Upper Division Requirement: 44 units

There are three different options within the mathematics major, and each student is required to complete the courses under one of them. The option that you choose should correspond to your interests and the use you plan to make of your major. You might also note that many courses are required for all three of the options, so that it is possible to delay choosing an option until well into your junior (or even senior) year.

Classes required for all options include: Introduction to Abstract Mathematics and Proofs (3000), Differential Equations (3331), Abstract Algebra I (3121), Analysis I (3300), and Linear Algebra (3100).

Two general recommendations are in order. First, the five courses above are basic to the major and should be taken early in upper division standing. Second, all majors need at least one of the sequences 3121-3122 and 3300-3301. The two parts of each sequence should be taken in consecutive quarters. This keeps basic material fresh in the mind, and also allows a better transition from one course to the next, with no overlaps or missing gaps. Note that courses required under any option can be used as electives in the other, so that you will probably not have any problems if you change your mind about the option you are working toward.

Each option requires upper division 44 units. The options do have a varying number of electives. In all cases, these can be chosen from the upper division mathematics courses, including the upper division cross-listed courses from Statistics and Computer Science. The exception is that they may not include Math 3898, 4021, 4022, 4023. Most electives are 4 unit courses; exceptions include Math 4900 and 4901.

Option A

This might be called the "general math" option. It is a good choice for many students. It includes sequences in what are sometimes thought of as the two most fundamental areas of mathematics, algebra and analysis. Those considering graduate school should definitely take both sequences, and may take this option.

Math 3000 Introduction to Abstract Mathematics and Proofs

Math 3331 Differential Equations

Math 3121-3122 Abstract Algebra, two course sequence

Math 3300-3301 Analysis, two course sequence

Math 3100 Linear Algebra

Sequence

One two-course sequence chosen from:

Math 3151-4151 Combinatorial Mathematics or

Math 3215-4215 Geometry or

Math 3361-4361 Differential equations or

Math 3750-4750 Numerical Analysis or

Math 3841-4841 Optimization

Electives

8 units of upper division mathematics courses.

Option B

Applied Mathematics. This option is aimed toward applications of mathematics. It is especially useful for students interested in scientific applications, computer science, or actuarial work.

Math 3000 Introduction to Abstract Mathematics and Proofs

Math 3331 Differential Equations

Math 3100 Linear Algebra

Math 3121 Abstract Algebra I

Math 3300 Analysis I

Math 3122 or Math 3301 Abstract Algebra II or Analysis II

Sequences

Two sequences chosen from

Math 3151-4151 Combinatorial Mathematics or

Math 3361-4361 Differential equations or

Math 3750-4750 Numerical Analysis or

Math 3841-4841 Optimization

Electives

4 units of upper division electives.

Option C

Mathematics Teaching. These courses include a wide background in mathematics, including its history. Many areas are represented; geometry and number theory are specifically required. These courses are chosen to prepare majors for careers in secondary school teaching. See section 3.3 which discusses the credential program.

Math 3000 Introduction to Abstract Mathematics and Proofs

Math 3331 Differential Equations

Math 3121 Abstract Algebra I

Math 3100 Linear Algebra

Math 3215 Geometry I

Math 3300 Analysis I

Math 3600 Number Theory

Math 4040 History of Mathematics

Stat 3401 Introduction to Probability Theory

Math 3122 or Math 3301 or Math 4215 Abstract Algebra II or Analysis II or Geometry II

Electives

4 units of upper division electives