Mathematics B.A.

Information and Policies

Introduction

The mathematics program provides an excellent liberal arts background from which to pursue a variety of career opportunities. UCSC graduates with degrees in mathematics hold teaching posts at all levels, as well as positions in law, government, civil service, insurance, software development, business, banking, actuarial science, forensics, and other professions where skills in logic, numerical analysis, and computing are required. In particular, students of mathematics are trained in the art of problem-solving, an essential skill in all professions.

Within the major, there are three concentrations leading to the Bachelor of Arts (B.A.) in mathematics: pure mathematics, computational mathematics, and mathematics education. 

Pure Mathematics

Students in the pure mathematics track often go on to graduate study in mathematics; the pathway emphasizes the importance of a well-rounded, in-depth mathematical education, and includes advanced coursework in algebra, analysis, and geometry.

Computational Mathematics

Students in the computational mathematics track explore applications of mathematics in other fields and gain experience in mathematical modeling of real-world phenomena using ordinary and partial differential equations, approximation and optimization techniques, programming, or game theory.

Mathematics Education

Students in the mathematics education track prepare for a career in K–12 mathematics education; students acquire in-depth knowledge of subjects covered at an introductory level in the classroom, including number theory, classical geometry, and the history of mathematics, and gain experience in teaching mathematics.

These programs are designed to give students a strong background for graduate study, for work in industry or government, or for teaching. Each concentration requires nine or ten courses, one of which must be a senior thesis or senior seminar. Please read the pure mathematics, computational mathematics, and mathematics education program descriptions below for specific information about course requirements. A minor in mathematics is also offered.

Academic Advising for the Program

The undergraduate adviser may be contacted via email at mathadvising@ucsc.edu. The adviser provides information about requirements, prerequisites, policies and procedures, learning support, scholarships, and special opportunities for undergraduate research. In addition, the adviser assists with the drafting of study plans, as well as certifying degrees and minors. Students are urged to stay informed and involved with their major, as well as to seek advice should problems arise.

The Mathematics Department website is a critical resource for students. Here you will find a link to the undergraduate program; the materials at that link constitute the undergraduate handbook. Students should visit this first to seek answers to their questions, because it hosts a wealth of information. Each student in the major is encouraged to regularly review the materials posted to stay current with requirements, course curriculum, and departmental policy. Transfer students should consult the Transfer Information and Policy section. 

 

Getting Started in the Major

It should be emphasized that the nature of mathematics changes dramatically between lower-division and upper-division courses. Students often find that the material becomes far more abstract and theoretical. In addition, the role of computation in assignments diminishes and a greater weight is placed on deductive reasoning and the integral role of mathematical proofs. The Mathematics Department recommends that students interested in a mathematics major enroll in MATH 100 as early as prerequisites allow in order to decide whether they are interested in upper-division mathematics courses. It is strongly recommended that only students who earn grades of B- or better in MATH 100 consider applying to the major in mathematics. Students with a grade less than B in MATH 100 are urged to take MATH 101.

Program Learning Outcomes

Learning outcomes summarize the most important knowledge, skills, abilities and attitudes that students are expected to develop over the course of their studies. The program learning outcomes clearly communicate the faculty’s expectations to students, provide a framework for faculty evaluation of the curriculum based on empirical data, and help improve and measure the impact of implemented changes.

Mathematics Undergraduate Student Learning Objectives

The mathematics program promotes mathematical skills and knowledge for their intrinsic beauty, effectiveness in developing proficiency in analytical reasoning, and utility in modeling and solving real world problems. To responsibly live within and participate in the transformation of a rapidly changing, complex, and interdependent society, toward a sustainable and socially just society, students must develop and unceasingly exercise their analytical abilities. Students who have learned to logically question assertions, recognize patterns, and can distinguish the essential from the irrelevant aspects of problems can think deeply and precisely. Students equipped with these skills will be in a position to help solve the "big" problems of our time such as climate change. 

Students majoring in mathematics attain proficiency in:

Critical thinking. The ability to identify, reflect upon, evaluate, integrate, and apply different types of information and knowledge to form independent judgments including analytical and logical thinking and the habit of drawing conclusions based on quantitative information.

