DEPARTMENT OF MATHEMATICS
MATHEMATICS MAJOR BROCHURE

Undergraduate Office
Hill Center 303 (Busch Campus) – (732) 445-2390
www.math.rutgers.edu

This brochure describes the mathematics major and minor at RU–New Brunswick/Piscataway, as well as interdisciplinary majors, and five-year Bachelor's/Master's programs which begin with a major in mathematics. It also describes special opportunities and facilities available to undergraduates through the mathematics department.

Students should consult with their academic advisors about the ways in which mathematics courses can satisfy college requirements. Questions about courses preceding first-semester calculus should be addressed to the director of precalculus instruction, Prof. Lewis Hirsch, Lucy Stone Hall B, room 102A, telephone (732) 445-2288. Further information about advising is found here. New students and prospective students should review the information on our web page for prospective students.

For additional information students should contact the Undergraduate Office.

TABLE OF CONTENTS
The Mathematics Major
Requirements
Options
Standard Option
Option A
Computer Oriented
Option B
Honors Track
Option C
Interdisciplinary Majors and the Minor
Statistics/Mathematics Major Biomathematics Major SAS Mathematics Minor
Five-Year B.A.–M.A. Programs
Statistics Economics Operations Research Industrial and Systems Engineering Mathematics Education (K–12) Mathematical Finance
Special Opportunities
Departmental Honors Programs Scholarships, Awards, Prizes Taking Graduate Courses as an Undergraduate
Independent Study Undergraduate Research in Mathematics
Advising
Current Information for Majors Choosing Courses to Fit Career Goals
Related Areas
Computer Science Physics Statistics
Facilities
Undergraduate Common Room Computer Accounts Mathematical Software


THE MAJOR IN MATHEMATICS

REQUIREMENTS FOR THE MAJOR IN MATHEMATICS (CURRICULUM CODE 640)

Mathematics majors must complete:

To be admitted into the mathematics major program, a student must normally have completed three terms of calculus with a grade of C or better in each course. To continue as a mathematics major, a student is expected to make satisfactory progress toward completing the program. Under normal circumstances, satisfactory progress for a full-time student means completion of at least one mathematics course each term, at an appropriate level, with a grade of C or better.

To complete the mathematics major (subject code 640) in any of its three options, a student must receive grades of C or better in each of 01:640:250, 251 and 252, and in all but at most one of the further mathematics courses. Moreover, a student must receive grades of C or better in all courses in other departments (e.g., computer science) that are used to fulfill the requirements of the mathematics major.

Mathematics 300 (Mathematical Reasoning) is a pre-requisite for the abstract courses Math 311, 350, and 351, as well as many other upper-level mathematics courses.

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MATHEMATICS MAJOR OPTIONS (640)

Option A. Standard Mathematics Major

In addition to the requirements above, to complete the standard mathematics major a student must pass eight additional 3-credit mathematics (subject code 640) courses at the 300- or 400-level, including Math 311 (analysis), and Math 350 or 351 (algebra), and excluding any courses with less than three credit hours. All but one of these courses must be passed with a grade of C or better. At least four of the upper-level courses used to complete the major must be taken at Rutgers–New Brunswick/Piscataway, including one of 01:640:311, 312, 411, 412, and one of 01:640:350, 351, 352, 451, 452. An appropriate Rutgers graduate mathematics course may be substituted for the required analysis and/or algebra course, with departmental approval.

Option B. Computer-Oriented Mathematics Major

The Option A requirement of eight mathematics courses at the 300-400 level is replaced by the following two-part requirement:

(i)  Six mathematics courses at the 300-400 level, including Math 311 (or 411) and including 350 or 351 or 451, including 373, 477 and either 374 or 454, and excluding 491,492. At least four of the upper-level courses used to complete the major must be taken at RU–New Brunswick/Piscataway including one of 01:640:311, 312, 411, 412, and one of 640:350, 351, 352, 451, and

(ii) Four computer science courses, including 01:198:112, 211, and 344 and one course to be elected from the following: 01:198:314, 416, 424, 425, 436 and 452. Prerequisites for some computer science courses may be satisfied by appropriate mathematics courses; students should consult with the head adviser of the computer science department.

