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The major programs in both Mathematics and Applied Mathematics are appropriate for students who plan to continue their training in graduate school. The major in Mathematical Sciences combines the elements of Mathematics, Computer Science and Statistics. It is designed to prepare students for employment in business, administration, and finance, and also give excellent background for someone planning graduate study in a social science field. Students who plan to obtain a teaching qualification in mathematics should plan their course of study carefully with an advisor, since courses that are too far from mathematics do not count towards certification.

**For a major in Mathematics: **14 courses as follows:

Four courses in calculus or Honors Mathematics A-B, including Advanced Placement Credit. Six courses in mathematics numbered at or above 2000, and four courses in any combination of mathematics and cognate courses. The courses in mathematics must include:

- V 2010 Linear Algebra (or Honors Mathematics A-B)
- W 4041–2 Introduction to Modern Algebra*
- W 4061–2 Introduction to Modern Analysis*
- V 3951x, 3952y Undergraduate Seminar in Mathematics (at least one term)

However, students who are not contemplating graduate study in mathematics may replace one or both of the two terms of MATH W4061-W 4062 by one or two of the following courses: MATH V2500, V3007, or W4032 and may replace MATH W4042 by one of MATH V3020 or MATH V3025. In exceptional cases, the chair will approve the substitution of certain more advanced courses for those mentioned above.

*Note: It is strongly recommended that the sequences Math W 4041-2 and W 4061-2 be taken in separate years.

**For a major in Applied Mathematics:** 14 courses including Junior Seminar in Applied Mathematics:

Four courses in calculus or Honors Mathematics A-B, including Advanced Placement Credit.

- V 2010 Linear Algebra
- W 4061 Introduction to Modern Analysis
- APMA E 4901 Seminar in Applied Mathematics: Fall, Junior year
- APMA E 4903 Seminar in Applied Mathematics: Fall, Senior year
- APMA E 3900 Undergraduate Research in Applied Mathematics

(APMA E 3900 may be replaced by the combination APMA E 4902/4904, second semester of the junior and senior applied mathematics seminar, when these are offered or, with approval, another technical elective for seniors that involves an undergraduate thesis or creative research report.)

Additional electives, to be approved by the Applied Math Committee, e.g.:

- V 2500 Analysis and Optimization
- V 3007 Complex Variables
- V 3027 Ordinary Differential Equations
- V 3028 Partial Differential Equations
- V 3030 Dynamical Systems
- W 4032 Fourier Analysis
- SIEO W 3658 Probability
- APMA E 4300 Numerical Methods

**For a major in Mathematical Sciences: **14 courses:

6 from Mathematics, 5 from a combination of Statistics and Computer Science and 3 electives from a combination of Mathematics, Statistics, Computer Science.

**MATHEMATICS:** 6 required courses:

- MATH V1101, V1102, V1201 Calculus I, II, III (or equivalent, including advanced placement credit)
- MATH V2010 Linear Algebra
- MATH V2000 Introduction to Higher Math
- MATH E1210 (or Math V3027) Ordinary Differential Equations

and possible further courses selected from: V1202 Calculus IV, V2500 Analysis and Optimization, V3020 Number theory and Cryptography, V3025 Making and breaking Codes, or any 3 credit MATH course numbered 2000 or above

**STATISTICS: **at least one course from

- STAT W1211 Intro to Stats (with calculus), SIEO W4150 Intro Probability and Statistics, or the pair STAT W3105, W3107 Intro to Probability and Intro to Statistical Inference

and possible further courses selected from: STAT 2024 Applied Linear Regression Analysis, STAT 2025 Applied Statistical Methods, STAT 3026 Applied Data Mining, or other courses from the Statistics major list

**COMPUTER SCIENCE:** At least one programming course:

- One of COMS W1003 – W1007, with W1004 preferred

and possible further courses selected from: other classes from the Computer Science Core or COMS 3203 Discrete Math: Introduction to combinatorics and Graph Theory, COMS 3210 Scientific Computation (prerequisite COMS 1004), COMS 3251 Computational Linear Algebra.

