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:

Plus one of the following options:

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:

Plus one of the following options:*

Plus one of the following:

AM 10 is preferred 

Plus one of the following:

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:

Plus one of the following courses:

Plus one of the following courses:

Plus one of the following options:

Plus one of the following options:

Plus one of the following programming courses

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:

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):

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:

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:

Plus one of the following courses:

Plus one of the following courses:

Plus one of the following courses:

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

Possible CSE Electives

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

Possible EART Electives

Note that many require lower-division PHYS or CHEM courses:

Either of the following courses:

Either of the following courses:

Possible ECE Electives

Lecture-lab combinations count as one course.

Possible ECON Electives

Note that many require ECON lower-division courses:

Possible MATH Electives

Possible OCEA Electives

Note that some require lower-division PHYS electives, or upper-division ESCI electives:

Either of the following courses:

Either of the following courses:

Possible PHYS Electives

Note that many require lower-division PHYS courses:

Possible STAT Electives

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.

* 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.

* 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.

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.