Option B is not available to students who declare multiple majors including both mathematics and computer science

Option C. Honors Track

The mathematics department offers a special honors track to qualified students. Students should normally apply no later than the end of the first term of their sophomore year. Students in the honors track will have their progress reviewed by the Honors Committee, and are expected to earn B's or better in their advanced math courses (300 level and above). Students who successfully complete the honors track with a GPA in their upper-level math courses of at least 3.4 will qualify for graduation with honors in mathematics.

Each student in the honors track will be assigned a faculty adviser. Together with the adviser, he or she will formulate a proposed course plan, subject to the approval of the mathematics Honors Committee. This course of study will normally include 01:640:192, 291, and 292 (01:640:151, 152, 251, and 252 may be accepted if approved by the Honors Committee); 01:198:107, 01:640:250, 300H, 411-412, and 451-452; two terms of 1-credit honors seminar, at least one at the junior/senior level; and four mathematics electives as approved by the Honors Committee. Computer Science 01:198:111 may be taken in place of 01:198:107, and is recommended for students with a particular interest in computation.

Admission to the honors track is by application. Application forms are available from the mathematics undergraduate office or from the honors track website, which also contains further information.

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INTERDISCIPLINARY MAJORS AND THE MINOR IN MATHEMATICS

INTERDISCIPLINARY MAJORS

In addition to the three major options listed above, two interdisciplinary majors are available at RU–New Brunswick/Piscataway. Students electing one of these majors should consult with the mathematics department and the allied department early and continually to make sure they are making appropriate progress towards the degree.

Statistics/Mathematics Interdisciplinary Major (curriculum code 961):   This major is administered by the Department of Statistics.  Consult Professor Harold Sackrowitz of the that department, telephone (732) 445 2693, http://www.stat.rutgers.edu/people/faculty/sackrow.html.

Biomathematics Interdisciplinary Major (curriculum code 122):   This major requres 63-67 credits: 33 in mathematics and 30-34 in biology and cognate fields. Students must earn a minimum grade-point average of 2.0 in courses credited toward the major. The major is administered by the mathematics department. For the precise course requirements and other details, consult the web site for the biomathematics major. This site includes a useful list of biology and mathematical biology links.


SCHOOL OF ARTS AND SCIENCES MINOR IN MATHEMATICS

A minor in mathematics consists of three terms of calculus (ordinarily 01:640:151, 152, 251), Introduction to Linear Algebra (01:640:250), and four additional 3-credit courses chosen from 01:640:252, 244 and 300-400 level courses in the mathematics department (01:640:491, 492 do not satisfy this requirement). Grades of C or better are required in 01:640:250 and 251; at most one D is permitted in the four courses beyond 01:640:250. At least three out of the four elective courses must be taken at RU–New Brunswick/Piscataway.

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FIVE-YEAR B.A.–M.A. (or M.S.) PROGRAMS

The Department of Mathematics offers a number of programs which make it easy to move on from an undergraduate major in mathematics to a Master's degree in fields where graduates are in demand.

In the most standard path, at Rutgers or elsewhere, students apply to a Master's program in their senior year of college. Others apply after a period of employment. A Master of Science (M.S.) or Master of Arts (M.A.) degree can usually be completed in 2 years of full-time graduate study. Part-time study is often permitted.

In the intensive five-year B.A.-M.A. sequence at Rutgers, students take extra credits before graduating from college, work which can be transferred to the Master's program. Students apply in their third undergraduate year. With careful planning, the Master's degree can be earned in one year of full-time study after completion of the undergraduate degree. See the web page on the B.A.–M.A. programs at Rutgers. Here is some information on each of these programs:

Statistics

Economics

Operations Research

Mathematical Finance

Mathematics Education (K–12)

New Jersey certification as a mathematics teacher is available to students who complete the Graduate School of Education's five-year mathematics teacher certification program. For such students, the eight courses required at the 300- to 400-level for the mathematics major must include 01:640:300; 311 or 411; 351 or 451; 435; 436; 477; 481; and an applied mathematics course, in addition to an extra mathematics elective and the courses required for certification.

Students interested in teacher certification should read the GSE's web page on the five-year teacher education program. They should also contact Professor Keith Weber Graduate School of Education as early in their undergraduate career as possible to obtain advice and further information.

