Applied Mathematics B.S.

• Information and Policies
• Requirements and Planners

Information and Policies

Introduction Expand and Collapse

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 Expand and Collapse

Baskin Engineering's Undergraduate Advising Office is located in the Baskin Engineering Building, Room 225. It can be contacted by email at [e-mail] 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 Expand and Collapse

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 Expand and Collapse

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 Expand and Collapse

Transfer Admission Screening Policy Expand and Collapse

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 Expand and Collapse

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 Expand and Collapse

Major Qualification Expand and Collapse

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

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 Expand and Collapse

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 Expand and Collapse

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 Expand and Collapse

Baskin Engineering requires letter grades for all courses in an engineering major.

Course Substitution Policy Expand and Collapse

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 Expand and Collapse

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 Expand and Collapse

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 Expand and Collapse

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

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Course Requirements Expand and Collapse

Course requirements are divided into foundational lower-division courses and advanced upper-division courses:

Lower-Division Courses Expand and Collapse

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

AM 10 is preferred.

Plus one of the following courses:

AM 20	Mathematical Methods for Engineers II	5
MATH 24	Ordinary Differential Equations	5

AM 20 is preferred.

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.

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
ASTR 19	Practical 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 Expand and Collapse

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 5A	Introduction to Physics I	5
PHYS 5B	Introduction to Physics II	5
PHYS 5C	Introduction to Physics III	5
PHYS 6A	Introductory Physics I	5
PHYS 6B	Introductory Physics II	5
PHYS 6C	Introductory Physics III	5
ASTR 21	The 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 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. Note that lecture/lab combinations count as one course.

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 7L	Statistical Methods for the Biological, Environmental, and Health Sciences Laboratory	2
STAT 17	Statistical Methods for Business and Economics	5
STAT 17L	Statistical 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 20A	Cell and Molecular Biology	5
BIOE 20C	Ecology and Evolution	5

Upper-Division Courses Expand and Collapse

Complete the following core courses:

AM 100	Mathematical Methods for Engineers	5
AM 129	Foundations of Scientific Computing for Scientists and Engineers	5

Plus one of the following courses:

AM 147	Computational Methods and Applications	5
MATH 148	Numerical Analysis	5

Plus the following courses:

AM 112	Introduction to Partial Differential Equations	5
AM 114	Introduction to Dynamical Systems	5

Plus one of the following courses:

STAT 131	Introduction to Probability Theory	5
CSE 107	Probability and Statistics for Engineers	5

Upper-Division Electives Expand and Collapse

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 112	Physics of Stars	5
ASTR 113	Introduction to Cosmology	5
ASTR 119	Introduction to Scientific Computing	5

Possible BME electives

BME 160

Research 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 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:

EART 112	Geophysical Data Science	5
EART 118	Seismotectonics	5
EART 119A	Introduction to Scientific Programming	5
EART 121	The Atmosphere	5
EART 124	Modeling Earth's Climate	5
EART 160	Planetary Science	5
EART 162	Planetary Interiors	5
EART 163	Planetary Surfaces	5
EART 164	Planetary Atmospheres	5

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

MATH 105A	Real Analysis	5
MATH 105B	Real Analysis	5
MATH 105C	Real Analysis	5
MATH 110	Introduction to Number Theory	5
MATH 111A	Algebra	5
MATH 111T	Algebra	5
MATH 114	Introduction to Financial Mathematics	5
MATH 115	Graph Theory	5
MATH 116	Combinatorics	5
MATH 117	Advanced Linear Algebra	5
MATH 118	Advanced Number Theory	5
MATH 120	Coding Theory	5
MATH 121A	Differential Geometry	5
MATH 121B	Differential Geometry and Topology	5
MATH 124	Introduction to Topology	5
MATH 130	Celestial Mechanics	5
MATH 134	Cryptography	5
MATH 140	Industrial Mathematics	5
MATH 152	Programming for Mathematics	5
MATH 160	Mathematical 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 267	Applied Environmental Time Series Analysis	5
OCEA 286	Introduction to Ocean Modeling	5

Either of the following courses:

OCEA 100	Physical Oceanography	5
OCEA 200	Physical Oceanography	5

Either of the following courses:

OCEA 111	Climate Dynamics	5
OCEA 211	Climate Dynamics	5

Possible PHYS Electives

Note that many require lower-division PHYS courses:

PHYS 105	Mechanics	5
PHYS 110A	Electricity, Magnetism, and Optics	5
PHYS 110B	Electricity, Magnetism, and Optics	5
PHYS 139A	Quantum Mechanics I	5
PHYS 139B	Quantum 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 108	Linear Regression	5
STAT 132	Classical and Bayesian Inference	5
STAT 205	Introduction 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 Expand and Collapse

The DC requirement in the Applied Mathematics B.S. is satisfied by completing the capstone course AM 170A (see below).

Comprehensive Requirement Expand and Collapse

Students satisfy the senior comprehensive requirement by receiving a passing grade in the two Mathematical Modeling courses:

AM 170A	Mathematical Modeling 1	5
AM 170B	Mathematical Modeling 2	5

Planners Expand and Collapse

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