• 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