All three tracks (Standard, Pure Mathematics, and Secondary Teaching) include the calculus, bridge, fundamentals, and computer programming requirement. Additionally, all three tracks will result in the same math degree; the course sequences are what set them apart.

## 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.

## 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.

(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 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 sequence 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.

## Accelerated Master’s Program

The accelerated master’s program allows students to begin working toward a master’s degree in mathematics while still finishing a bachelor’s degree. This is informally known as a “4+1” program, meaning that it can allow you to complete a bachelor’s degree in four years and a master’s degree in one additional year.

The requirements for earning a master’s degree are as follows:

- Complete at least 45 credit hours in graduate‐level classes (500 and above), at least 30 of which are in math. You must have a GPA of 3.25 or better in all graduate classes, and 3.00 or better in all 600‐level graduate classes.
- Complete at least three of the sequences below, at least one of which is at the 600‐level:
- Math 513, 514, 515 (Introduction to Analysis)
- Math 531, 532, 533 (Intro to Topology & Intro to Differential Geometry)
- Math 544, 545, 546 (Introduction to Abstract Algebra)
- Math 647, 648, 649 (Abstract Algebra)
- Math 634, 635, 636 (Algebraic Topology)
- Math 637, 638, 639 (Differential Geometry)
- Math 616, 617, 618 (Real Analysis)
- Math 616, 672, 673 (Theory of Probability)
- Math 607, 607, 607 (Applied Mathematics)

Note that the 500‐level classes above are 4 credits each, while the 600‐level classes can be taken for either 4 credits or 5 credits each.

Starting at the time when you are formally enrolled in the accelerated master’s program (typically at the beginning of your fourth undergraduate year), you will be allowed to enroll in 500‐level and 600‐level classes and to count up to 16 credits from these classes simultaneously toward your bachelor’s degree and your master’s degree. For example, you would be allowed to take Math 513‐514‐515 in your last undergraduate year, count it toward the departmental and university requirements for a bachelor’s degree in math, and start your fifth year with one sequence and 12 graduate credits already completed.

### Course Prerequisites

If you are applying for the accelerated master’s program, you should make sure that you will have the prerequisites that you need for you to take the required sequences. For example, if you intend to take the Abstract Algebra sequence in your master’s year, then you should make sure that you are on track to complete the Introduction to Abstract Algebra sequence (at either the 400‐level or the 500‐level) by the end of your bachelor’s degree.

The Differential Geometry, Theory of Probability, and Applied math sequences are only offered every other year, so if you are interested in any of those sequences, you should be aware of the schedule.

### Application Requirements

You may apply for the accelerated master’s program at any time during your final year as a UO math major, or during the spring or summer before your final year as a UO math major. You must have:

- Completed 316‐317 or 391‐392 or 347‐348 or other math courses of comparable level of sophistication.
- A GPA of 3.0 or better in math classes at the 300‐level and above.
- A letter of support from one Math Department faculty member.

To apply, please email Graduate Coordinator, Amy Massoud, including your student ID number and the name of the faculty member who will be writing you a letter of support. Please ask that faculty member to email their letter to Amy Massoud, as well. Applications to enter the accelerated master’s program in the fall should be received by the end of July. Applications to enter the program in the winter or spring should be received by Week 5 of the preceding term.

To earn the Master’s degree, you must fulfill all of the course requirements and conditions, and meet with the chair of the Master's Degree Subcommittee before the end of the second week of the term the degree is to be received in order to verify that the requirements have been met.

For more information, view the Graduate Student Handbook.