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Applied Mathematics B.S.

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:

  1. 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.
  2. To be competent with a number of analytical methods for the solution of linear algebra problems, as well as ordinary and partial differential equations.
  3. To be competent with constructing numerical algorithms for the solution of linear algebra problems and ordinary differential equations.
  4. 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.
  5. To be able to analyze critically the results from the model obtained, and identify when the model is inappropriate.
  6. 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 10Mathematical Methods for Engineers I

5

AM 20Mathematical Methods for Engineers II

5

AM 30Multivariate Calculus for Engineers

5

Plus one of the following options:
Either these courses

MATH 19ACalculus for Science, Engineering, and Mathematics

5

MATH 19BCalculus for Science, Engineering, and Mathematics

5

or these courses

MATH 20AHonors Calculus

5

MATH 20BHonors 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 19ACalculus for Science, Engineering, and Mathematics

5

MATH 19BCalculus for Science, Engineering, and Mathematics

5

or these courses

MATH 20AHonors Calculus

5

MATH 20BHonors Calculus

5

Plus one of the following options
AM 30Multivariate Calculus for Engineers

5

or these courses

MATH 23AVector Calculus

5

MATH 23BVector Calculus

5

AM 30 is preferred

Plus one of the following:
AM 10Mathematical Methods for Engineers I

5

MATH 21Linear Algebra

5

AM 10 is preferred

Plus one of the following:
AM 20Mathematical Methods for Engineers II

5

MATH 24Ordinary 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 19ACalculus for Science, Engineering, and Mathematics

5

MATH 19BCalculus for Science, Engineering, and Mathematics

5

or these courses

MATH 20AHonors Calculus

5

MATH 20BHonors 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 10Mathematical Methods for Engineers I

5

MATH 21Linear Algebra

5

AM 10 is preferred.

Plus one of the following courses:
AM 20Mathematical Methods for Engineers II

5

MATH 24Ordinary Differential Equations

5

AM 20 is preferred.

Plus one of the following options:
AM 30Multivariate Calculus for Engineers

5

or these courses

MATH 23AVector Calculus

5

MATH 23BVector Calculus

5

AM 30 is preferred.

Plus one of the following options:
CSE 16Applied Discrete Mathematics

5

MATH 100Introduction 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 20Beginning Programming in Python

5

CSE 13SComputer Systems and C Programming

7

ECE 13Computer Systems and C Programming

7

ASTR 19Practical Programming for the Sciences

5

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. Lecture/lab combinations count as one course. Associated labs are required only when required by the lecture.

PHYS 5AIntroduction to Physics I

5

PHYS 5BIntroduction to Physics II

5

PHYS 5CIntroduction to Physics III

5

PHYS 6AIntroductory Physics I

5

PHYS 6BIntroductory Physics II

5

PHYS 6CIntroductory Physics III

5

ASTR 21The Diverse Universe: Stars, Planets, and Galaxies

5

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 30Programming Abstractions: Python

7

ECE 9Statics 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. Note that lecture/lab combinations count as one course.

ECON 1Introductory Microeconomics: Resource Allocation and Market Structure

5

ECON 2Introductory Macroeconomics: Aggregate Economic Activity

5

STAT 7Statistical Methods for the Biological, Environmental, and Health Sciences

5

STAT 7LStatistical Methods for the Biological, Environmental, and Health Sciences Laboratory

2

STAT 17Statistical Methods for Business and Economics

5

STAT 17LStatistical Methods for Business and Economics Laboratory

2

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:

BIOL 20ACell and Molecular Biology

5

BIOE 20CEcology and Evolution

5

Upper-Division Courses

Complete the following core courses:
AM 100Mathematical Methods for Engineers

5

AM 129Foundations of Scientific Computing for Scientists and Engineers

5

Plus one of the following courses:
AM 147Computational Methods and Applications

5

MATH 148Numerical Analysis

5

Plus the following courses:
AM 112Introduction to Partial Differential Equations

5

AM 114Introduction to Dynamical Systems

5

Plus one of the following courses:
STAT 131Introduction to Probability Theory

5

CSE 107Probability and Statistics for Engineers

5

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 (100-199) or graduate (200-299) AM course that is not already a core course. AM 198 can only be used once for elective credit. AM 200, 211, 296, 297, and 299 may not be used.

Possible ASTR electives
ASTR 112Physics of Stars

5

ASTR 113Introduction to Cosmology

5

ASTR 119Introduction to Scientific Computing

5

Possible BME electives
BME 160Research Programming in the Life Sciences

6

Possible CSE Electives

Note that many require lower-division CSE courses. Lecture/lab combinations count as one course.