Problem solving. The ability to assess and interpret complex situations, choose among several potentially appropriate mathematical methods of solution, persist in the face of difficulty, and present full and cogent solutions that include appropriate justification for their reasoning.

Effective communication. The ability to communicate and interact effectively with different audiences, collaborate intellectually and creatively in diverse contexts, and appreciate ambiguity and nuance, while emphasizing the importance of clarity and precision in communication and reasoning.

Students acquire and enhance these abilities in mathematical contexts, but the acquired habits of rigorous thought and creative problem solving are invaluable in all aspects of life. These skills are acquired through experience in the context of studying specific mathematical topics and exploring problems chosen to challenge students’ abilities, spurring them on to acquire new techniques and to abandon familiar but restrictive habits of thought. The overarching objectives can be realized in terms of more focused, appraisable objectives specific to mathematics described on the Mathematics Department website.

Curriculum Matrix

All of the key objectives are addressed to some extent in all courses. For example, the ability to formulate precise mathematical statements and to reason logically are essential skills that are progressively developed throughout the curriculum. However, some skills are more heavily emphasized and utilized in some courses than in others. Some courses are specifically intended to help students move to a new level of proficiency with a particular portfolio of skills, while others are accessible only to students who have already reached a given level; the latter courses make heavy use of particular skills, and thus enhance and reinforce the student’s mastery of them, but the skills themselves are not the primary focus of such courses. Some connections between the key objectives, main subject-specific areas, and courses are indicated in the tables of lower- and upper-division mathematics courses at the Mathematics Department’s website.

Major Qualification Policy and Declaration Process

While enrolled in or after finishing the final required qualification courses a student should follow the directions to apply on the Mathematics Department Major Declaration webpage.

Major Qualification

Admission to the mathematics major (all concentrations) is contingent on students successfully passing the following introductory courses or their equivalents:

Choose one of the following courses:
MATH 19ACalculus for Science, Engineering, and Mathematics

5

MATH 20AHonors Calculus

5

Plus one of the following courses:
MATH 19BCalculus for Science, Engineering, and Mathematics

5

MATH 20BHonors Calculus

5

Plus all of the following courses:
MATH 21Linear Algebra

5

MATH 23AVector Calculus

5

MATH 23BVector Calculus

5

MATH 100Introduction to Proof and Problem Solving

5

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, C-, D+, D, D-, or F in the introductory courses are not eligible to declare in the major. 

Appeal Process

Students who are not eligible to declare may submit an appeal to the department's undergraduate vice chair. Students are strongly encouraged to file an appeal as soon as a student is no longer qualified to declare. The mathematics adviser will subsequently notify the student, and their college, of the decision, no later than 15 business days after the submission of the appeal. An appeal decision may be in the form of an approval, denial or conditional approval. For students who have not completed all of the major qualification courses, conditional approvals are based on subsequent performance in the remainder of the qualification courses.

How to Declare a Major

See the Mathematics Department website for directions on How to Declare the Major.

Transfer Information and Policy

Transfer Admissions Screening Policy

The Mathematics Department welcomes applications from transfer students who have completed the necessary coursework to transfer to our program.

To be considered for admission to UCSC as a participant in any of the mathematics majors, transfer students must pass equivalents of the following courses:

MATH 19ACalculus for Science, Engineering, and Mathematics

5

MATH 19BCalculus for Science, Engineering, and Mathematics

5

MATH 21Linear Algebra

5

MATH 23AVector Calculus

5

The above major preparation courses are highly recommended, and will be required beginning with applications to transfer in Fall 2020. More information about qualifying for the major as a transfer applicant is at the admissions website.

Students planning to transfer to UC Santa Cruz from a California community college should reference the assist website to determine which courses are equivalent to these required courses.

To obtain equivalency for MATH 23A, transfer students will have taken a course that may also be equivalent to MATH 23B. Students are encouraged to contact the undergraduate adviser to determine if this applies to their situation.

 

Getting Started at UCSC as a Transfer Student

While enrolled in or after finishing the final required qualification courses, a student should follow the directions to apply to declare the major on the Mathematics Department Major Declaration webpage.

