Information and Policies
Introduction
Applied mathematics is a field of research specializing in the development and application of analytical and numerical tools and techniques toward the solution of complex quantitative problems in science and engineering. A Bachelor of Science (B.S.) in Applied Mathematics prepares graduates for careers in the industry (usually in research and development) or academia (either in teaching and/or in research at university or governmental laboratories or agencies). It can be a terminal degree, or prepare students for graduate school in applied mathematics or related fields.
The applied mathematics major at the University of California, Santa Cruz, provides students with a holistic training in mathematical modeling. The core of the degree program includes six courses that introduce modern analytical (and semi-analytical) techniques as well as general aspects of scientific computing. Students gain further depth or breadth by taking three (or more) electives among a large list of upper-division or graduate courses offered by applied mathematics faculty or in related subject areas. Finally, students learn to apply the techniques and tools learned through two capstone courses that focus on modeling “real- life” quantitative problems in science and engineering. In these courses, students also learn additional skills such as mathematical abstraction, critical thinking, and disciplinary communication.
The major has been designed to allow students to easily pursue an additional minor or major in an area of applications of mathematics (such as physics, astrophysics, Earth sciences, computer sciences, computer engineering, electrical engineering), and/or to pursue the 4+1 pathway into the Master of Science (M.S.) degree program in Scientific Computing and Applied Mathematics also offered by the Department of Applied Mathematics.
Academic Advising for the Program
Baskin Engineering's Undergraduate Advising Office is located in the Baskin Engineering Building, Room 225. It can be contacted by email at bsoeadvising@ucsc.edu or at the Undergraduate Advising website.
Transfer students to the program should consult the Transfer Students section of the Baskin Engineering Undergraduate Affairs page.
Program Learning Outcomes
Recipients of a B.S. degree in applied mathematics at UC Santa Cruz are expected to have the following skills and experiences:
- To be able to take a real-life science or engineering problem, and create a mathematical model for it, under the supervision of a professor.
- To be competent with a number of analytical methods for the solution of linear algebra problems, as well as ordinary and partial differential equations.
- To be competent with constructing numerical algorithms for the solution of linear algebra problems and ordinary differential equations.
- To be competent in at least two scientific computing languages such as: Fortran, C, Python, R, Matlab, etc. and to be familiar with other computational elements such as Unix-type operating systems, the use of compilers, professional scientific computing libraries, efficient IO algorithms, data visualization tools, etc.
- To be able to analyze critically the results from the model obtained, and identify when the model is inappropriate.
- To be able to communicate clearly and coherently with professionals (orally and/or in writing), in order to: (1) understand what is needed of the mathematical model prior to the investigation; and (2) report on the results of the model after the investigation
Getting Started in the Major: Frosh
It is recommended that high school students intending to apply to this major have completed four years of mathematics (through advanced algebra and trigonometry) and three years of science in high school. Comparable college mathematics and science courses completed at another institution also serve to properly prepare students for these majors.
This is a course-intensive and/or sequential program, and students who intend to pursue this major must begin taking classes for the major in their first year at UC Santa Cruz.
Math placement may be required for one or more of the foundational courses for this major. For more information, please review the Math Placement website.
Transfer Information and Policy
Transfer Admission Screening Policy
To be considered for admission to the applied mathematics major, incoming transfer students should complete the following courses:
All of the following courses:
| AM 10 | Mathematical Methods for Engineers I | 5 |
| AM 20 | Mathematical Methods for Engineers II | 5 |
| AM 30 | Multivariate Calculus for Engineers | 5 |
Plus one of the following options:
| | Either these courses | |
| MATH 19A | Calculus for Science, Engineering, and Mathematics | 5 |
| MATH 19B | Calculus for Science, Engineering, and Mathematics | 5 |
| | or these courses | |
| MATH 20A | Honors Calculus | 5 |
| MATH 20B | Honors Calculus | 5 |
Transfer students should have completed as many general education requirements as possible if they wish to graduate in two years.
