## Overview

The combined 4+1 BA/MS or BS/MS in Mathematics program is designed to allowed for strong and motivated undergraduate students to complete a bachelor’s degree in mathematics and master’s of science degree in mathematics in a total of five year: the bachelor's degree (BA or BS) will be completed in four years, and the MS degree will be completed in one additional year. This program, as with the MS program, has two tracks:

*Theory track*: This track is oriented towards students who are interested in mathematics as an abstract discipline. These students may be considering a Ph.D. in mathematics or in a related discipline. Core coursework for this track includes fundamental topics in advanced abstract mathematics.*Industry track*: This track is designed for students who intend to use mathematics in engineering, computer science, medicine, business, industry, social science, or other fields. Core coursework for this track requires at least two courses from a field related to mathematics, such as computer science or engineering, which will help students see how advanced mathematics is used in practical contexts.

Each of these tracks will include a thesis option.

## Application Requirements

Mathematics majors can apply to the 4+1 program as early as the second semester of sophomore year, but no later than the summer before their senior year. Students interested in applying are should initiate a discussion with the undergraduate mathematics adviser, Joshua Himmelsbach (himmelsbach@cua.edu), as soon as possible.

For the application, standard university guidelines for eligibility will apply, in addition to the following:

- GPA of at least 3.25 in math courses or permission of the Graduate Committee
- Completion of Math 121 (Calculus I), Math 122 (Calculus II), Math 221 (Calulus III), and solid progress in, or completion of, Math 248 (Fundamentals of Advance Mathematics).
- At least one letter of recommendation from a math faculty
- A statement of purpose

The application must include a list of a maximum of four courses, approved by the math department, that may be taken for both undergraduate and graduate credit. Any subsequent changes in these designated courses will require departmental approval. In addition, courses for such "double" credit must be so designated before the beginning of the semester in which they are taken.

The application requires approvals from the mathematics department, the associate dean of graduate programs, and the associate dean for undergraduate programs. These approvals are subject to review of academic progress at the end of the junior year.

During the senior year, the student must complete an application for graduate studies. This application process is the same as for regular graduate applicants, with the exception of letters of recommendation (which are waived) and GRE results (which are waived). In the fifth year, the student must be registered as a graduate student in mathematics, indicating the chosen track in either theory or industry.

## Requirements and Coursework

The BA or BS in Mathematics requires 40 courses and the MS in Mathematics requires 10 courses. Students in the 4+1 program can take as many as four graduate courses in mathematics (with at most two from a related field) that will count towards both the BA (or BS) and the MS in Mathematics, enabling them to complete both degrees with as few as 46 courses total. Students who successfully complete the requirements of this 4+1 program will receive a BA (or BS) in Mathematics at the end of the fourth year, and an MS in Mathematics at the end of the fifth year.

Students in either the theory track or the industry track will have a thesis option. Specifically, they can complete the requirements of the program between their junior year and their fifth year by taking either 10 courses, or 8 courses plus two semesters of thesis work in their 5th year (under guidance of a math faculty).

### Requirements for the Theory Track

The theory track requires

- a graduate abstract algebra course,
- a graduate topology course,
- six mathematics electives (of which at most two can be approved courses in a related field), and
- two additional mathematics electives, which can be substituted if the thesis option is selected.

An example of a possible sequence of courses for the theory track is as follows:

*Year 1*: Math 121 (Calculus I), Math 122 (Calculus II)

*Year 2*: Math 221 (Calculus III), Math 222 (Differential Equations), Math 248 (Fundamentals of Advanced Mathematics)

*Year 3*: Math 301 (Linear Algebra), Math 321 (Abstract Algebra I), Math 506 (Abstract Algebra II), Undergrad math elective

*Year 4*: Math 421 (Introductory Analysis I), Math 520 (Topology), Math 524 (Complex Variables), Undergrad math elective

*Year 5*: Eight grad math electives OR six grad math electives and two semester of thesis work

**Requirements for the Industry Track**

The industry track requires

- a graduate statistics course,
- two approved graduate courses in a related field,
- five mathematics electives (of which at most two can be approved courses in a related field), and
- two additional mathematics electives, which can be substituted if the thesis option is selected.

An example of a possible sequence of courses for the theory track is as follows:

*Year 1*: Math 121 (Calculus I), Math 122 (Calculus II)

*Year 2*: Math 221 (Calculus III), Math 222 (Differential Equations), Math 248 (Fundamentals of Advanced Mathematics)

*Year 3*: Math 301 (Linear Algebra), Math 321 (Abstract Algebra I), Math 506 (Abstract Algebra II), Undergrad math elective

*Year 4*: Math 421 (Introductory Analysis I), Math 524 (Complex Variables), Math 531 (Probability and Statistics with Applications I), Math 532 (Probability and Statistics with Applications II), Undergrad math elective

*Year 5*: Six grad math electives and two grad non-math electives OR four grad math electives, two grad non-math electives, and two semester of thesis work