## Mathematics Major Requirements

**The following courses are required for the major in mathematics.****By the time of Moderation**:

- Mathematics 141, Calculus I
- Mathematics 142, Calculus II
- Mathematics 242, Linear Algebra
- Mathematics 261, Proofs and Fundamentals

**By the time of graduation:**

- Mathematics 141, Calculus I
- Mathematics 142, Calculus II
- Mathematics 242, Linear Algebra
- Mathematics 255, Vector Calculus
- Mathematics 261, Proofs and Fundamentals
- Mathematics 331, Abstract Linear Algebra, OR Mathematics 332, Abstract Algebra
- Mathematics 361, Real Analysis
- Two elective mathematics courses numbered 300 or above
- Computer Science 141, Object-Oriented Programming, OR Computer Science 143, Object-Oriented Programming with Robots, OR another programming-based computer science course with approval of the Mathematics Program, preferably before beginning the Senior Project

**Substitutions:**

- Physics 221, Mathematical Methods I, taken alone, can substitute for Mathematics 255, Vector Calculus
- Physics 221, Mathematical Methods I, and Physics 222, Mathematical Methods II, taken together, can substitute for both Mathematics 242, Linear Algebra, and Mathematics 255, Vector Calculus

**Placing out of required courses:**

- Students who place out of some of the courses required for the mathematics major must take a minimum of eight college mathematics courses at the level of calculus or higher

**Additional requirements:**

- Moderation into the Mathematics Program
- A Senior Project in Mathematics
- First-Year Seminar and the college-wide distribution requirements

## Moderation Procedure

- Students in the Mathematics Program are expected to follow the standard Bard College procedure for Moderation (PDF).
- Students moderating into the Mathematics Program must demonstrate a basic knowledge of LaTeX by submitting a page or two of mathematics written in LaTeX. Students determine the content of these pages; homework from a course or material learned from a mathematics text are possibilities.

## Senior Project

Titles of all recent Senior Projects in mathematics, and PDF copies of some of them, may be found on the Student Research page.

Please review the Bard College Senior Project Preparation and Presentation Guidelines.

During the course of writing a Senior Project in mathematics, the student must:

- Give a brief prospectus talk describing the project in the first semester of their Senior Project (12 minute presentation).
- Submit a short write-up toward the end of the first semester (10 pages, written in LaTeX using the Bard Senior Project style file.)
- Have a midway Senior Project board at the start of the second semester.
- Have a final Senior Project board after the project is completed; the board commences with a 20-minute presentation that is open to the public.
- Participate in the Division of Science, Mathematics, and Computing Senior Project Poster Session.

## Mathematics Second Focus Requirements

**The following courses are required for the second focus in mathematics.**

- Mathematics 141, Calculus I
- Mathematics 142, Calculus II
- Mathematics 242, Linear Algebra
- Mathematics 255, Vector Calculus
- Mathematics 261, Proofs and Fundamentals
- One elective mathematics course numbered 300 or above, excluding courses offered by other programs that are cross-listed with mathematics

**Substitutions:**

- Physics 221, Mathematical Methods I, taken alone, can substitute for Mathematics 255, Vector Calculus
- Physics 221, Mathematical Methods I, and Physics 222, Mathematical Methods II, taken together, can substitute for both Mathematics 242, Linear Algebra, and Mathematics 255, Vector Calculus

**Placing out of required courses:**

- Students who place out of some of the courses required for the mathematics second focus must take a minimum of five college mathematics courses at the level of calculus or higher

## Interested in Studying Mathematics and Another Field?

Students who are interested in pursuing studies in mathematics in addition to another discipline have four options. For most students, the first two options are preferable.

## Interested in Studying Mathematics and Another Field?

**A) Single Major — major in mathematics, and take a lot of courses in another area of study:** This option is the easiest, because it requires no special Moderation or approval, and is often quite satisfactory. For example, a student might major in mathematics and take a lot of courses in economics; doing so is usually sufficient for acceptance to graduate schools in economics.

**B) Single Major with Concentration — major in mathematics and concentrate in another area of study:** This option is applicable only with those concentrations offered at Bard that can be effectively combined with mathematics. For example, a student might major in mathematics and concentrate in cognitive science.

**C) Double Major — major in mathematics and major in another program with separate Senior Projects: **In this option a student separately completes all the requirements for each of mathematics and the other program, including two Moderations and two Senior Projects. For example, a student might major in mathematics and in literature. The advantage of this option is that there need not be any relation between the two majors. The disadvantage of this option is the burden of writing two Senior Projects. To double major in mathematics and in another program, the two Senior Projects may not overlap, and hence one Senior Project must be done in the junior year, which is not always feasible.

**D) Joint Major — major in mathematics and major in another program with a single combined Senior Project:** In this option a student completes all the requirements for each of mathematics and the other program, including two Moderations, but completes a single Senior Project that contains sufficient work in both disciplines to be considered a Senior Project in each. For example, a student might jointly major in mathematics and physics. If at the end of a joint Senior Project the advisers decide that the project involves substantial work in only one of the disciplines, then the student will graduate as a single major in that program. At any time during the writing of the joint Senior Project, the student may elect to continue as a single major in either program with the consent of the advisers.

Joint majors are reserved for very strong students who have found advisers in each of mathematics and the other program who are willing to supervise the project jointly, and who have been approved to do a joint major by both the Mathematics Program and the Faculty Executive Committee. Additionally, a GPA of 3.5 or higher in the courses in each of mathematics and in the other program is required for approval by the Mathematics Program. Simply moderating into mathematics and another program does not automatically make a student eligible for a joint major.

A moderated student who wishes to do a joint Senior Project combining mathematics and another program must do the following: First, in the semester prior to the start of the Senior Project, the student must find an adviser in each of mathematics and the other program who are willing to supervise a project jointly. Second, the student must have a meeting with the two prospective advisers to formulate a plan for a joint Senior Project. Third, the student must submit a proposal to do a joint Senior Project to the chair of the Mathematics Program by November 27 for Senior Projects to begin the following spring, and by April 27 for Senior Projects to begin the following fall; the proposal should include the names of the proposed advisers, a description of the proposed topic, and a discussion of how the topic relates to both mathematics and the other program. If the Mathematics Program approves the proposal, it must then be sent to the Faculty Executive Committee for approval by the beginning of the first semester of the project (typically the fall semester).