# Mathematics Theory and Computation B.S.

## Information and Policies

### Introduction

The Mathematics Theory and Computation B.S. provides an excellent scientific background from which to pursue a variety of career opportunities. UC Santa Cruz 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.

### 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.

### 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.

### 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 the University of California, 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.

### 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 Theory and Computation B.S. major is contingent on students successfully passing the following introductory courses or their equivalents. **Transfer Students: **in addition to satisfying the Transfer Admission Screening Requirements listed below, you must complete MATH 100 during your first quarter in order to declare

the major.

##### 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 one of the following courses:

MATH 21 | Linear Algebra | 5 |

AM 10 | Mathematical Methods for Engineers I | 5 |

MATH 21 is preferred

##### Plus all of the following courses:

MATH 23A | Vector Calculus | 5 |

MATH 100 | Introduction to Proof and Problem Solving | 5 |

Students should submit a petition to declare as soon as they complete the major qualification courses or reach their declaration deadline quarter (whichever comes first). 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. Students who are not eligible to declare may appeal. The advising office will subsequently notify the student, and the college of the decision, no later than 15 business days after the submission of the appeal.

Students petitioning when the campus declaration deadline is imminent will either be approved, denied, or provided with conditions that will be resolved within at most one more enrolled quarter, even if they have not completed major qualification courses.

#### 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. The Mathematics Department will reply to appeals within 15 days of submission.

#### How to Declare a 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.

The Petition for Major/Minor declaration form can be accessed by going to MyUCSC and navigating to the Student Homepage and selecting the Undergraduate Student eForms tile > Petition for Major/Minor.

### Transfer Information and Policy

#### Transfer Admission 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.

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 |

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.

#### Recommended Course for Transfer Students

In addition, the following course is recommended prior to transfer to ensure timely graduation.

MATH 24 | Ordinary Differential Equations | 5 |

#### 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.

To obtain equivalency for MATH 23A, transfer students may have taken a course that could also be equivalent to MATH 23B, and in rare circumstances it is possible that this equivalency has not yet been formally recognized and is, therefore, not listed in assist.org. Students who have equivalency for MATH 23A but not MATH 23B should contact the undergraduate advisor to determine if this applies to their situation.

### Letter Grade Policy

There are no restrictions on grading options for Mathematics Department courses. Please see UC Santa Cruz policies on grading options.

### Course Substitution Policy

The Mathematics Department undergraduate vice chair approves requests for course substitutions. See the department website for details on requesting an exception to policy or course substitution.

### Double Majors and Major/Minor Combinations Policy

Students who are declared in the Computer Science B.S. and wish to double major in Mathematics Theory and Computation B.S. may petition to use computer science and engineering courses toward the upper-division coding requirement and the three required upper-division electives for the mathematics theory and computation B.S. major.

### Education Abroad Program (EAP)

Studying abroad is encouraged and most practical in fall quarter. It is possible to take classes abroad that will satisfy math major requirements. Intention of using an abroad course as a math requirement must be approved prior to taking the course. Students may submit a syllabus for the course abroad with an exception to policy request through the Mathematics Department homepage.

### 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.

## Requirements and Planners

### Course Requirements

The Mathematics Theory and Computation B.S. is intended to prepare students for technical careers in industry or government while providing a solid mathematical background.

#### 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 one of the following courses:

AM 10 | Mathematical Methods for Engineers I | 5 |

MATH 21 | Linear Algebra | 5 |

MATH 21 is preferred.

##### Plus all of the following courses:

MATH 23A | Vector Calculus | 5 |

MATH 23B | Vector Calculus | 5 |

##### Plus one of the following courses:

AM 20 | Mathematical Methods for Engineers II | 5 |

MATH 24 | Ordinary Differential Equations | 5 |

Math 24 is preferred.

#### Upper-Division Courses

The following course:

MATH 100 | Introduction to Proof and Problem Solving | 5 |

##### Coding Requirement

Plus one of the following courses or equivalent:

MATH 152 | Programming for Mathematics | 5 |

ASTR 119 | Introduction to Scientific Computing | 5 |

EART 112 | Geophysical Data Science | 5 |

EART 119A | Introduction to Scientific Programming | 5 |

PHYS 115 | Computational Physics | 5 |

MATH152 is preferred. ASTR 119, EART 112, EART 119A and PHYS 115 are intended for double major students.