More generally, electives may be any course with a prerequisite of at least one semester of Calculus, Statistics or Computer Science with the prior approval of the Mathematics Chair.

The Capstone Experience can be fulfilled by a significant thesis written under the supervision of faculty of any one of the three departments or by the Undergraduate Seminar in Mathematics.

**For a major in Mathematics-Statistics: **14 courses:

Five courses in mathematics:

- V 1101, V 1102 and V 1201 Calculus I, II and III or equivalent
- MATH V 2010 Linear Algebra
- MATH V 2500 Analysis and Optimization

Five courses in statistics:

- One of STAT W1001, STAT W1111, STAT W1211 Introduction to Statistical Reasoning or Introduction To Statistics.
- STAT W3105 Introduction To Probability or STAT W4105 Probability
- STAT W3107 Introduction to Statistical Inference or STAT W4107 Statistical Inference
- STAT W3315 or Stat W4315 Linear Regression Models
- STAT W4606 Elementary Stochastic Processes or STAT W4635 Stochastic Processes for Finance

One course in computer science that requires substantial work in programming.

Three courses of electives: An approved selection of advanced courses in mathematics, statistics, applied mathematics, computer science, or mathematical methods courses in physical or social sciences, including biology, economics, and physics.

Students should plan to include a senior thesis or the Undergraduate Seminar in Mathematics in their program, in consultation with their advisors.

*Note:* Students must obtain approval from an adviser in each of the two departments before selecting electives. Students should take MATH V 2010 Linear Algebra in the second semester of the second year.

**For a major in Mathematics-Computer Science **15 courses:

Courses in mathematics:

- V 1101, V 1102, V 1201, V 1202 Calculus I, II, III, IV (including AP Credit)
- or V 1207, V 1208 Honors Math A-B (Note A)
- V 2010 Linear Algebra
- V 3020* Number Theory and Cryptography (Note B)
- W 4041 Introduction to Modern Algebra
- V 3951 or V 3952 Undergraduate Seminars in Mathematics

Courses in computer science:

- W 1004 Computer Science I (or AP credit)
- W 1007 Computer Science II
- W 3137 Data Structures and Algorithms
- W 3157 Computer Science III (Advanced Programming)
- W 3203 Discrete Mathematics
- W 3261 Computability and Models of Computation
- W 3827 Fundamentals of Computer Systems
- W 4231* Analysis of Algorithms I
- W 4241* Numerical Algorithms and Complexity I

*Electives--take two of four; in exceptional cases, other courses may be substituted with the approval of departmental representatives of both departments.

*Note A: *The Honors sequence also fulfills the MATH V 2010 Linear Algebra requirement.*Note B: *May substitute MATH V 3021 or BC 2006 or MATH V 1103.*Note C:* May substitute MATH V 2500, V 3007, V 4032, V 3386, or W 4051.

Students seeking to pursue a Ph.D. program in either discipline are urged to take additional courses, in consultation with their advisers.

**For a major in Economics and Mathematics, see the catalogue.**

**REQUIREMENTS FOR THE MINOR IN MATHEMATICS**

For a minor in Mathematics or Applied Mathematics: Six courses from any of the courses offered by the department except Math W 1003 College Algebra and Analytic Geometry, Math V 1101/2 Calculus I/II. Some cognate courses are also acceptable with prior approval from the department chair.

**REQUIREMENTS FOR THE MINOR IN MATHEMATICAL SCIENCES**

The minor in Mathematical Sciences comprises 6 courses, at least two from Mathematics and one from each of Statistics and Computer Science. There should be a minimum of three courses in Statistics and Computer Science. Eligible courses are any listed in the Mathematical Sciences Major with the exception of Calculus I and II.

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