Letter Grade Policy

There are no restrictions on grading options for Mathematics Department courses. Please see the UCSC-wide policies on grading options.

Course Substitution Policy

The Mathematics Department undergraduate vice chair reviews requests for course substitutions. Email mathadvising@ucsc.edu to request a course substitution review. 

Honors

Honors in the Mathematics Department are awarded to graduating students whose academic performance in the major demonstrates excellence at a GPA of 3.5 or above. Highest honors are determined by a cumulative review of student performance in mathematics courses. They are awarded to students who excel in challenging courses and in their capstone projects.

Pure Mathematics Concentration

This concentration is intended for students who desire a comprehensive understanding of mathematics, including those considering graduate studies in the physical sciences.

Course Requirements

Lower-Division Courses

Choose one of the following courses:
MATH 19ACalculus for Science, Engineering, and Mathematics

5

MATH 20AHonors Calculus

5

Plus one of the following courses:
MATH 19BCalculus for Science, Engineering, and Mathematics

5

MATH 20BHonors Calculus

5

Plus all of the following courses:
MATH 21Linear Algebra

5

MATH 23AVector Calculus

5

MATH 23BVector Calculus

5

MATH 24Ordinary Differential Equations

5

Upper-Division Courses

All of the following courses:
MATH 100Introduction to Proof and Problem Solving

5

MATH 103AComplex Analysis

5

MATH 105AReal Analysis

5

MATH 117Advanced Linear Algebra

5

Plus one of the following courses:
MATH 111AAlgebra

5

MATH 111TAlgebra

5

Plus one of the following courses:
MATH 121ADifferential Geometry

5

MATH 124Introduction to Topology

5

MATH 128AClassical Geometry: Euclidean and Non-Euclidean

5

MATH 129Algebraic Geometry

5

Plus one of the following courses:
MATH 194Senior Seminar

5

MATH 195Senior Thesis

5

Electives

The remaining three courses are selected by the student from among any mathematics course numbered above 100 (excluding Mathematics 188 and Mathematics 189) and Applied Mathematics (AM) or Statistics (STAT) 100 or above. Only one of the three courses can be from the AM or STAT series.

Disciplinary Communication (DC) Requirement

Students of every major must satisfy that major’s upper-division Disciplinary Communication (DC) requirement. The DC requirement in mathematics is satisfied by

MATH 100Introduction to Proof and Problem Solving

5

Plus one of the following courses:
MATH 194Senior Seminar

5

MATH 195Senior Thesis

5

Comprehensive Requirement

The comprehensive exit requirement in mathematics is satisfied by one of the following courses:

MATH 194Senior Seminar

5

MATH 195Senior Thesis

5

Planners

Pure Mathematics B.A.: Sample Freshmen Academic Plan

  Fall Winter Spring
1st (frosh) MATH 19A
or MATH 20A
MATH 19B
or MATH 20B
MATH 21
    MATH 23A
     
2nd (soph) MATH 23B MATH 103A Elective
MATH 100    
     
3rd (junior) MATH 24 MATH 105A Elective
    MATH 128A
     
 4th (senior) MATH 117 MATH 111A MATH 194
or MATH 195
    Elective
     

This course plan satisfies the MF general education requirement. Students must satisfy all other general education requirements.

Pure Mathematics B.A.: Sample Transfer Academic Plan

For students who have completed MATH 19A, MATH 19B, MATH 21, and MATH 23A equivalents.

  Fall Winter Spring
1st (junior) MATH 23B MATH 103A MATH 121A
MATH 100 Elective  Elective
     
2nd (senior) MATH 24 MATH 105A MATH 194
or MATH 195
MATH 111A Elective MATH 117
     

Computational Mathematics Concentration

This concentration is intended to prepare students for technical careers in industry or government while providing a solid mathematical background.

