# Degree Requirements

The catalog is the document of record for major and program requirements. It is updated annually.

Students may follow the degree requirements from either the UCSC General Catalog published at the time of entering UCSC or subsequent catalog(s). Students need not follow a catalog in its entirety, but may elect to follow different catalog years for their college requirements, university and general education requirements, the requirements of their major(s), and the requirements of any minor(s). The catalog year will initially be set for the first year of enrollment at UCSC. Students may elect to follow major or minor requirements from other catalog years(s) when filing the Petition for Declaration of Major/Minor.

Following are excerpts of degree requirements from the current year catalog (18-19):

- Pure Mathematics B.A.
- Computational Mathematics B.A.
- Mathematics Education B.A.
- Mathematics Subject Matter Program
- Mathematics Minor
- Economics/Mathematics Combined Major

Archive of Previous Years' General Catalogs

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## Pure Mathematics BA: Major Requirements

INTRODUCTORY REQUIREMENTS: 6 total

Students may only declare once they have passed all introductory courses or their equivalent courses with a grade of C or better. Students who receive two grades of NP, D, or F in the introductory courses are not eligible to declare in the major or minor. Students who are not eligible to declare may appeal.

Calculus: MATH 19A + 19B OR MATH 20A + 20B

Linear Algebra: MATH 21

Vector Calculus: MATH 23A + MATH 23B

Intro to Proof & Problem Solving: MATH 100

ADVANCED REQUIREMENTS: 9 total

Core Math:

MATH 24: Ordinary Differential Equations

MATH 103A Complex Analysis

MATH 105A Real Analysis

MATH 111A Algebra

MATH 117 Advanced Linear Algebra

Geometry: ONE of the following.

MATH 121A Differential Geometry

MATH 124 Introduction to Topology

MATH 128A Classical Geometry: Euclidian & Non-Euclidian

MATH 129 Algebraic Geometry

Electives: THREE of the following.

Any MATH course numbered above 100 (excluding MATH 188 or 189) One of your electives may be an AMS course (100 or above)

Comprehensive: MATH 194 Senior Seminar OR MATH 195 Senior Thesis

Disciplinary Communication Requirement (DC): Students satisfy this requirement by successfully completing courses MATH 100 and either MATH 194 or MATH 195. The DC course requirement must be taken at UCSC

In addition to the major requirements, students are encouraged to take as many mathematics courses as possible. Completion of a full analysis sequence with MATH 105B and full algebra sequence with MATH 111B are highly recommended. Students are also invited to enroll in graduate courses, provided course prerequisites are met and students have the necessary background.

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## Computational Mathematics BA: Major Requirements

INTRODUCTORY REQUIREMENTS: 6 total

Students may only declare once they have passed all introductory courses or their equivalent courses with a grade of C or better. Students who receive two grades of NP, D, or F in the introductory courses are not eligible to declare in the major or minor. Students who are not eligible to declare may appeal.

Calculus: MATH 19A + 19B OR MATH 20A + 20B

Linear Algebra: MATH 21

Vector Calculus: MATH 23A + MATH 23B

Intro to Proof & Problem Solving: MATH 100

ADVANCED REQUIREMENTS: 9 total

Math: MATH 24 Ordinary Differential Equations

MATH 110 Introduction to Number Theory

MATH 111A Algebra OR MATH 117 Advanced Linear Algebra

Differential Equations: ONE of the following.

MATH 106 Systems of Ordinary Differential Equations

MATH 107 Partial Differential Equations

Analysis: ONE of the following.

MATH 103A Complex Analysis

MATH 105A Real Analysis

Computational: ONE of the following.

MATH 145/L Introduction to Chaos & Lab

MATH 148/L Numerical Analysis

AMS 114 Introduction to Dynamical Systems

AMS 147 Computational Methods and Applications

Electives: TWO of the following.

