# Guide to the Math Major

This page gives the overall picture of the course offerings for the mathematics major. For the precise requirements for the major and minor, please see the Mathematics Section of the Catalog.

There is also a joint Math/Computer Science major (MACS). Information about this can be found in the MACS Section of the Catalog.

**Warning:** the information contained on this page is no substitute for consulting an official advisor in the department of mathematics!

## Major Requirements

### Calculus Requirement

Calculus is a core area of mathematics, and is a prerequisite for many courses required by the major. The major can be thought of as requiring a year of calculus at the outset (material prior to calculus must be made up first if it was not taken before entering the university). There are several calculus options open to potential math majors.

- Our standard sequence is Math 251-253 which emphasizes mathematical and physical applications of calculus.
- A similar option is Math 246-247-253, which emphasizes applications in the life sciences and is equivalent to 251-253 for purposes of math majors.
- Our calculus with theory sequence (Math 261-263) covers the same material as 251-253 and in addition covers the theoretical grounding of calculus (WHY things work the way they do rather than just HOW things work). Because of this, Math 261-262 satisfy the Bridge requirement and students who take Math 261-263 are exempt from the Fundamentals requirement for Math 316-317.

(Note that Math 241-242 is our calculus for business majors and does not satisfy the requirements for mathematics majors.)

### Bridge Requirement

Before taking most upper division courses, students are required to take courses that deal with some mathematical proof at an elementary level. In addition to this, students are required to take a selection of Math Lab courses (Math 201-206), which are two-credit courses focusing on mathematical problem solving, use of mathematical technology, and skills for communicating mathematics. There are no prerequisites for the Math Lab courses, and students are recommended to start taking them as soon as possible after they have decided to be a math major.

There are three options for meeting the Bridge Requirement:

- Math 307 and four Math Labs. The Math 307 course is an introduction to proof. The mathematical focus is typically problems from set theory, combinatorics, logic and discrete math although the real point of the course is giving students practice and feedback so that they can learn how to do mathematical proofs. The prerequisite is Math 252 or equivalent.
- Math 261-262 and two Math Labs. The Math 261-262 courses are the first two terms of our calculus with theory sequence (discussed briefly above). This includes not only the calculational techniques and applications of calculus, but also the theoretical underpinnings of the subject, and thus this course emphasizes proof.
- Math 231-232 and two Math Labs. The Math 231-232 sequence is two terms of discrete math. The sequence is essential for students with a computer science major, but the material is of interest for mathematics students as well.

### Fundamentals Requirement

All math majors must take a two-quarter upper division sequence that explores an area of proof-based mathematics in depth. There are three choices:

- Math 316-317: Fundamentals of Analysis. This sequence explores limits, continuity, and the other foundational ideas of calculus from a theoretical viewpoint. The prerequisite for 316 is Math 253 and the bridge requirement.
- Math 347-348: Fundamentals of Number Theory. This sequences explores the theory of prime numbers, modular arithmetic, and other topics from modern number theory. The prerequisite for Math 347 is Math 253 and the bridge requirement.
- Math 391-392: Fundamentals of Algebra. This sequence provides an introduction to groups, rings, and related notions from modern abstract algebra. The prerequisite for 391 is Math 341 and the bridge requirement.

Note that students are strongly advised to take their Fundamentals sequence very soon after satisfying the bridge requirement.

### Computer Science Requirement

All math majors must take a course on computer programming. This is because for most people wanting to get a job that uses mathematics, possession of some computer programming skills will be essential. CIS 122 satisfies this requirement, but almost any CIS course above 122 will also satisfy it; talk to a mathematics advisor to make sure.

### Tracks for the Math Major

There are three tracks: Standard, Pure Mathematics, and Secondary Teaching. Most students will do the Standard Track. The Pure Mathematics track is recommended for students who are considering graduate school in mathematics, and has a stronger focus on proof-based mathematics. The Secondary Teaching track is best for students who plan to teach math at the middle school level or higher.

Note that the track you choose does not show up on your diploma or transcript. At the end all tracks lead to the same math degree!

All the tracks include the calculus, bridge, fundamentals, and computer programming requirement. After that they differ.

### Standard Track

Here students must take the following two sequences:

- Math 281-282: Vector Calculus. This course concerns calculational techniques and applications of calculus generalized to functions with more than one variable. The prerequisite is Math 253 or equivalent.
- Math 341-342: Linear Algebra. This course is concerned with applications of groups of linear equations in more than one variable, vectors and vector spaces, matrices and matrix algebra, etc. The prerequisite is Math 252 or equivalent.

In addition, students will take four elective courses (including at least one two-term sequence) from our upper-division offerings.

### Pure Mathematics Track

Here students are required to take

- Math 281-282: Vector Calculus.
- Math 341-342: Linear Algebra.
- Math 316-17: Fundamentals of Analysis
- Math 391-392 or Math 444-445: Fundamentals of Algebra or Introduction to Abstract Algebra

In addition, students take two elective courses from our upper-division offerings.

### Secondary Teaching Track

Here students take:

- Math 281: First term of multivariable calculus. Prerequisite: Math 253 or equivalent.
- Math 341: First term of linear algebra. Prerequisite: Math 252 or equivalent.
- Math 394-395: Geometries from an Advanced Viewpoint. Prerequisite: Math 253 or equivalent and bridge requirement.
- Two sequences from Math 316-317, Math 347-348, and Math 391-392.
- Math 343: Statistical Models and Methods. Prerequisite: Math 252.
- Math 397: History and Applications of Calculus. Prerequisite: Math 252 and bridge requirement.