Information and Policies
Introduction
The mathematics bachelor of arts (B.A.) program provides an excellent liberal arts background from which to pursue a variety of career opportunities. University of California, Santa Cruz, graduates with a B.A. 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 are trained in the art of problem-solving--- an essential skill in all professions.
Within the major, there are two concentrations leading to the Bachelor of Arts in Mathematics: pure mathematics and computational mathematics.
Pure Mathematics
This pathway emphasizes the importance of a well-rounded, in-depth mathematical education, and includes advanced coursework in algebra, analysis, and geometry. Students often pursue a career with a focus on research and theory.
Computational Mathematics
Students explore ways math can be used to answer questions in many other fields. They gain experience in mathematical modeling of real-world phenomena via ordinary and partial differential equations, approximation and optimization techniques, programming, or game theory.
Both of these concentrations 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 10 courses, one of which must be a senior thesis or senior seminar. A minor in pure mathematics is also offered.
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.
Academic Advising for the Program
The undergraduate advisor may be contacted via email at mathadvising@ucsc.edu. The advisor provides information about requirements, prerequisites, policies and procedures, learning support, scholarships, and special opportunities for undergraduate research. In addition, the advisor 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: Frosh
This major is highly course intensive; students who intend to pursue this major must begin taking classes for the major in their first quarter at UC Santa Cruz. Math placement is required for one or more of the foundational courses for this major. For more information, please review the Math Placement website.
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.
Transfer Information and Policy
Transfer Admissions Screening Policy
The following courses or their equivalents are required prior to transfer, by the end of the spring term for students planning to enter in the fall.
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.
Prospective students are encouraged to prioritize recommended major preparation, and may additionally complete courses that articulate to UC Santa Cruz general education requirements as time allows.
| MATH 19A | Calculus for Science, Engineering, and Mathematics | 5 |
| MATH 19B | Calculus for Science, Engineering, and Mathematics | 5 |
| MATH 21 | Linear Algebra | 5 |
| MATH 23A | Vector Calculus | 5 |
Getting Started in the Major: Transfer Students
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.
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 advisor to determine if this applies to their situation.
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
It is strongly recommended that only students who earn grades of B- or better in MATH 100 consider applying to the major in mathematics.
Admission to the mathematics major (all concentrations) is contingent on students successfully passing the following introductory courses or their equivalents (see below). Transfer Students: see Transfer Admission Screening Requirements.
Choose one of the following courses:
| MATH 19A | Calculus for Science, Engineering, and Mathematics | 5 |
| MATH 20A | Honors Calculus | 5 |
Plus one of the following courses:
| MATH 19B | Calculus for Science, Engineering, and Mathematics | 5 |
| MATH 20B | Honors Calculus | 5 |
Plus all of the following courses:
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
If a student completes major qualification courses but does not meet the major qualification criteria, and appeals, the department may accept or reject the appeal or place conditions on the student that will be resolved within at most one more enrolled quarter. To submit an appeal see the department website for Appealing the Major.
How to Declare a Major
See the Mathematics Department website for directions on How to Qualify for and Petition to Declare a Math Major.
Students should submit a petition to declare as soon as they complete the major qualification requirements or reach their declaration deadline quarter (whichever comes first).
Students petitioning when the campus declaration deadline is imminent (i.e., in their sixth quarter, for students admitted as frosh), will either be approved, denied, or provided with conditions (e.g., completion of some courses with certain grades) that will be resolved within at most one more enrolled quarter, even if they have not completed major qualification courses.
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’s undergraduate vice chair approves requests for course substitutions. See the department website for details on requesting an exception to policy or course substitution.
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.
Course Requirements
Lower-Division Courses
Choose one of the following courses:
| MATH 19A | Calculus for Science, Engineering, and Mathematics | 5 |
| MATH 20A | Honors Calculus | 5 |
Plus one of the following courses:
| MATH 19B | Calculus for Science, Engineering, and Mathematics | 5 |
| MATH 20B | Honors Calculus | 5 |
Plus all of the following courses:
Upper-Division Courses
The following course:
| MATH 100 | Introduction to Proof and Problem Solving | 5 |
Plus one of the following courses:
Plus one of the following courses:
Plus one of the following courses:
Plus one of the following courses:
Electives
The remaining three courses are selected by the student from among any mathematics course numbered above 100 (excluding MATH 188 and MATH 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 100 | Introduction to Proof and Problem Solving | 5 |
Plus one of the following courses:
Comprehensive Requirement
The comprehensive exit requirement in mathematics is satisfied by one of the following courses:
Planners
The tables below are for informational purposes and do not reflect all university, general education, and credit requirements. See Undergraduate Graduation Requirements for more information.