Students who are declared in the Computer Science B.S. and wish to double major in the Mathematics Theory and Computation B.S. may petition to use CSE courses toward the upper-division coding requirement and the three required upper-division electives for the Mathematics Theory and Computation B.S. major.

##### Analysis Theory Requirement

Plus one of the following courses:

MATH 103A | Complex Analysis | 5 |

MATH 105A | Real Analysis | 5 |

##### Algebra Theory Requirement

Plus one of the following courses:

MATH 110 | Introduction to Number Theory | 5 |

MATH 111A | Algebra | 5 |

MATH 111T | Algebra | 5 |

MATH 117 | Advanced Linear Algebra | 5 |

##### Analysis Computation Requirement

Plus one of the following courses:

MATH 145 | Introductory Chaos Theory | 5 |

MATH 148 | Numerical Analysis | 5 |

AM 114 | Introduction to Dynamical Systems | 5 |

AM 147 | Computational Methods and Applications | 5 |

Students who take more than one course from the Analysis Computation Requirement may use the extra courses toward the three major electives requirement.

##### Algebra Computation Requirement

Plus one of the following courses:

MATH 115 | Graph Theory | 5 |

MATH 116 | Combinatorics | 5 |

MATH 134 | Cryptography | 5 |

MATH 140 | Industrial Mathematics | 5 |

MATH 160 | Mathematical Logic I | 5 |

MATH 162 | Introduction to Computably Enumerable Functions and Sets and their Degrees | 5 |

Students who take more than one course from the Algebra Computation Requirement may use the extra courses toward the three major electives requirement.

##### Comprehensive Requirement

Plus one of the following courses:

MATH 194 | Senior Seminar | 5 |

MATH 195 | Senior Thesis | 5 |

#### Electives

Three elective courses are required. If a student takes more than one course from the Analysis or Algebra Computation requirement lists, the extra course(s) can be counted toward the elective requirements. Other elective options are listed below. Courses from departments other than Mathematics, Statistics or Applied Math will have significant prerequisites and are intended for double major students.

Students who are declared in the Computer Science B.S. and wish to double major in the Mathematics Theory and Computation B.S. may petition to use CSE courses toward the upper-division coding requirement and the three required upper-division electives for the Mathematics Theory and Computation B.S. major.