Getting Started in the Major: Transfer Students
Transfer students should declare their major in their first quarter at UC Santa Cruz. Instructions for declaring a major in Baskin Engineering are on the department's major declaration page.
Major Qualification Policy and Declaration Process
Major Qualification
In order to be admitted into the applied mathematics major, students must be listed as a proposed major within the Baskin Engineering or within the Division of Physical and Biological Sciences. Please refer to Prepare to Declare a Baskin Engineering Major.
Transfers to the program should consult the Transfer Admission Screening Requirements and the Transfer Students section of the Baskin Engineering Undergraduate Affairs page.
In addition to being listed as a proposed Baskin Engineering or Physical and Biological Sciences major, admission to the applied mathematics major is based on passing the following foundational courses:
Foundation Courses
One of the following series:
| | Either these courses | |
| MATH 19A | Calculus for Science, Engineering, and Mathematics | 5 |
| MATH 19B | Calculus for Science, Engineering, and Mathematics | 5 |
| | or these courses | |
| MATH 20A | Honors Calculus | 5 |
| MATH 20B | Honors Calculus | 5 |
Plus one of the following options:*
| AM 30 | Multivariate Calculus for Engineers | 5 |
| | or these courses | |
| MATH 23A | Vector Calculus | 5 |
| MATH 23B | Vector Calculus | 5 |
AM 30 is preferred.
*Revised: 09/29/23
Plus one of the following:
| AM 10 | Mathematical Methods for Engineers I | 5 |
| MATH 21 | Linear Algebra | 5 |
AM 10 is preferred
Plus one of the following:
| AM 20 | Mathematical Methods for Engineers II | 5 |
| MATH 24 | Ordinary Differential Equations | 5 |
Declaration of the major can happen no sooner than the student's second quarter, and no later than the campus deadline.
At most, one unsuccessful attempt (grade C-, D+, D, D-, F, or NP) for a foundation course is permitted.
Appeal Process
Denials of admission to the major may be appealed by submitting a letter to Baskin Engineering's Undergraduate Advising office, addressed to the program undergraduate director within 15 days from the date the notification was mailed. The appeal letter must describe why the prior performance is not an accurate reflection of the student's potential. Within 15 days of receipt of the appeal, the Undergraduate Advising office will notify the student and their college of the decision.
How to Declare a Major
There are four steps to declaring a Baskin Engineering major. For a detailed guide to this process, please consult Baskin Engineering's Declare Your Major website.
Students should start the declaration of major process by completing Step One on the BSOE "Declare Your Major" website as soon as they complete the major qualification courses 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
Baskin Engineering requires letter grades for all courses in an engineering major.
Course Substitution Policy
Undergraduate engineering students who wish to substitute a major course with a course from UC Santa Cruz must first consult Baskin Engineering's Undergraduate Advising Office. The advising office requires a Petition for Course Substitution be approved before credit for an alternate course can be applied to any Baskin Engineering major requirement. Petition forms are available at the undergraduate advising office and on the Baskin Engineering advising website.
Petitions and procedures for approval must be obtained from and submitted to the Undergraduate Advising Office.
Double Majors and Major/Minor Combinations Policy
Students who are planning a double-major with physics can replace the AM 100 and AM 112 courses with the PHYS 116A and PHYS 116C courses. Special approval by both undergraduate directors will be required to do so.
Honors
Students must obtain a GPA of 3.8 or higher in the courses in the major to be considered for the distinction of “Highest Honors in the Major.” Students must obtain a GPA of 3.5 or higher in the courses in the major to be considered for the distinction of “Honors in the Major.” Baskin Engineering reserves the right to withhold honors based on other criteria, such as an incident of academic dishonesty.
Baskin Engineering Policies
Please refer to Baskin Engineering's Admission to School of Engineering Majors section of the catalog for additional policies that apply to all Baskin Engineering programs. These policies include admission to the major and the need for students to obtain preapproval before taking courses elsewhere.