CSE 101Introduction to Data Structures and Algorithms

5

CSE 102Introduction to Analysis of Algorithms

5

CSE 104Computability and Computational Complexity

5

CSE 106Applied Graph Theory and Algorithms

5

CSE 108Algorithmic Foundations of Cryptography

5

CSE 113Parallel and Concurrent Programming

5

CSE 140Artificial Intelligence

5

CSE 142Machine Learning

5

CSE 144Applied Machine Learning: Deep Learning

5

CSE 160Introduction to Computer Graphics

7

CSE 161Introduction to Data Visualization

5

CSE 161LData Visualization Laboratory

2

CSE 162Advanced Computer Graphics and Animation

5

CSE 162LAdvanced 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:

EART 112Geophysical Data Science

5

EART 118Seismotectonics

5

EART 119AIntroduction to Scientific Programming

5

EART 121The Atmosphere

5

EART 124Modeling Earth's Climate

5

EART 160Planetary Science

5

EART 162Planetary Interiors

5

EART 163Planetary Surfaces

5

EART 164Planetary Atmospheres

5

Either of the following courses:
EART 125Statistics and Data Analysis in the Geosciences

5

EART 225Statistics 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 101Introduction to Electronic Circuits

5

ECE 101LIntroduction to Electronic Circuits Laboratory

2

ECE 103Signals and Systems

5

ECE 115Introduction to Solid Mechanics

5

ECE 135Electromagnetic Fields and Waves

5

ECE 135LElectromagnetic Fields and Waves Laboratory

2

ECE 136Engineering Electromagnetics

5

ECE 141Feedback Control Systems

5

ECE 145Estimation and Introduction to Control of Stochastic Processes

5

ECE 149Introduction to Cyber-physical Systems

5

ECE 151Communications Systems

5

ECE 153Digital Signal Processing

5

ECE 163Introduction to Small-Scale UAV Theory and Practice

7

ECE 179Decision 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 100AIntermediate Microeconomics

5

ECON 100BIntermediate Macroeconomics

5

ECON 100MIntermediate Microeconomics, Math Intensive

5

ECON 100NIntermediate Macroeconomics, Math Intensive

5

ECON 101Managerial Economics

5

ECON 113Introduction to Econometrics

5

ECON 114Advanced Quantitative Methods

6

ECON 115Introduction to Management Sciences

5

ECON 124Machine 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
MATH 105AReal Analysis

5

MATH 105BReal Analysis

5

MATH 105CReal Analysis

5

MATH 110Introduction to Number Theory

5

MATH 111AAlgebra

5

MATH 111TAlgebra

5

MATH 114Introduction to Financial Mathematics

5

MATH 115Graph Theory

5

MATH 116Combinatorics

5

MATH 117Advanced Linear Algebra

5

MATH 118Advanced Number Theory

5

MATH 120Coding Theory

5

MATH 121ADifferential Geometry

5

MATH 121BDifferential Geometry and Topology

5

MATH 124Introduction to Topology

5

MATH 130Celestial Mechanics

5

MATH 134Cryptography

5

MATH 140Industrial Mathematics

5

MATH 152Programming for Mathematics

5

MATH 160Mathematical Logic I

5

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 267Applied Environmental Time Series Analysis

5

OCEA 286Introduction to Ocean Modeling

5

Either of the following courses:
OCEA 100Physical Oceanography

5

OCEA 200Physical Oceanography

5

Either of the following courses:
OCEA 111Climate Dynamics

5

OCEA 211Climate Dynamics

5

Possible PHYS Electives

Note that many require lower-division PHYS courses:

PHYS 105Mechanics

5

PHYS 110AElectricity, Magnetism, and Optics

5

PHYS 110BElectricity, Magnetism, and Optics

5

PHYS 139AQuantum Mechanics I

5

PHYS 139BQuantum Mechanics II

5

PHYS 150
/CSE 109
Quantum Computing

5

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

5

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 108Linear Regression

5

STAT 132Classical and Bayesian Inference

5

STAT 205Introduction to Classical Statistical Learning

5

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:

AM 170AMathematical Modeling 1

5

AM 170BMathematical Modeling 2

5

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 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 AM100
3rd Year AM114 AM 170A Upper-div elective
Upper-div elective AM112
4th Year AM 129 AM 147 AM 170B
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 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
AM 114 AM 170A Upper-div elective
4th Year AM 129 AM 112 AM 170B
Upper-div elective 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 for the comprehensive exam track. For the thesis track, replace two (or three) M.S. electives with Independent Studies. Note that the planner must ensure that there are at least 35 credits taken as a graduate student during the M.S. year.

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 112 AM 170B
AM 114 AM 170A Upper-div elective
M.S. Year M.S. elective AM 213A AM 213B
M.S. elective AM 160 AM 250
Seminar M.S. elective Seminar