Semester(s) Offered: Fall, Spring
• Credits: 3
• SAS Core Certified: QQ, QR
• Counts toward math major/minor?: No
• Prerequisites: Math 025 or placement

General Information

This course is intended for future teachers, but not necessarily those who will specialize in teaching mathematics.  Although intended primarily for those who will teach at the K-8 level, it is valuable as a foundation for K-12 teaching as well.

Math 107 will probably seem like quite a change of pace from your typical math course. It reexamines many of the mathematical ideas with which you are already familiar, placing them in the context of the subject as a whole but in addition viewing them from the perspective of young students first learning them. The emphasis will be on reasoning and communication, and you will do much more written explanation than in a typical math course. Much of the time in class will be spent on interactive work, rather than classical lectures.

This course is taught during both fall and spring semesters but does require a special permission number.  
Please apply for an SPN via Special Permission for K-8 Teaching Courses. The course is typically offered in the spring semester.

Prerequisite:  Elementary Algebra.  Students must have taken or placed out of Elementary Algebra to enter this course.

Admission to the course is by permission of the department. This does not use our online system, but is handled separately by .

Textbook

Textbook:  For current textbook please refer to our Master Textbook List page

Syllabus

Topics to be covered:

1.     .  Place Value
2. Algorithms for Whole Numbers
   1.        Addition
   2.        Subtraction
   3.        Multiplication
   4.        Division
   5.        Non-Base Ten Algorithms
3.        Signed Numbers
4. Fractions
   1.        Defining Fractions
   2.        Addition and Subtraction of Fractions
   3.        Multiplication of Fractions
   4.        Division of Fractions
      
   5.        Comparing Fractions
5.        Ratio and Proportion
6. Decimals
   1.        Addition and Subtraction of Decimals
   2.        Multiplication of Decimals
   3.        Division of Decimals
   4.        Rational vs Irrational
   5.        Converting and Comparing: Decimals and Fractions 

Archives

Previous semesters:

• Fall 2007, 2008. Professor Beals.
• Fall 2006, Professor Beals.
• Listed first as 103 T1 and then as 107, taught by Professor Beals.

Schedule of Sections

01:640:107 Schedule of Sections

• Course Code: 01:640:106
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 3
• SAS Core Certified: QQ, QR
• Counts toward math major/minor?: No
• Prerequisites: Math 025 or Math 103 or placement

Course Description

This course is an introduction to the uses of college level mathematics in personal finance applications. Similar to Math 103 in its target audience, this course is intended for students not majoring in the mathematical or natural sciences. The subject matter is more focused than in 103, and is highly applicable. Topics include simple interest, simple discount, compound interest, annuities, investments, retirement plans, mortgages, student loans, leasing, inflation, and insurance. Some biological analogies and applications are considered throughout the course. The course is designed so that reinforcement of basic skills is integrated into the learning of the subject matter. The emphasis is on problem solving, with some derivation of formulas and consideration of why the formulas make sense. You will never wonder, “what is this kind of math actually good for in real life?”

Textbooks

Textbook:  For current textbook please refer to our Master Textbook List page

Syllabus

The following list of topics, classes, and exams is approximate. The actual topics and exam dates are determined by each instructor. See the instructor of a specific section for details.

SAS Core Curriculum Learning Goals

Math 106 fulfills both the Quantitative Information (QQ) and Mathematical or Formal Reasoning (QR) learning goals of the SAS Core Curriculum: 
QQ: Formulate, evaluate, and communicate conclusions and inferences from quantitative information. 
QR: Apply effective and efficient mathematical or other formal processes to reason and to solve problems.

Additional Information

This course may not be used as an elective for the math major or minor. It is not intended for students majoring in business, economics, or STEM fields. Rutgers Business School will not give its students credit for taking this course.

Schedule of Sections

• Course Code: 01:640:104
• Semester(s) Offered: Fall, Spring
• Credits: 3
• SAS Core Certified: QQ, QR
• Counts toward math major/minor?: No
• Prerequisites: Math 025 or Math 103 or placement

General Information

Textbook:  For current textbook please refer to our Master Textbook List page

Credits: 3

The course gives a mathematical yet accessible and concrete introduction to probability. Most of the course is devoted to understanding how probability works, and how it is applied in a number of areas, including medical testing and some decision making. The end of the course discusses some statistics and applications. You will never be left wondering, "What is this good for? What does this have to do with real life?" 

This is an "elementary" course for liberal arts majors, in the sense that it does not presume any knowledge of precalculus or calculus. It is, however, more challenging than Math 103, and more focused in its subject matter. Many students who take Math 104 have already taken Math 103 or 106, although these are not prerequisites.