Any AMS course numbered 100 and aboveBME 110 Computational Biology Tools

CMPE 107 Probability and Statistics for Engineers

CMPE 108 Data Compression

CMPE 153 Digital Signal Processing

CMPE 177 Applied Graph Theory & Algorithms

CMPS 101 Algorithms & Abstract Data Types

CMPS 102 Introduction to Analysis of Algorithms

CMPS 104A Fundamental of Compiler Design I

CMPS 109 Advanced Programming

CMPS 112 Comparative Programming Languages

CMPS 130 Computational Models

CMPS 132 Computability & Computational Complexity

CMPS 142 Machine Learning & Data Mining

EART 172 Geophysical Fluid Dynamics

ECON 113 Introduction to Statistics & Econometrics

EE 103 Signals & Systems

EE 130 Introduction to Optoelectronics & Photonics w/lab

EE 135/L Electromagnetic Fields & Waves w/lab

EE 151 Communications Systems

EE 154 Feedback Control Systems

Math 115 Graph Theory

Math 116 Combinatorics

Math 120 Coding Theory

Math 134 Cryptography

Math 145/L Introduction to Chaos & Lab

Math 148 Numberical Analysis

Math 152 Programming for Mathematics

Math 160 Mathematical Logic

PHYS 107 Fluid Dynamics

PHYS 115 Computational Physics

Comprehensive: MATH 194 Senior Seminar OR MATH 195 Senior Thesis

Disciplinary Communication Requirement (DC): Students satisfy this requirement by successfully completing courses MATH 100 and either MATH 194 or MATH 195. The DC course requirement must be taken at UCSC.

In addition to the major requirements, students are encouraged to take any additional Mathematics and Engineering courses that are of interest. If students plan to apply to graduate work in Mathematics, they should complete Math 103A and 105A along with Math 111A and Math 117 thereby satisfying both the "Pure" and "Computational" concentrations. Students are also invited to enroll in graduate courses, provided course prerequisites are met and students have the necessary background.

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## Mathematics Education BA: Major Requirements

INTRODUCTORY REQUIREMENTS:

Students may only declare once they have passed all introductory courses or their equivalent courses with a grade of C or better. Students who receive two grades of NP, D, or F in the introductory courses are not eligible to declare in the major or minor. Students who are not eligible to declare may appeal.

Calculus: MATH 19A + 19B OR MATH 20A + 20B

Linear Algebra: MATH 21

Vector Calculus: MATH 23A + MATH 23B

Intro to Proof & Problem Solving: MATH 100

ADVANCED REQUIREMENTS: 9 total

Math:

MATH 110 Introduction to Number Theory

MATH 111A Algebra

MATH 128A Classical Geometry: Euclidian & Non-Euclidian

MATH 181 History of Mathematics

MATH 188, Supervised Teaching Experience; or Education 50B, CalTeach 1: Mathematics, plus Education 100B, CalTeach 2: Mathematics

AMS 5 Statistics

AMS 131 Introduction to Probability Theory

Analysis: ONE of the following.

MATH 103A Complex Analysis

MATH 105A Real Analysis

Comprehensive: MATH 194 Senior Seminar OR MATH 195 Senior Thesis

Disciplinary Communication Requirement (DC): Students satisfy this requirement by successfully completing courses MATH 100 and either MATH 194 or MATH 195. The DC course requirement must be taken at UCSC

*In addition to the major requirements, students may wish to augment their program with courses that satisfy the Subject Matter Program if they wish to bypass the CSET series of exams before entering a California teaching credential program. These courses include the more advanced theoretical courses MATH 24 Ordinary Differential Equations, Math 101 Mathematical Problem Solving, Math 115 Graph Theory, or CMPE 16 Applied Discrete Mathematics. In particular, Math 101 includes material very helpful to teachers. Students may also wish to complete both 103A Complex Analysis and 105A Real Analysis, if there is a chance of returning to school later for a Master's or Ph.D. degree program.

Students considering a teaching career should contact the Education Department. The Education Department offers an undergraduate minor in education and a Single Subject Math credential at the graduate level.

Mathematics Subject Matter Program (Optional)

Listed below are the courses (or alternatives) in addition to the Mathematics Education BA requirements, you must take if you want to bypass the CSET series of exams before entering a California teaching credential program. Equivalents from other institutions are accepted on approval from the Mathematics Department.

Education: Educ 185B Introduction to Math Education

Additional Math: ONE from the following...

Math 24 Ordinary Differential Equations

Math 101 Mathematical Problem Solving

Math 115 Graph Theory

CMPE 16 Applied Discrete Mathematics

Computer Science: ONE from the following

CMPS 10 Introduction to Computer Science

CMPS 5C Introduction to Programming in C/C++

CMPS 5J Introduction to Programming in Java

CMPS 5P Introduction to Programming in Python

# Mathematics Minor Requirements

INTRODUCTORY REQUIREMENTS:

Calculus: MATH 19A + 19B OR MATH 20A + 20B

Linear Algebra: MATH 21

Vector Calculus: MATH 23A + 23B

Introduction to Proof and Problem Solving: MATH 100

ADVANCED REQUIREMENTS:

FOUR MATH courses numbered 100 and above. One course may be from AMS numbered above 100.