Industrial and Systems Engineering

Students entering the five-year dual degree program in Industrial and Systems Engineering must complete a standard math major. They must have Math 477; Engineering Economics (14:540:343)–: see catalogue for prerequisites, Linear Programming (Math 354 or Math 453; Math 453 is preferred); and facility with a programming language like C++.   For students who do not major in engineering, I.S.E. sets a cumulative g.p.a. of 3.2 or better as one guideline for admissibility into the Master's program. Grades in mathematics courses and other technical courses are most important.

Select at least some math electives from Math 321 (Introduction to Applied Mathematics), Math 424 (Stochastic Models in Operations Research), Math 429 (Case Studies in Industrial Mathematics), Math 478 (Probability II), Math 481 (Mathematical Statistics), Math 428 (Graph Theory), and Math 454 (Combinatorics).

Select at least some general electives from computer sciencescourses beyond C.S. 111 or 107; Economics 406 (Game Theory), ISE 338 (Probability Models in Operations Research), ISE 433 (Quality Engineering and Statistics), Statistics 384 (Intermediate Statistical Analysis), Statistics 390 (Introductory Computing for Statistics), Statistics 401 (Basic Statistics for Research), and Statistics 484 (Basic Applied Statistics). For more information, see the Industrial and Systems Engineering web page.

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ADVISING

Each math major should see an adviser in the department at least once each semester, during the process of registering for the following semester.  The head undergraduate adviser maintains regular hours in Hill Center 308 throughout each term, and can also be seen by appointment. The advising schedule is at http://www.math.rutgers.edu/undergrad/AdvSched.html. Information is also available by telephone, (732) 445-2390, or email, advisor@math.rutgers.edu. The head adviser is available outside the pre-registration period for formal advising about major and graduation requirements, etc.

The department faculty provides informal advice and discussion to students throughout the year. The department encourages students to consult with faculty members for general advice on mathematical and scientific matters, and to maintain their contact with former instructors after courses end. Although instructors feel obligated to give priority during office hours to students in their current courses, most faculty members are happy to talk to anyone who stops in during office hours (or at any time when they're not under time pressure to do something else). A list of faculty and their areas of interest is at: http://www.math.rutgers.edu/people/faculty.html

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SOURCES OF CURRENT INFORMATION FOR MAJORS

The mathematics department maintains a web site, http://www.math.rutgers.edu/undergrad, with useful information for undergraduates, including new courses, special seminars, mathematics competitions, and job opportunities. Students are encouraged to visit this web site frequently.

During the spring, the mathematics department often gets calls and letters from organizations offering employment to graduating seniors. Less frequently, the department receives inquiries seeking candidates for part-time or summer jobs. Information about these employment opportunities and about a great variety of graduate programs for which mathematics majors are eligible are posted on bulletin boards adjacent to the doors of the main undergraduate office, Hill Center 303.

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CHOOSING COURSES TO FIT CAREER GOALS

The department encourages all its majors to take a diverse program, and students will usually sample courses from a variety of categories before they decide whether to concentrate on one or more areas. The syllabi for mathematics courses are at http://www.math.rutgers.edu/courses/courseware.html . However, students should be aware that syllabi for upper-division courses are often not very detailed; instructors can introduce variations into the contents of the course while remaining within catalogue descriptions. The best way to get an idea of the details is usually to consult the intructor.

It is important to take Math 300 as early as possible, since it is a prerequisite for the abstract courses Math 311, 350, 351, 361, 435, 441, and 461.

It is impossible to make a single, rigid list of the courses a mathematics major should take. Experience has suggested, however, that the following guidelines offer good choices for students who already have some idea of the type of program they would like to pursue.   All math majors are encouraged to talk to the head adviser on this subject. See also the recommendations on related areas, below.

(a) A student planning to study abstract mathematics at the graduate level is advised to take as many courses as possible from this list: Math 411-412, Math 451, Math 403, 432, Math 477, and Math 441. Students interested in undergraduate seminars or honors courses such as 300:H or Math 451-452 should discuss the matter with a member of the department's honors committee.