Math 104 is typically not appropriate for majors in STEM fields. Math 104 may not be used as an elective for the Mathematics major or minor, and may not be taken for credit simultaneously with or after a student has received credit for any of the following courses: 01:640:477, 01:198:206, 01:960:379, 01:960:381, 14:332:226.  But Math 104 may be taken for credit before any of the courses on this list, and some students find it helpful to do so, especially before 01:640:477.

Prerequisite: 01:640:026 or appropriate performance on the placement test in mathematics. May not be used as an elective for the math major or minor.

SAS Core Curriculum Learning Goals

Math 104 fulfills both the Quantitative Information (QQ) and Mathematical or Formal Reasoning (QR) learning goals of the SAS Core Curriculum: 
QQ: Formulate, evaluate, and communicate conclusions and inferences from quantitative information. 
QR: Apply effective and efficient mathematical or other formal processes to reason and to solve problems.

Hybrid sections

In fall 2017, there will be one hybrid and two traditional sections of the course, so that students can choose the format which is best for their learning style. The hybrid section implements the flipped classroom model, so that students first learn the subject matter, on their own time, from carefully working through a series of video lecture segments posted on Sakai interspersed with practice problems. The weekly class meeting follows up on the students' online work, beginning with a quiz on that work, and proceeding with a highly interactive workshop session. A hybrid section has only half the in-person class time of a regular section, but this does not mean that it requires half as much work! On the contrary, the hybrid format requires a certain extra discipline, to keep up with the online component of the course. But it does have the advantage that students can rewatch the videos as often as they need to, and can also benefit from a more interactive classroom experience. 

Syllabus

There is some variation between sections, but  this section  is representative of the course.

Previous semesters:

• Spring 2009. Michael Weingart
• Fall 2008. Michael Weingart
• Spring 2008. Daniel Cranston
• Spring 2007. Michael Weingart

Schedule of Sections

• Course Code: 01:640:115
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 4
• SAS Core Certified: QQ, QR
• Counts toward math major/minor?: No
• Prerequisites: Math 026 or placement

Read more: 01:640:115 - Precalculus College Mathematics

• Course Code: 01:640:123
• Semester(s) Offered: Fall, Spring
• Credits: 2
• Counts toward math major/minor?: No
• Prerequisites: By application only. This is a half-semester course for students switching out of Calc I.

Course Description

Math 123: Preparation for Calculus I is a half-semester course. It is designed for students currently enrolled in Calculus I (Math 135 or Math 151) that need additional preparation to successfully complete the course. Rather than continuing to struggle in Calculus I, these students can switch to Math 123. This course is an opportunity for a productive second half of the semester and for students to best set themselves up for future success in calculus.

Students in this course will work through a review of algebra and precalculus topics. This is not simply a shorter version of existing precalculus courses. Rather, the course is designed specifically to include only material that is important for success in calculus.

In order to enroll in Math 123, students must drop Calculus I (which will be done so that students do not get a W in Calculus I). This course is 4 credits - 2 are academic credits (counting toward graduation) and 2 are E credits (counting toward your registration total). Thus students who switch from Calculus I to Math 123 will maintain the same registration total.

If you have questions about the course, send an email to the Math 123 coordinator.

Course Format

This course meets twice a week. This course is taught in a flipped format, where students are introduced to the material before class through videos and online homework, then spend the majority of class time working on problems in groups.

Most class meetings will include a quiz and there will be two exams (midterm and final).

Textbook

Students in this course must purchase access to the online homework system Knewton Alta for the duration of the course. All other course materials, such as videos or textbook readings, will be available in Knewton Alta or on the Canvas site.

Spring 2026 Sections

Section 3: Mon, Wed, 9:20-10:40pm (Busch)
Section 4: Tues, Thurs, 9:20-10:40pm (Liv)

Enrollment in Math 123

Students can only enroll in this course if they are currently enrolled in Math 135 or Math 151. Enrollment in Math 123 is by application only.

application for Math 123

Applications will be processed in three rounds. Students who apply during an earlier round have a higher chance of being approved over those applying in a later round.

Round 1: ends Thursday, February 19 at 11:59pm, students will be notified by Monday, February 25.

Round 2: ends Thursday, February 26, at 11:59pm, students will be notified by Friday, February 27.

Round 3: ends Monday, March 2, at 11:59pm. Students will be notified as soon as possible to attend the relevant section.

The first day of class is Monday, March 2. 

If you have questions about the application, send an email to the Math 123 coordinator.

Students whose applications are approved will be enrolled in Math 123 and dropped from Calculus I. You should not submit an application if you do not want to drop Calculus I.

FAQs

How do I decide if I should switch to Math 123?

