# BA in Mathematics

Mathematics and statistics play a critical role in our efforts to understand the nature of the physical universe and in the continuing development of our technological society. Students majoring in mathematics and statistics gain skills related to abstract thinking and critical reasoning through courses across a variety of mathematical disciplines. Mathematicians and statisticians are in demand in all sectors of society, ranging from government to business and industry, to universities and research labs. Undergraduate training in mathematics and statistics also provides an excellent background for graduate study in these and related computational fields.

## Learning Outcomes

Students graduating with a major in Mathematics, Pure and Applied Track, will:

- Demonstrate a mature understanding of single and multivariable calculus up through and including differential equations and of linear algebra.
- Demonstrate a clear understanding of the concept of mathematical proof and be able to present a rigorous proof of basic theorems.
- Demonstrate depth of understanding of one of the core areas of pure or applied mathematics.

Students graduating with a major in Mathematics in the Statistics Track will:

- Understand fundamental concepts and develop analytical skills associated with classical statistical methods.
- Demonstrate a mature understanding of the theoretic underpinnings of statistics including probability theory, and at least one of the areas of mathematical statistics and stochastic processes.
- Demonstrate a breadth of knowledge in topics related to advanced statistical theory and practice.

## Requirements

All first-year, first-time students will pursue coursework in the BU Hub, a general education program that is integrated into the entire undergraduate experience. BU Hub requirements are flexible and can be satisfied in many different ways, through coursework in and beyond the major and, in some cases, through cocurricular activities. Students majoring in Mathematics will ordinarily, through coursework in the major, satisfy BU Hub requirements in Quantitative Reasoning. Remaining BU Hub requirements will be satisfied by selecting from a wide range of available courses outside the major or, in some cases, cocurricular experiences.

### Classification of Elementary Courses

For the purpose of stating prerequisites, elementary courses are grouped under the titles listed below. Any one course in a group satisfies a requirement, and only one course in each group may be taken for credit.

- Elementary Statistics I: CAS MA 113, 115, 213
- Elementary Statistics II: CAS MA 116, 214, 614
- Calculus I: CAS MA 121, 123
- Calculus II: CAS MA 122, 124, 127, 129 (MA 129
*may*be taken for credit by students with AP credit for CAS MA 124) - Multivariate Calculus: CAS MA 225, 230
- Differential Equations: CAS MA 226, 231
- Linear Algebra: CAS MA 142, 242, 442
- Discrete Math: CAS MA 193, 293
- Modern Algebra: CAS MA 294 (may not be taken after MA 541 or 542)

### Required Courses

Students majoring in mathematics must satisfy the sets of requirements for either the Specialty in Pure and Applied Mathematics or the Specialty in Statistics. Courses may be credited toward the major only if a grade of C or higher is earned. Unless otherwise noted, all courses are 4 credit hours.

### Specialty in Pure and Applied Mathematics

#### Lower Division Courses

- Calculus: CAS MA 123 and 124, or 127, or 129, or equivalent
- Multivariate calculus: CAS MA 225 or 230
- Elementary differential equations: CAS MA 226 or 231
- Linear algebra: CAS MA 242 or 442
- Introduction to computer science: CAS CS 111
- One additional mathematics or computer science course selected in consultation with a mathematics faculty advisor.

#### Upper Division Courses

At least one of the two following sequences:

- CAS MA 411, 412 Advanced Calculus and Complex Variables
- CAS MA 511, 512 Introduction to Analysis I & II

At least one of the following sequences:

- CAS MA 531, 532 Mathematical Logic and Foundations of Mathematics
- CAS MA 539, 555 Methods of Scientific Computing and Numerical Analysis I
- CAS MA 541, 542 Modern Algebra I & II
- CAS MA 555, 556 Numerical Analysis I & II
- CAS MA 561, 562 Methods of Applied Mathematics I & II
- CAS MA 563, 564 Introduction to Differential Geometry/Introduction to Topology
- CAS MA 565, 579 Mathematical Models in the Life Sciences and Numerical Methods for Biological Sciences
- CAS MA 569, 570 Optimization Methods of Operations Research and Stochastic Methods of Operations Research
- CAS MA 573, 579 Qualitative Theory of Ordinary Differential Equations and Numerical Methods for Biological Sciences
- CAS MA 581, 582, 583 Probability, Mathematical Statistics, and Introduction to Stochastic Processes (any two)

Four additional CAS mathematics courses numbered 200 or above are required. Two of these four can be related courses. For specific information concerning related courses, contact the department.

### Specialty in Statistics

#### Lower Division Courses

- Calculus: CAS MA 123 and 124, or 127, or 129, or equivalent
- Multivariate calculus: CAS MA 225 or 230
- Linear algebra: CAS MA 242 or 442
- Introduction to probability and statistics: CAS MA 213, 214
- Introduction to computer science: CAS CS 111.

#### Upper Division Courses

- CAS MA 416 Analysis of Variance
- CAS MA 575 Linear Models

Two of the following three courses:

- CAS MA 581 Probability
- CAS MA 582 Mathematical Statistics
- CAS MA 583 Introduction to Stochastic Processes

Four additional CAS mathematics courses are required: two at the 200 level or above, and two chosen from among MA 500–599 and GRS MA 684.

## Joint Programs with Other Departments/Schools

- BA in Economics & Mathematics
- BA in Economics & Mathematics/MA in Economics
- BA in Mathematics & Computer Science
- BA in Mathematics & Philosophy
- BA in Mathematics & Mathematics Education
- BA in Statistics & Computer Science

## Honors in the Major

Students may earn the distinction of departmental Honors in the Major by achieving a GPA of 3.3 or greater in their major courses and successfully completing a senior work-for-distinction research project under the supervision of a faculty member. This project culminates in a written thesis and oral defense before a committee of three faculty (including the project supervisor). Students may complete their thesis project as part of the CAS MA 401–402 honors thesis sequence. Qualified students interested in pursuing a work-for-distinction project should contact the director of undergraduate studies no later than the second semester of their junior year.