(b) The honors track has higher requirements regarding courses and grades. Each honors track student's program of study must be approved by the honors committee. For details, see the honors track web page, http://www.math.rutgers.edu/undergrad/Honors/Track/index.html.

(c) A student planning to study applied mathematics at the graduate level is advised to take Math 477 as early as possible, and also to take Math 311-312, and other courses in applicable mathematics, such as Math 336, 338, 354 or 453, 357, 428, 454. It is also advisable to take courses in such areas of application as physics, biology, and economics, and computer science.

(d) Students interested in the area of application in some of our dual degree BA/MA programs (statistics, economics, operations research, industrial and systems engineering, mathematics education, mathematical finance) should consult the mathematics department and the other department as early as possible. They should also look at the information on dual degree programs.

(e) For students planning to seek employment as mathematicians in industry, experience has shown that Math 477 is crucial: it is a prerequisite for several important courses. Students should take 477 as early as they can so that they are prepared to take courses for which it is a prerequisite. They should also take at least one course in mathematical modeling, such as Math 321, 338, or 424. Also courses drawn from among Math 348, 354, 357, 373, 428, 429, 454, 478 and 481. It is also advisable to take courses in such areas of application as physics, biology, and economics—and especially in computer science, a field in which many mathematics majors find career opportunities. Computer Science courses drawn from among 112, 211, 314, 344, 416, 431, 436, and 452 are particularly recommended. Some firms are only willing to consider applications from persons who have had at least two terms of computer science.

(f) There is no separate actuarial major. A good preparation for a career as an actuary begins with a major in mathematics, together with a appropriate courses in economics and statistics. The electives in mathematics should also be chosen with this career goal in mind. To see the list of courses presently recommended by Rutgers, and other useful information on the subject, see the actuarial information page.

Some current publications of the Society of Actuaries dealing with their examination program, etc., are available at the undergraduate mathematics office, Hill 303. A student interested in a career as an actuary should begin by acquiring these publications and becoming acquainted with their contents; he or she should also refer to the home page of the Society of Actuaries. For advice see Professor Daniel Ocone, Hill 518, telephone (732) 445-1320, http://www.math.rutgers.edu/~ocone/.

(g) Students interested in combining mathematics with biology, computer science, or statistics should consider the interdisciplinary programs listed above.

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RELATED AREAS

The department recommends that each mathematics major take at least one two-semester sequence of two mathematically oriented courses in some other discipline. For areas with dual degree programs, refer to the respective list of recommended courses.

Computer Science

The introductory course is 01:198:111, a course that is required of all mathematics majors. A new course, 01:640:107, will probably be in place by the Fall '06 semester; it will take the place of 01:198:111 as a requirement for mathematics majors. For additional current information on computer science courses, consult the catalogue and an adviser from the Department of Computer Science. Here is a list of computer science advisers and their office hours. This list is also posted in the Computer Science undergraduate office, Hill Center 390 (Busch campus).

Physics

Students begin with either 01:750:123-124 (taken by physics majors), 01:750:271-272-273 (honors sequence, physics department permission required) or 01:750:203-204. To follow the introductory sequence, one possible choice would be 01:750:323-324. Students who did well in the first courses and want to study physics seriously should instead take either 01:750:381-382 (Mechanics) or 01:750:385-386 (Electromagnetism). Students of analysis will find the last-named sequence to be particularly illuminating.

Statistics

Sophomores interested in statistics courses can take 01:960:379-380. Students who have already had Math 477-481 should omit Stat 379. Stat 380 is an applied statistics course which may be taken after Math 481, although either 01:960:381 or Math 481 satisfies the prerequisite for upper-level statistics courses. Some of the upper-level courses that mathematics majors should consider are Stat 463, 476, 486, and 490. Note that credit is not given for both Stat 381-382 and Math 477-481; however, either of those sequences may follow 01:960:379-380. Among these courses, only those with subject code 640 count towards the major or minor in mathematics.

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SPECIAL OPPORTUNITIES IN MATHEMATICS FOR UNDERGRADUATES

DEPARTMENTAL HONORS PROGRAMS

The Department of Mathematics offers or participates in several honors programs that provide richer educational experiences and greater opportunities for recognition than the normal curriculum does. These programs are related to each other but distinct. One of them is the honors track described above. There are also honors courses, honors sections of regular courses, and student seminars. For further details, see the honors programs web page.