Course Requirements

Lower-Division Courses

Choose one of the following courses:
MATH 19ACalculus for Science, Engineering, and Mathematics

5

MATH 20AHonors Calculus

5

Plus one of the following courses:
MATH 19BCalculus for Science, Engineering, and Mathematics

5

MATH 20BHonors Calculus

5

Plus all of the following courses:
MATH 21Linear Algebra

5

MATH 23AVector Calculus

5

MATH 23BVector Calculus

5

MATH 24Ordinary Differential Equations

5

Upper-Division Courses

All of the following courses:
MATH 100Introduction to Proof and Problem Solving

5

Plus one of the following courses:
MATH 103AComplex Analysis

5

MATH 105AReal Analysis

5

Plus one of the following courses:
MATH 106Systems of Ordinary Differential Equations

5

MATH 107Partial Differential Equations

5

Plus the following course:
MATH 110Introduction to Number Theory

5

Plus one of the following courses:
MATH 111AAlgebra

5

MATH 111TAlgebra

5

MATH 117Advanced Linear Algebra

5

Plus one of the following options:
Either these courses

MATH 148Numerical Analysis

5

MATH 148LNumerical Analysis Laboratory

1

or this course

MATH 145Introductory Chaos Theory

5

or this course

AM 114Introduction to Dynamical Systems

5

or this course

AM 147Computational Methods and Applications

5

Plus one of the following courses:
MATH 194Senior Seminar

5

MATH 195Senior Thesis

5

Electives

Two courses selected from the following:

AM 100 or above

STAT 100 or above

BME 110Computational Biology Tools

5

CSE 101Algorithms and Abstract Data Types

5

CSE 102Introduction to Analysis of Algorithms

5

CSE 103Computational Models

5

CSE 104Computability and Computational Complexity

5

CSE 106Applied Graph Theory and Algorithms

5

CSE 107Probability and Statistics for Engineers

5

CSE 110AFundamentals of Compiler Design I

5

CSE 111Advanced Programming

5

CSE 112Comparative Programming Languages

5

CSE 142Machine Learning

5

EART 172
/OCEA 172
Geophysical Fluid Dynamics

5

ECE 103Signals and Systems

5

ECE 135Electromagnetic Fields and Waves

5

ECE 130Introduction to Optoelectronics and Photonics

5

ECE 141Feedback Control Systems

5

ECE 151Communications Systems

5

ECE 153Digital Signal Processing

5

ECON 113Introduction to Econometrics

5

MATH 115Graph Theory

5

MATH 116Combinatorics

5

MATH 120Coding Theory

5

MATH 134Cryptography

5

MATH 145Introductory Chaos Theory

5

MATH 148Numerical Analysis

5

MATH 152Programming for Mathematics

5

MATH 160Mathematical Logic I

5

PHYS 115Computational Physics

5

Some of these courses have prerequisites within their departments. Students are encouraged to plan their computational electives early, so that all prerequisites can be satisfied in a timely manner. Other upper-division courses with heavy emphasis on computational mathematics may occasionally be accepted by the mathematics undergraduate vice chair.

Disciplinary Communication (DC) Requirement

Students of every major must satisfy that major’s upper-division Disciplinary Communication (DC) requirement. The DC requirement in mathematics is satisfied by

MATH 100Introduction to Proof and Problem Solving

5

Plus one of the following courses:
MATH 194Senior Seminar

5

MATH 195Senior Thesis

5

Comprehensive Requirement

The comprehensive exit requirement in mathematics is satisfied by one of the following courses:

MATH 194Senior Seminar

5

MATH 195Senior Thesis

5

Planners

Computational Mathematics B.A.: Sample Freshmen Academic Plan

  Fall Winter Spring
1st (frosh) MATH 19A
or MATH 20A
MATH 19B
or MATH 20B
MATH 21
    MATH 23A
     
2nd (soph) MATH 23B MATH 110 MATH 145 & MATH 145L
or MATH 148
MATH 100    
     
3rd (junior) MATH 24 MATH 106 Elective
Elective    
     
4th (senior) MATH 111A
or MATH 117
MATH 103A
or MATH 105A
MATH 194
or MATH 195
    Elective
     

This course plan satisfies the MF general education requirement. Students must satisfy all other general education requirements.