Math 123 will review prerequisite material, such as algebra and trigonometry. Students who are struggling with this aspect of Calculus I could benefit from a review of this material and should consider switching to Math 123. Students may also discuss their performance in Calculus I so far with their instructors to get a more accurate assessment of whether they should consider switching to Math 123.

Can I take Math 123 without dropping Calculus I?

No, in order to enroll in Math 123, students will be dropped from Calculus I. The courses may not be taken simultaneously. You should not submit an application if you do not want to drop Calculus I.

Will I receive a W for Calculus I when I switch?

No. Students who switch into Math 123 from either Math 135 or Math 151 will not receive a W for their calculus enrollment. Instead, Calculus I will be removed from the student's schedule.

If I take Math 123, do I get credit for Calculus I?

 No. You will get credit for Math 123. To get credit for Calculus I, you must retake it in a later semester.

Are my exam scores in Calculus I a part of my grade in Math 123?

No. None of the scores from Calculus I affect your Math 123 grade. Your Math 123 grade is based solely on your performance in Math 123 starting in week 7.

If I retake Calculus I, do my exam scores carry over?

No. If you retake Calculus I, you will start with a blank slate. No scores from a prior semester will be used during a later semester.

Course Schedule

1.2 - Exponents and Scientific Notation

1.3 - Radicals and Rational Exponents

1.4 - Polynomials

1.5 - Factoring Polynomials

1.6 - Rational Expressions

2.2 - Linear and Rational Equations in One Variable

2.5 - Quadratic Equations

2.6 - Other Types of Equations

2.7 - Linear Inequalities and Absolute Value Inequalities

2.8 - Inequalities Requiring Factoring

3.1 - Functions and Function Notation

3.3 - Domain and Range

3.4 - Rates of Change and Behavior of Graphs

3.5 - Composition of Functions

4.1 - Linear Functions

5.2 - Graphs of Polynomial and Power Functions

5.5 - Rational Functions

6.2 - Graphs of Exponential Functions

6.3 - Logarithmic Functions

6.4 - Graphs of Logarithmic Functions

6.5 - Logarithmic Properties

6.6 - Exponential and Logarithmic Equations

6.7 - Exponential and Logarithmic Models

7.1 - Angles as Rotations and Arc Length

7.2 - Right Triangle Trigonometry

7.3 - The Unit Circle

7.4 - The Other Trigonometric Functions

8.1 - Sine and Cosine Graphs

8.2 - Graphs of Other Trigonometric Functions

9.1 - Fundamental Trigonometric Identities

9.5 - Solving Trigonometric Equations

14.1 - Finding Limits Using Numerical and Graphical Approaches

14.2 - Finding Limits Analytically

14.3 - Continuity

14.4 - Derivatives

Schedule of Sections:

01:640:123 Schedule of Sections

• Course Code: 01:640:112
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 2
• SAS Core Certified: QQ, QR
• Counts toward math major/minor?: No
• Prerequisites: Math 111

• Math 112 Exam 1 Review: Spring 2026
• Math 112 Exam 2 Review: Spring 2026
• Math 112 Final Exam Review: Spring 2026
• Math 112 Final Exam Formula Sheet: Spring 2026
• Current Semester Sections

*This document requires Acrobat 5.0 or above in order to view it.

Course Description

01:640:112
Math 112 Precalculus II (2)
Prerequisite: 01:640:111. Corequisites: 01:640:012 for 01:640:112. This course with 01:640:111 covers the same material as 01:640:115, but at a slower pace. Students may not receive more that 4 normal credits for any combination of 01:640:111-112, and 115.

Exponential, logarithmic, and trigonometric functions.

Schedule of Sections:

01:640:112 Schedule of Sections

• Course Code: 01:640:111
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 2
• Counts toward math major/minor?: No
• Prerequisites: Math 026 or placement

Precalculus I (2)

Prerequisite: 01:640:026 or appropriate performance on the placement test in mathematics. Corequisites: 01:640:011 for 01:640:111. This course with 01:640:112 covers the same material as 01:640:115, but at a slower pace. Students may not receive more that 4 normal credits for any combination of 01:640:111-112, and 115.

Algebraic expressions, algebraic equations, inequalities, functions, and graphing.