TAKING GRADUATE COURSES AS AN UNDERGRADUATE

One of the prime reasons for students to select a major university for their undergraduate work is the presence of a research-active faculty and graduate programs. Strong mathematics majors, especially those considering graduate study in mathematics, should take advantage of the opportunities that RU–New Brunswick/Piscataway presents and discuss with their advisers the possibility of taking graduate courses during the senior year (or even sooner in certain cases).

Once the student and major adviser agree that a course is appropriate, the student should get the approval of the course instructor and/or the director of the mathematics graduate program. The student can then either sign up for the course during the pre-enrollment period or register during the add/drop period at the start of the term. (more) .

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INDEPENDENT STUDY COURSES

These are courses tailored to specific student purposes and carried out with the help and supervision of a mentor in the department. They require special registration arrangements and the specific permission of the department. The following restrictions apply.

For advice and permission, students should consult the head adviser.


SCHOLARSHIPS, AWARDS, AND PRIZES

Each year, the mathematics department offers a few scholarships, awards, and prizes to deserving students. Some of these prizes depend on students'performance on the prize examinations, which are held towards the end of March. For information on these subjects and to see a list of students who have received these honors in the past few years, see http://www.math.rutgers.edu/undergrad/Activities/undergradprizes.html


UNDERGRADUATE RESEARCH IN MATHEMATICS

The mathematics department offers Research Experiences for Undergraduates (REUs), see http://math.rutgers.edu/~reu/ . During the academic year, interested students can get a taste of mathematical research working with professors on an individual basis. Participating students are expected to have a strong mathematical background; good computer skills may also be required. Their research projects must have department approval.

During the summer an intensive eight-week REU program is available for a limited number of undergraduates. Each student's individual research project will be assisted by a faculty adviser. The program includes seminars and other social and professional activities. Students are selected on the basis of their academic performance and their compatibility with the available projects. Participating undergraduates receive a stipend and housing. Under NSF rules, only citizens or permanent residents of the U. S. are eligible. Women, members of minorities, and disabled students are encouraged to apply.

For other REU opportunities in mathematics at Rutgers, see the web site dimacs.rutgers.edu/REU/; for nationwide programs, see the AMS web site www.ams.org/employment/reu.html, and the NSF website http://www.nsf.gov/crssprgm/reu/reu_search.cfm .

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Facilities

UNDERGRADUATE COMMON ROOM

Hill Center 323 is a place for undergraduate math majors to meet, discuss mathematics, and use computers. The room is also used for meetings of the undergraduate honors seminar, and for special talks for undergraduates about mathematics or careers in the mathematical sciences.


COMPUTER ACCOUNTS

All Rutgers students are entitled to an account on the university computer eden and every campus in RU–New Brunswick/Piscataway has fully equipped computer labs for the use of students.

The computer terminals in the undergraduate common room are for math majors only. To use them it is necessary to open an account on the department's computer gauss. This computer is for declared mathematics majors. Interested majors should inquire in Hill 322 (see Risa Hynes).


MATHEMATICAL SOFTWARE

The department offers several courses which require the use of software packages capable of sophisticated scientific calculation, three-dimensional graphics, and symbolic manipulation.

In some courses, including third-semester calculus, differental equations, and numerical analysis, Maple is used. Rutgers has a license that makes Maple available on many systems, including eden , the PC labs on every campus, and the mathematics department's servers.

In other courses, for example the computer sections of linear algebra (Math 250, C sections), and Math 357, Matlab is used.  Matlab is available on gauss and at the Rutgers computer labs.

For information on software and the servers where it is available, see the list of campus computing facilities.

Full-scale versions of these software packages are costly. Student versions are available at a moderate price at the Rutgers University Bookstore and elsewhere. These student versions can handle only objects of moderate size (adequate for most uses) and do not include user support.

Although formal courses dealing solely with the use of these packages do not constitute college-level work, it should be part of every mathematics student's out-of-class education to become thoroughly familiar with at least one such package.

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last full revision April, 2006 (ec)

tweaked 2/07 (ugvc)