# 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 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 breadth of understanding of the core areas of pure mathematics.

Students graduating with a major in Mathematics, 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 a variety of techniques used in modern applied mathematics.
- Demonstrate depth of understanding of two core areas of applied mathematics.

Students graduating with a major in Mathematics, 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 BU undergraduate students, including both entering first-year and transfer students, will pursue coursework in the BU Hub, the University’s general education program that is integrated into the entire undergraduate experience. BU Hub requirements can be satisfied in a number of ways, including coursework in and beyond the major as well as 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 Mathematics, the Specialty in 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 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

- CAS MA 511, Introduction to Analysis I
- CAS MA 541, Modern Algebra I
- CAS MA 412, Complex Variables
- Five additional CAS MA courses numbered 200 or above. At least two of these must be numbered 500 or above.

Due to its similarity with MA 511, Advanced Calculus, MA 411, may not be used to satisfy any of the requirements of this track. Students wishing to pursue a PhD in Mathematics after completion of their undergraduate degree are strongly encouraged to take as two of their electives MA 512 and MA 542, as well as additional courses numbered 500 or above.

### Specialty in 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

- Students are required to choose two of the following five focus areas and take at least two courses within each focus area (4 courses total):
- Mathematical analysis: CAS MA 411, CAS MA 412, CAS MA 511, CAS MA 512. Students can use only one of CAS MA 411 and CAS MA 511 to satisfy this focus area requirement.
- Mathematical methods in the biological/life sciences: CAS MA 565, CAS MA 573, CAS MA 579.
- Mathematical modeling and analysis in the physical sciences: CAS MA 561, CAS MA 562, CAS MA 573.
- Numerical analysis and methods of computational mathematics: CAS MA 539, CAS MA 555, CAS MA 556, CAS MA 589.
- Probability and mathematical statistics: CAS MA 581, CAS MA 582, CAS MA 583.

- Four additional courses numbered 200 or above. At least one of these must be numbered 500 or above.

Students can use at most one of CAS MA 411 and CAS MA 511 to fulfill the requirements of this specialty. Students planning to go to graduate school in a related field are strongly encouraged to take CAS MA 412, CAS MA 511, and CAS MA 512, as well as a numerics course. A major advisor can approve one roughly equivalent upper-level course, either inside or outside the Department of Mathematics & Statistics, as a substitute for one of the courses in one focus area. The Probability and Mathematical Statistics track is meant for students working in mathematics and related applied fields who are looking to use the fundamental tools of probability and statistics in their field of study. Students who plan to pursue graduate study or a career in statistics should, in consultation with their major advisor, consider pursuing the Specialty in Statistics.

### 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.