Computational Mathematics B.A: Sample Transfer Academic Plan

For students who have completed MATH 19A, MATH 19B, MATH 21 and MATH 23A equivalents.

  Fall Winter Spring
1st (junior) MATH 23B MATH 103A
or MATH 105A
MATH 145 & MATH 145L
or MATH 148 & MATH 148L
MATH 100 MATH 110  
     
2nd (senior) MATH 24 MATH 106 MATH 194
or MATH 195
MATH 111A 
or MATH 117
Elective Elective
     

Mathematics Education Concentration

This concentration is intended to introduce students to the mathematics necessary for a career teaching kindergarten through high school (K-12) mathematics.

Course Requirements

Lower-Division Courses

The following course:
STAT 5Statistics

5

Plus one of the following courses:
MATH 19ACalculus for Science, Engineering, and Mathematics

5

MATH 20AHonors Calculus

5

Plus one of the following courses:
MATH 19BCalculus for Science, Engineering, and Mathematics

5

MATH 20BHonors Calculus

5

Plus all of the following courses:
MATH 21Linear Algebra

5

MATH 23AVector Calculus

5

MATH 23BVector Calculus

5

Upper-Division Courses

The following course:
MATH 100Introduction to Proof and Problem Solving

5

Plus one of the following courses:
MATH 103AComplex Analysis

5

MATH 105AReal Analysis

5

Plus all of the following courses:
MATH 110Introduction to Number Theory

5

MATH 128AClassical Geometry: Euclidean and Non-Euclidean

5

STAT 131Introduction to Probability Theory

5

MATH 181History of Mathematics

5

Plus one of the following courses:
MATH 111AAlgebra

5

MATH 111TAlgebra

5

Plus one of the following options:
Either this course

MATH 188Supervised Teaching

5

or these courses

EDUC 50BCAL Teach 1: Mathematics

2

EDUC 100BCal Teach 2: Mathematics

2

Plus one of the following courses:
MATH 194Senior Seminar

5

MATH 195Senior Thesis

5

UCSC students can pursue a degree in mathematics while preparing to teach at the secondary level. In California, students seeking a single-subject credential (for secondary teaching) in mathematics are required to take the CSET, a series of examinations that must be passed in order to enter a teaching-credential program (formerly The National Teachers Examination). Students who complete the mathematics education track, plus three additional specified courses, qualify for the California Single Subject Program, exempting themselves from the CSET. Both the Mathematics Department undergraduate adviser, the Mathematics Department’s website and the Education Department advising office have more information about the additional required courses for the Subject Matter Program.

Disciplinary Communication (DC) Requirement

Students of every major must satisfy that major’s upper-division Disciplinary Communication (DC) requirement. The DC requirement in mathematics is satisfied by

MATH 100Introduction to Proof and Problem Solving

5

Plus one of the following courses:
MATH 194Senior Seminar

5

MATH 195Senior Thesis

5

Comprehensive Requirement

The comprehensive exit requirement in mathematics is satisfied by one of the following courses:

MATH 194Senior Seminar

5

MATH 195Senior Thesis

5

Planners

Mathematics Education B.A.: Sample Freshmen Academic Plan

  Fall Winter Spring
1st (frosh) MATH 19A
or MATH 20A
MATH 19B
or MATH 20B
STAT 5
    MATH 23A
     
2nd (soph) MATH 21 MATH 100 MATH 110
 MATH 23B    
     
3rd (junior) MATH 128A MATH 181 STAT 131
EDUC 50B EDUC 100B  
     
4th (senior) MATH 111A MATH 103A
or MATH 105A
MATH 194
or MATH 195
     
     

This course plan satisfies the MF, TA and SR general education requirements. Students must satisfy all other general education requirements.

Mathematics Education B.A.: Sample Transfer Academic Plan

For students who have completed MATH 19A, MATH 19B, MATH 21 and MATH 23A equivalents.

  Fall Winter Spring
1st (junior) MATH 23B MATH 103A
or MATH 105A
MATH 110
MATH 100 MATH 181 STAT 5
     
2nd (senior) MATH 128A MATH 111A MATH 194
or MATH 195
EDUC 50B EDUC 100B STAT 131