Requirements and Planners
Course Requirements
Course requirements are divided into foundational lower-division courses and advanced upper-division courses:
Lower-Division Courses
Choose one of the following series:
| | Either these courses | |
| MATH 19A | Calculus for Science, Engineering, and Mathematics | 5 |
| MATH 19B | Calculus for Science, Engineering, and Mathematics | 5 |
| | or these courses | |
| MATH 20A | Honors Calculus | 5 |
| MATH 20B | Honors Calculus | 5 |
Credit for one or both MATH 19A and MATH 19B may be granted with adequate performance on the CEEB calculus AB or BC Advanced Placement examinations.
Plus one of the following courses:
| AM 10 | Mathematical Methods for Engineers I | 5 |
| MATH 21 | Linear Algebra | 5 |
Plus one of the following courses:
| AM 20 | Mathematical Methods for Engineers II | 5 |
| MATH 24 | Ordinary Differential Equations | 5 |
Plus one of the following options:
| AM 30 | Multivariate Calculus for Engineers | 5 |
| | or these courses | |
| MATH 23A | Vector Calculus | 5 |
| MATH 23B | Vector Calculus | 5 |
Plus one of the following options:
| CSE 16 | Applied Discrete Mathematics | 5 |
| MATH 100 | Introduction to Proof and Problem Solving | 5 |
MATH 100 is strongly recommended for students who eventually wish to take some upper-division electives in mathematics.
Plus one of the following programming courses
| CSE 20 | Beginning Programming in Python | 5 |
| CSE 13S | Computer Systems and C Programming | 7 |
| ECE 13 | Computer Systems and C Programming | 7 |
The programming requirement can be satisfied if students have a prior programming course, or clearing the “Test-out” bar.
Students who did not take either AM 10 or AM 20 as part of the lower-division core requirement are strongly encouraged to study the Matlab self-paced tutorial prior to taking AM 114 and AM 147.
Lower-Division Electives
Students are required to take two lower-division electives from the following list, in preparation for the upper-division electives they are later required to take. Students are encouraged to plan ahead carefully in consultation with undergraduate advising in making their selection.
EART, ECE, PHYS lower-division electives
Students interested in EART, ECE, PHYS upper-division electives should consider taking some of the following PHYS lower-division electives:
Only one course out of PHYS 5A and PHYS 6A, one course out of PHYS 5B and PHYS 6B, and one course out of PHYS 5C and PHYS 6C can be taken. Several of these courses have corequisite lab courses.
CSE or ECE lower-division electives
Students interested in CSE or ECE upper-division electives should consider taking some of the following CSE or ECE lower-division electives (in addition to possible PHYS electives):
| CSE 30 | Programming Abstractions: Python | 7 |
| ECE 9 | Statics and Mechanics of Materials | 5 |
ECON and STAT lower-division electives
Students interested in ECON or STAT upper-division electives should consider taking some of the following ECON or STAT lower-division electives:
| ECON 1 | Introductory Microeconomics: Resource Allocation and Market Structure | 5 |
| ECON 2 | Introductory Macroeconomics: Aggregate Economic Activity | 5 |
| STAT 7 | Statistical Methods for the Biological, Environmental, and Health Sciences | 5 |
| STAT 17 | Statistical Methods for Business and Economics | 5 |
STAT 17 (and associated lab STAT 17L) are strongly recommended for students wishing to take upper-division electives in economics.
Lower-division electives for mathematical biology
Students interested in mathematical biology (in particular AM 115) should consider taking some of the following BIOL or BIOE lower-division electives:
Upper-Division Courses
Complete the following core courses:
| AM 100 | Mathematical Methods for Engineers | 5 |
| AM 129 | Foundations of Scientific Computing for Scientists and Engineers | 5 |
| AM 147 | Computational Methods and Applications | 5 |
Plus one of the following courses:
| AM 112 | Introduction to Partial Differential Equations | 5 |
| AM 212A | Applied Partial Differential Equations | 5 |
Plus one of the following courses:
| AM 114 | Introduction to Dynamical Systems | 5 |
| AM 214 | Applied Dynamical Systems | 5 |
Plus one of the following courses:
| STAT 131 | Introduction to Probability Theory | 5 |
| CSE 107 | Probability and Statistics for Engineers | 5 |
Students who are potentially interested in pursuing a M.S. degree in scientific computing and applied mathematics later are strongly encouraged to take the AM 212A and AM 214 options instead of AM 112 and AM 114, otherwise they will have to take additional graduate courses during their M.S. year to replace AM 212A and AM 214.