MATH 106 | Systems of Ordinary Differential Equations | 5 |

MATH 107 | Partial Differential Equations | 5 |

MATH 118 | Advanced Number Theory | 5 |

MATH 120 | Coding Theory | 5 |

MATH 124 | Introduction to Topology | 5 |

MATH 125 | Applied Topology | 5 |

STAT 108 | Linear Regression | 5 |

STAT 131 | Introduction to Probability Theory | 5 |

STAT 132 | Classical and Bayesian Inference | 5 |

AM 107
/PHYS 107
| Introduction to Fluid Dynamics | 5 |

AM 115 | Stochastic Modeling in Biology | 5 |

AM 129 | Foundations of Scientific Computing for Scientists and Engineers | 5 |

AM 148 | GPU Programming for Scientific Computations | 5 |

ASTR 111 | Order-of-Magnitude Astrophysics | 5 |

EART 124 | Modeling Earth's Climate | 5 |

EART 125 | Statistics and Data Analysis in the Geosciences | 5 |

EART 162 | Planetary Interiors | 5 |

EART 172
/OCEA 172
| Geophysical Fluid Dynamics | 5 |

ECE 103 | Signals and Systems | 5 |

ECE 130 | Introduction to Optoelectronics and Photonics | 5 |

ECE 135 | Electromagnetic Fields and Waves | 5 |

ECE 141 | Feedback Control Systems | 5 |

ECE 151 | Communications Systems | 5 |

ECE 153 | Digital Signal Processing | 5 |

ECON 104 | Is There Truth in Numbers: The Role of Statistics in Economics | 5 |

ECON 113 | Introduction to Econometrics | 5 |

ECON 114 | Advanced Quantitative Methods | 6 |

ECON 124 | Machine Learning for Economists | 5 |

ECON 166A
/CSE 166A
| Game Theory and Applications I | 5 |

ECON 166B
/CSE 166B
| Game Theory and Applications II | 5 |

PHYS 116C | Mathematical Methods in Physics | 5 |

PHYS 139A | Quantum Mechanics I | 5 |

PHYS 139B | Quantum Mechanics II | 5 |

PHYS 171
/ASTR 171
| General Relativity, Black Holes, and Cosmology | 5 |

#### Comprehensive Requirement

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

MATH 194 | Senior Seminar | 5 |

MATH 195 | Senior Thesis | 5 |

#### Disciplinary Communication (DC) Requirement

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

MATH 100 | Introduction to Proof and Problem Solving | 5 |

##### Plus one of the following courses:

MATH 194 | Senior Seminar | 5 |

MATH 195 | Senior Thesis | 5 |

### Planners

**Mathematics Theory and Computation B.S Freshmen Students Starting at MATH 19A or MATH 20A**

Fall | Winter | Spring | |
---|---|---|---|

1st Year(frosh) |
MATH 19A or MATH 20A | MATH 19B or MATH 20B | MATH 23A |

Core/Writing | Core/Writing | Core/Writing | |

GE/ME | GE/ME | GE/ME | |

2nd Year(soph) |
MATH 21 | MATH 24 | Elective 1 |

MATH 23B | MATH 100 | ||

GE/ME | |||

3rd Year(junior) |
Elective 2 | MATH 103A or MATH 105A | MATH 148 & MATH 148L |

MATH 152 | |||

4th Year(senior) |
MATH 110 or MATH 111A or MATH 117 |
MATH 115 or MATH 116 or MATH 134 or MATH 140 or MATH 160 |
MATH 194 or MATH 195 |

Elective 3 |

MF GE requirement fulfilled through this plan.

**Mathematics Theory and Computation B.S Freshmen Students Starting at MATH 3**

Fall | Winter | Spring | |
---|---|---|---|

1st Year(frosh) |
MATH3 | MATH 3 | MATH 19A |

Core/Writing | Core/Writing | Core/Writing | |

GE/ME | GE/ME | GE/ME | |

2nd Year(soph) |
MATH 23A | MATH 21 | MATH 100 |

GE/ME | MATH 23B | ||

3rd Year(junior) |
MATH 24 | MATH 103A or MATH 105A |
MATH 148 &MATH 148L |

Elective 1 | MATH 152 | ||

4th Year(senior) |
MATH 110 or MATH 111A or MATH 117 |
MATH 115 or MATH 116 or MATH 134 or MATH 140 or MATH 160 |
MATH 194 or MATH 195 |

Elective 2 | Elective 3 |

MF GE requirement fulfilled through this plan.

**Mathematics Theory and Computation B.S Freshmen Students Starting at MATH 2**

Fall | Winter | Spring | |
---|---|---|---|

1st Year(frosh) |
MATH 2 | MATH 3 | MATH 19A |

Core/Writing | Core/Writing | Core/Writing | |

GE/ME | GE/ME | GE/ME | |

2nd Year(soph) |
MATH 19B | MATH 21 | MATH23B |

GE/ME | MATH 23A | MATH 100 | |

3rd Year(junior) |
MATH 24 | MATH 103A or MATH 105A |
MATH 148 &MATH 148L |

Elective 1 | MATH 152 | Elective 2 | |

4th Year(senior) |
MATH 110 or MATH 111A or MATH 117 |
MATH 115 or MATH 116 or MATH 134 or MATH 140 or MATH 160 |
MATH 194 or MATH 195 |

Elective 3 |

MF GE requirement fulfilled through this plan

**Mathematics Theory and Computation B.S Transfer Students with no lower-division needs**

Fall | Winter | Spring | |
---|---|---|---|

1st Year(junior) |
MATH 100 | MATH 103A or MATH 105A | MATH 148 & MATH 148L |

MATH 152 | Elective 1 | ||

2nd Year(senior) |
MATH 110 or MATH 111A or MATH 117 |
MATH 115 or MATH 116 or MATH 134 or MATH 140 or MATH 160 |
MATH 194 or MATH 195 |

Elective 2 | Elective 3 | ||

**Mathematics Theory and Computation B.S Transfer Students who need Math 23B and 24**

Fall | Winter | Spring | |
---|---|---|---|

1st Year(junior) |
MATH 23B | MATH 24 | MATH 148 & MATH 148L |

MATH 100 | MATH 152 | Elective 1 | |

2nd Year(senior) |
MATH 110 or MATH 111A or MATH 117 |
MATH 115 or MATH 116 or MATH 134 or MATH 140 or MATH 160 |
MATH 194 or MATH 195 |

Elective 2 | MATH 103A or MATH 105A | Elective 3 | |