What Are the Math Major Requirements at UCSD?

The University of California San Diego (UCSD) is a public research university in San Diego, California.

It's part of the University of California System and offers several undergraduate and graduate degrees.

One of those degrees is a bachelor's degree in mathematics.

This degree is offered through the Department of Mathematics and has several requirements students need to fulfill.

Keep reading to learn about the UCSD math major requirements.

What are the UCSD Math Major Requirements for Admissions?

There are no unique requirements for admission to the Department of Mathematics at UCSD.

Students must instead meet the requirements set by the university.

To be accepted as a first-year student at UCSD, you'll need to:

• Have completed the necessary high school courses
• Have a GPA of at least 3.0 if you're a California resident or a GPA of at least 3.4 if you're a non-resident
• Answer personal insight questions on your application

The university does not consider SAT or ACT scores in admissions.

In the fall of 2022, UCSD accepted 24% of undergraduate applicants.

What are the UCSD Math Major Course Requirements?

The math major at UCSD requires a total of 14 major courses in addition to general education courses.

One lower division course is required in either linear algebra, which is the study of linear equations, vectors, and matrices, or calculus, which is the study of continuous change.

At the upper-division level, all math major students are required to take Mathematical Reasoning, which introduces rigorous mathematical proof with an emphasis on:

• Quantifiers
• Induction
• Negation
• Proof by contradiction
• Naive set theory
• Equivalence relations
• Epsilon-delta proofs

Analysis Courses

Students must also choose between two sequences: two Foundations of Real Analysis Courses or two Introduction to Analysis courses and Elements of Complex Analysis.

The first Foundations of Real Analysis course covers topics like the real number system, basic topology, numerical sequences and series, and continuity.

The second covers topics like differentiation, the Riemann-Stieltjes integral, sequences and series of functions, power series, Fourier series, and special functions.

Introduction to Analysis covers topics like the real number system, numerical sequences and series, infinite limits, limits of functions, continuity, and differentiation in the first course.

The second course focuses on the Riemann integral, sequences and series of functions, uniform convergence, Taylor series, and introduction to analysis in several variables.

The program recommends that students who want to pursue graduate school take the Foundations of Real Analysis courses, including the third course in that series, though the third course is not required for graduation.

Algebra Courses

Students in the math major are also required to choose from two algebra sequences: two Abstract Algebra courses or two Modern Algebra courses and the Applied Linear Algebra course.

In the first Abstract Algebra course, students will cover topics like:

• Rings and ideals
• Unique factorization
• Fields

Students will also cover linear algebra from the perspective of linear transformations on vector spaces, including inner product spaces, determinants, and diagonalization

The second course covers linear transformations, including Jordan's canonical form and rational canonical form, as well as Galois's theory, including the unsolvability of the quintic.

The first Modern Algebra course introduces abstract algebra with an emphasis on group theory.

It covers topics like definitions and basic properties of groups, properties of isomorphisms, and subgroups.

In the second Modern Algebra course, students learn the definitions and basic properties of rings, fields, ideals, homomorphisms, and the irreducibility of polynomials.

The Applied Linear Algebra course continues where the required lower-level linear algebra course left off, covering things like:

• Elementary Hermitian matrices
• Schur's theorem
• Normal matrices
• Quadratic forms
• Moore-Penrose generalized inverse and least square problems
• Vectors and matrices

Elective Courses

Once students have taken the required courses and course sequences, they can fulfill the remainder of their 14 courses with upper-division mathematics electives.

Students can choose from nearly any upper-division bachelor's course. These courses focus on subjects such as:

• Computer graphics
• Differential equations
• Discrete mathematics
• Graph theory
• Mathematical biology
• Mathematical modeling
• Mathematical software
• Mathematical statistics
• Numerical analysis
• Teaching mathematics

When choosing electives, students should pick courses that correspond with their intended career path.

For example, someone looking to become a math teacher should choose courses on teaching mathematics.

General Education Courses

All students at UCSD, regardless of their major, are required to fulfill general education courses.

These are often completed during the student's first two years before they fully dive into their major.

The John Muir College at UCSD, which houses the Department of Mathematics, requires students to fulfill the following general education courses:

• Three writing courses
• Three courses in social sciences
• Three courses in mathematics or natural science
• Six courses in fine arts, humanities, or foreign language

Students in the math major can use the mathematics or natural science requirement to fulfill the calculus or linear algebra course required for the major.

Earn a Math Degree at UCSD

The UCSD math degree includes several core math requirements but also allows students to choose math electives.

To learn more about the math major at UCSD, reach out to Learn.org today.