Upper-Division Electives
Students are required to take three upper-division elective courses from the following list of possible electives. Up to one of these electives can be replaced by a 5-credit independent study to do research with one of the program faculty.
Note that many of these electives have lower-division prerequisites. Students should plan carefully which ones to take to ensure they are prepared for their selected upper-division electives. Also note that enrollment in the graduate courses is by permission of the instructor, who will verify adequate preparation.
Applied mathematics electives should ideally be selected to form a concentration that prepares the student for their desired career or future choice of graduate school. Students interested in pursuing graduate school in applied mathematics (at UC Santa Cruz or elsewhere) are encouraged to choose upper-division electives from AM or MATH. Students interested in graduate school in a different discipline are strongly encouraged to pursue a minor (or a double-major) in that discipline, and choose upper-division electives that count for both the applied mathematics major and the minor or double major. Students interested in a career in the private sector should select upper-division electives that prepare them for that career, with recommendations listed on this website.
Possible AM Electives
Any 5-credit upper-division AM course that is not already a core course. Any 5-credit graduate AM course with the exception of AM 200, AM 211, AM 212A and AM 214.
Possible ASTR electives
Possible BME electives
| BME 160 | Research Programming in the Life Sciences | 6 |
| BME 163 | Applied Visualization and Analysis of Scientific Data | 3 |
Possible CSE Electives
Note that many require lower-division CSE courses. Lecture-lab combinations count as one course.
| CSE 101 | Introduction to Data Structures and Algorithms | 5 |
| CSE 102 | Introduction to Analysis of Algorithms | 5 |
| CSE 104 | Computability and Computational Complexity | 5 |
| CSE 106 | Applied Graph Theory and Algorithms | 5 |
| CSE 108 | Algorithmic Foundations of Cryptography | 5 |
| CSE 113 | Parallel and Concurrent Programming | 5 |
| CSE 140 | Artificial Intelligence | 5 |
| CSE 142 | Machine Learning | 5 |
| CSE 144 | Applied Machine Learning: Deep Learning | 5 |
| CSE 160 | Introduction to Computer Graphics | 7 |
| CSE 161 | Introduction to Data Visualization | 5 |
| CSE 161L | Data Visualization Laboratory | 2 |
| CSE 162 | Advanced Computer Graphics and Animation | 5 |
| CSE 162L | Advanced Computer Graphics and Animation Laboratory | 2 |
Note that most of these courses require CSE 101 as prerequisite. Enrollment restrictions may apply to many of these courses on short notice, and some have multiple upper-division prerequisites, and may, therefore, only be appropriate for double majors (or major-minor combinations).
Possible EART Electives
Note that many require lower-division PHYS or CHEM courses:
Either of the following courses:
| EART 125 | Statistics and Data Analysis in the Geosciences | 5 |
| EART 225 | Statistics and Data Analysis in the Geosciences | 5 |
Either of the following courses:
| EART 172
/OCEA 172
| Geophysical Fluid Dynamics | 5 |
| EART 272
/OCEA 272
| Geophysical Fluid Dynamics | 5 |
Possible ECE Electives
Lecture-lab combinations count as one course.
| ECE 101 | Introduction to Electronic Circuits | 5 |
| ECE 101L | Introduction to Electronic Circuits Laboratory | 2 |
| ECE 103 | Signals and Systems | 5 |
| ECE 115 | Introduction to Solid Mechanics | 5 |
| ECE 135 | Electromagnetic Fields and Waves | 5 |
| ECE 135L | Electromagnetic Fields and Waves Laboratory | 2 |
| ECE 136 | Engineering Electromagnetics | 5 |
| ECE 141 | Feedback Control Systems | 5 |
| ECE 145 | Estimation and Introduction to Control of Stochastic Processes | 5 |
| ECE 149 | Introduction to Cyber-physical Systems | 5 |
| ECE 151 | Communications Systems | 5 |
| ECE 153 | Digital Signal Processing | 5 |
| ECE 163 | Introduction to Small-Scale UAV Theory and Practice | 7 |
| ECE 179 | Decision Analysis in Management | 5 |
Note that most of these courses require ECE 101 as prerequisite. Many of these courses have more than one upper-division prerequisite beyond those that are already part of the core requirements. These courses may only be appropriate for double majors (or major-minor combinations).