Pure Mathematics B.A.: Sample Freshmen Academic Plan Starting in MATH 19A or MATH 20A
| |
Fall |
Winter |
Spring |
| 1st (frosh) |
MATH 19A
or MATH 20A |
MATH 19B
or MATH 20B |
MATH 23A |
| |
|
|
| |
|
|
| 2nd (soph) |
MATH 21 |
MATH 100 |
MATH 103A |
| MATH 23B |
|
|
| |
|
|
| 3rd (junior) |
MATH 24 |
MATH 110 |
MATH 128A |
| |
|
|
| |
|
|
| 4th (senior) |
Elective |
Elective |
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 Freshmen Academic Plan Starting in MATH 3
| |
Fall |
Winter |
Spring |
| 1st (frosh) |
MATH 3 |
MATH 19A |
MATH 19B |
| |
|
|
| |
|
|
| 2nd (soph) |
MATH 21 |
MATH 23B |
MATH 103A |
| MATH 23A |
MATH 100 |
|
| |
|
|
| 3rd (junior) |
MATH 24 |
MATH 110 |
MATH 128A |
| |
|
|
| |
|
|
| 4th (senior) |
Elective |
Elective |
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 Freshmen Academic Plan Starting in MATH 2
| |
Fall |
Winter |
Spring |
| 1st (frosh) |
MATH 2 |
MATH 3 |
MATH 19A |
| |
|
|
| |
|
|
| 2nd (soph) |
MATH 19B |
MATH 21 |
MATH 23B |
| |
MATH 23A |
MATH 100 |
| |
|
|
| 3rd (junior) |
MATH 24 |
MATH 103A |
MATH 128A |
| MATH 110 |
|
|
| |
|
|
| 4th (senior) |
Elective |
Elective |
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 110 |
MATH 103A |
| MATH 100 |
|
MATH 128A |
| |
|
|
| 2nd (senior) |
MATH 24 |
Elective |
MATH 194
or MATH 195 |
| Elective |
|
Elective |
| |
|
|
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 19A | Calculus for Science, Engineering, and Mathematics | 5 |
| MATH 20A | Honors Calculus | 5 |
Plus one of the following courses:
| MATH 19B | Calculus for Science, Engineering, and Mathematics | 5 |
| MATH 20B | Honors Calculus | 5 |
Plus all of the following courses:
Upper-Division Courses
All of the following courses:
| MATH 100 | Introduction to Proof and Problem Solving | 5 |
Plus one of the following courses:
Plus one of the following courses:
| MATH 106 | Systems of Ordinary Differential Equations | 5 |
| MATH 107 | Partial Differential Equations | 5 |
Plus the following course:
Plus one of the following courses:
Plus one of the following options:
| MATH 148 | Numerical Analysis | 5 |
| MATH 145 | Introductory Chaos Theory | 5 |
| AM 114 | Introduction to Dynamical Systems | 5 |
| AM 147 | Computational Methods and Applications | 5 |
Plus one of the following courses:
Electives
Two courses selected from the following:
AM 100 or above
STAT 100 or above
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. Specifically, students may not be able to enroll in Computer Science and Engineering (CSE) courses unless they are also pursuing a major in the CSE Department. 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 100 | Introduction to Proof and Problem Solving | 5 |
Plus one of the following courses:
Comprehensive Requirement
The comprehensive exit requirement in mathematics is satisfied by one of the following courses:
Planners
The tables below are for informational purposes and do not reflect all university, general education, and credit requirements. See Undergraduate Graduation Requirements for more information.
Computational Mathematics B.A.: Sample Freshmen Academic Plan Starting in MATH 19A or MATH 20A
| |
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 |
Elective |
| MATH 100 |
|
|
| |
|
|
| 3rd (junior) |
MATH 24 |
MATH 106 |
MATH 148 |
| |
|
|
| |
|
|
| 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 Freshmen Academic Plan Starting in MATH 3
| |
Fall |
Winter |
Spring |
| 1st (frosh) |
MATH 3 |
MATH 19A |
MATH 19B |
| |
|
|
| |
|
|
| 2nd (soph) |
MATH 21 |
MATH 23B |
Elective |
| MATH 23A |
MATH 100 |
|
| |
|
|
| 3rd (junior) |
MATH 24 |
MATH 106 |
MATH 148 |
| MATH 110 |
|
|
| |
|
|
| 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 Freshmen Academic Plan Starting in MATH 2
| |
Fall |
Winter |
Spring |
| 1st (frosh) |
MATH 2 |
MATH 3 |
MATH 19A |
| |
|
|
| |
|
|
| 2nd (soph) |
MATH 19B |
MATH 21 |
MATH 23B |
| |
MATH 23A |
MATH 100 |
| |
|
|
| 3rd (junior) |
MATH 24 |
MATH 106 |
Elective |
| MATH 110 |
|
MATH 148 & MATH 148L |
| |
|
|
| 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 |
| |
|
|