• Exam 1 Review Exercises: Spring 2024
• Exam 2 Review Exercises: Spring 2022
• Exam 3 Review Exercises: Fall 2024
• Handout: The Language of Functions*
• Math 111 Final Exam Review Exercises: Fall 2025*
• Current Semester

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Schedule of Sections:

01:640:111 Schedule of Sections

• Course Code: 01:640:026
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 3
• Counts toward math major/minor?: No
• Prerequisites: Math 025 or placement

• Syllabus: Spring 2024
• Math 026 Final Exam Review Exercises: Fall 2023*
• Math 026 Final Exam Fall 2013
• Math 026 Final Exam Fall 2013 Answers

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Textbook:  For current textbook please refer to our Master Textbook List page

Schedule of Sections:

01:640:026 Schedule of Sections

• Course Code: 01:640:001
• Semester(s) Offered: Fall, Spring
• Credits: 1.5
• Counts toward math major/minor?: No
• Prerequisites: Placement

Course Description

A supplemental course to some sections of 640:025

Textbook:  For current textbook please refer to our Master Textbook List page

Schedule of Sections:

01:640:001 Schedule of Sections

• Course Code: 01:640:025
• Semester(s) Offered: Fall, Spring, Summer
• Credits: 3
• Counts toward math major/minor?: No
• Prerequisites: Placement

• Syllabus: Spring 2025
• Exam 1 Review Exercises: Spring 2023
• Exam 2 Review Exercises: Fall 2023
• Math 025 Final Exam Review Exercises: Spring 2021 (This document requires Acrobat 5.0 or above in order to view it.)

Textbook:  For current textbook please refer to our Master Textbook List page

Course Description

01:640:025 Math 025 EAL Elementary Algebra (E3)

Prerequisite: 

• Demonstrated proficiency in computational skills.
• Operations with polynomials, rational and square root expressions, exponents, solving linear equations and quadratic equations, basic applications and graphing.

SYLLABUS

Schedule of Sections:

01:640:025 Schedule of Sections

• Course Code: 01:640:103
• Semester(s) Offered: Fall, Spring
• Credits: 3
• SAS Core Certified: QQ, QR
• Counts toward math major/minor?: No
• Prerequisites: none

Textbook:  For current textbook please refer to our Master Textbook List page

Math 103 is a popular course taken by many undergraduates not majoring in the mathematical, physical, or life sciences, to satisfy a quantitative course requirement for graduation. It is intended to cohere well with students' liberal arts and social science interests, by investigating applications of mathematics, much of it developed only relatively recently, in contexts which are relevant to individuals who do not necessarily have strong interests in the sciences.

These topics include

• the mathematics of voting (when there are 3 or more candidates in an election, how do you decide who should win, and how can we define suitable notions of "fair" and "unfair" outcomes?),
• weighted voting systems (how much power does each party really have in a parliamentary system, or each nation on the UN Security council, or each state in the US electoral college?),
• the mathematics of apportionment (how many congressional seats is each state entitled to, and what mathematical difficulties can result from apportioning them?),
• fair division of goods (how can co-owners of a store location but with different retail businesses divide the year fairly? if siblings inherit an estate, what is a fair way to divide it?),
• financial mathematics and exponential growth (if you invest $100 every month at a certain interest rate, how much will be there in 30 years?),
• Euler circuits (what is an efficient way to drive over every road in your town, e.g., if you're plowing out the roads after a snowstorm?),
• the Traveling Salesman Problem (given a table of airfares, how do you find the cheapest itinerary for visiting 10 cities in any order?),
• and the mathematics of networks (to build the cheapest possible high speed rail system linking a certain group of cities, which pairs of cities should have direct links built between them?).

You will not be left wondering, "what does this have to do with real life?" The course is also intended to reinforce underlying mathematical skills. 

Flipped Sections

Each semester, we offer 2-3 traditional sections and the remainder of sections are of a flipped format so that students can choose the format which is best for their learning style. The flipped classroom model has students first learn the subject matter, on their own time, from carefully working through a series of video lecture segments posted on Canvas interspersed with practice problems. The weekly class meeting will follow up on the students' online work, beginning or ending with a quiz on that work, and proceeding with a highly interactive workshop session. The flipped format requires a certain extra discipline, to keep up with the online component of the course. But it does have the advantage that students can rewatch the videos as often as they need to, and can also benefit from a more interactive classroom experience.

SAS Core Curriculum Learning Goals

Math 103 fulfills both the Quantitative Information (QQ) and Mathematical or Formal Reasoning (QR) learning goals of the SAS Core Curriculum:
QQ: Formulate, evaluate, and communicate conclusions and inferences from quantitative information.
QR: Apply effective and efficient mathematical or other formal processes to reason and to solve problems.

General Syllabus and Review Materials

Please note that ultimate authority over the precise schedule of topics, quiz policy, and other details rests with the individual instructore in consultation with the course coordinator. The syllabus distributed in class and/or posted on the Canvas site for an individual section takes precedence over the one posted on this web site.

Final Exam Review Sheets:

Schedule of Sections:

01:640:103 Schedule of Sections