Possible ECON Electives
Note that many require ECON lower-division courses:
| ECON 100A | Intermediate Microeconomics | 5 |
| ECON 100B | Intermediate Macroeconomics | 5 |
| ECON 100M | Intermediate Microeconomics, Math Intensive | 5 |
| ECON 100N | Intermediate Macroeconomics, Math Intensive | 5 |
| ECON 101 | Managerial Economics | 5 |
| ECON 113 | Introduction to Econometrics | 5 |
| ECON 114 | Advanced Quantitative Methods | 6 |
| ECON 115 | Introduction to Management Sciences | 5 |
| ECON 124 | Machine Learning for Economists | 5 |
| ECON 166A
/CSE 166A
| Game Theory and Applications I | 5 |
Note that some of these courses require more than one upper-division ECON prerequisite. Also, some of these courses have enrollment restrictions, and may require permission by the instructor and may, therefore, only be appropriate for double majors (or major-minor combinations).
Possible MATH Electives
Note that most MATH electives require MATH 100 as a prerequisite, and that several of these courses have more than one upper division pre-requisite, or recommended prerequisites that students should take. These courses may only be appropriate for double majors, or for major-minor combinations.
Possible OCEA Electives
Note that some require lower-division PHYS electives, or upper-division ESCI electives:
| OCEA 260
/EART 260
| Introductory Data Analysis in the Ocean and Earth Sciences | 5 |
| OCEA 286 | Introduction to Ocean Modeling | 5 |
| OCEA 267 | Applied Environmental Time Series Analysis | 5 |
Either of the following courses:
Either of the following courses:
Possible PHYS Electives
Note that many require lower-division PHYS courses:
The prerequisites of PHYS 116A and PHYS 116C are waived for students who have taken AM 100 and AM 112.
PHYS 139A, PHYS 139B, PHYS 171 are courses that have more than one upper-division prerequisite beyond those that are already part of the core requirements. These courses may only be appropriate for double majors (or major-minor combinations).
Possible STAT Electives
| STAT 132 | Classical and Bayesian Inference | 5 |
| STAT 108 | Linear Regression | 5 |
| STAT 205 | Introduction to Classical Statistical Learning | 5 |
| STAT 266A
/CSE 266A
| Data Visualization and Statistical Programming in R | 3 |
| STAT 266B
/CSE 266B
| Advanced Statistical Programming in R | 3 |
All students, but especially those doing a double major or a major-minor combination, may also petition to count courses that are not already on the list as electives, subject to approval
Disciplinary Communication (DC) Requirement
The DC requirement in the Applied Mathematics B.S. is satisfied by completing the capstone course AM 170A (see below).
Comprehensive Requirement
Students satisfy the senior comprehensive requirement by receiving a passing grade in the two Mathematical Modeling 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.
The following are four sample academic plans that students can use to plan their sequence of courses in the major. The first two plans are suggested guidelines for students who begin their studies in their frosh year. Such students, if they plan carefully, will have several openings free to take other breadth courses they find interesting, or pursue an additional minor or major. The other two plans are for students transferring to UC Santa Cruz as juniors.
We generally encourage students to take AM 112/AM 212A later in their curriculum, as this course requires proficiency in many different aspects of applied mathematics.
Plan One: This is a possible planner for a student entering UCSC in their frosh year who is prepared to go directly into MATH 19A or MATH 20A.
| |
Fall |
Winter |
Spring |
Summer |
| Entering |
|
|
|
College 1A |
| |
|
|
Summer Edge (optional) |
| |
|
|
|
| 1st Year |
MATH 19A |
CSE 20 |
AM 20 |
|
| AM 10 |
MATH 19B |
CSE 16 |
|
| College 1 |
WRIT 1/WRIT 1E (if needed) |
Lower div elective |
|
| |
|
|
|
| 2nd Year |
AM 30 |
Lower-div elective |
STAT 131 |
|
| WRIT 2* |
Lower-div elective |
|
|
| |
|
|
|
| 3rd Year |
AM 100 |
AM 170A |
Upper-div elective |
|
| AM 114 |
Upper-div elective |
|
|
| |
|
|
|
| 4th Year |
AM 129 |
AM 147 |
AM 170B |
|
| Upper-div elective |
AM 112 |
|
|
* WRIT 2 should be taken in or before spring quarter of the second year.
The SI general education requirement is satisfied by passing the capstone course AM 170B. The MF general education requirement is satisfied by passing any of the lower-division mathematical foundations requirements.
Plan Two: This is a possible planner for a student entering UCSC their frosh year who needs to take preparatory courses prior to MATH 19A to ensure a successful outcome in this course.
| |
Fall |
Winter |
Spring |
Summer |
| Entering |
|
|
|
College 1A |
| |
|
|
Summer Edge (optional) |
| |
|
|
|
| 1st Year |
MATH 2 |
MATH 3 |
MATH 19A |
|
| |
Lower-div elective |
Lower-div elective |
|
| |
WRIT 1/WRIT 1E (if needed) |
|
|
| 2nd Year |
AM 10 |
AM 20 |
AM 30 |
|
| MATH 19B |
CSE 20 |
CSE 16 |
|
| WRIT 2* |
|
|
|
| 3rd Year |
AM 100 |
AM 147 |
STAT 131 |
|
| |
Upper-div elective |
Upper-div elective |
|
| |
|
|
|
| 4th Year |
AM 129 |
AM 112 |
AM 170B |
|
| AM 114 |
AM 170A |
Upper-div elective |
|
* WRIT 2 should be taken in or before spring quarter of the second year.
The SI general education requirement is satisfied by passing the capstone course AM 170B. The MF general education requirement is satisfied by passing any of the lower-division mathematical foundations requirements.
Plan Three:This is a sample planner for a transfer student. It assumes the student has taken the majority of their general education requirements prior to joining UCSC.
| |
Fall |
Winter |
Spring |
Summer |
| Entering |
|
|
|
KRSG 1T |
| |
|
|
Summer Edge (optional) |
| |
|
|
|
| Junior Year |
CSE 20 |
AM 147 |
STAT 131 |
|
| AM 100 |
Lower-div elective |
Upper-div elective |
|
| Lower-div elective |
CSE16 |
|
|
| Senior Year |
AM 114 |
AM 170A |
AM 170B |
|
| AM 129 |
AM 112 |
Upper-div elective |
|
| Upper-div elective |
|
|
|
Plan Four: This is a sample planner for a transfer student interested in the 4+1 program (e.g. thesis track; replace Independent Study with M.S. elective for coursework track). Note that students must take the graduate version of PDEs and Dynamical Systems courses (212A and 214 respectively) to count toward the M.S. core requirements. One additional elective must be taken during the M.S. year to ensure that there are at least 35 credits taken as a graduate student.
| |
Fall |
Winter |
Spring |
Summer |
| Entering |
|
|
|
KRSG 1T |
| |
|
|
Summer Edge (optional) |
| |
|
|
|
| Junior Year |
CSE 20 |
AM 147 |
Upper-div elective |
|
| AM 100 |
CSE16 |
STAT 131 |
|
| Lower-div elective |
Lower-div elective |
Upper-div elective |
|
| Senior Year |
AM 129 |
AM 212A |
AM 170B |
|
| AM 214 |
AM 170A |
Upper-div elective |
|
| |
|
|
|
| M.S. Year |
M.S. elective |
AM 213A |
AM 213B |
|
| Indep Study |
Indep Study |
AM 250 |
|
| |
|
Indep Study |
|