2024-25 Edition

Applied and Computational Mathematics, B.S.

The Department offers a B.S. in Applied and Computational Mathematics. Within this program there are four tracks; besides the standard track, there is one specialization (in Mathematical Biology) and two concentrations (in Mathematical Finance and Data Science). In addition, the Department offers a B.S. in Mathematics (which focuses more on topics in pure mathematics) and minors in Mathematics and Mathematics for Biology.

Undergraduate mathematics courses are of several kinds: courses preparatory to advanced work in mathematics, the exact sciences, and engineering; courses for students of the social and biological sciences; and courses for liberal arts students and those planning to enter the teaching field.

Students may be admitted to the Applied and Computational Mathematics major upon entering the University as freshmen, via change of major, or as transfer students from other colleges and universities. Information about change of major policies is available in the Physical Sciences Student Affairs Office and at the UCI Change of Major Criteria website. For transfer student admission, preference will be given to junior-level applicants with the highest grades overall and who have satisfactorily completed the required coursework of one year of approved calculus. Additional course work in multivariable calculus, linear algebra, and differential equations is strongly recommended.

All students must meet the University Requirements.
School Requirements: None.
Core Requirements for all Applied and Computational Mathematics Majors
Lower-Division Requirements:
A. Complete the following:
MATH 2A- 2B Single-Variable Calculus I
and Single-Variable Calculus II
MATH 2D Multivariable Calculus I
MATH 2E Multivariable Calculus II
MATH 3A Introduction to Linear Algebra
MATH 3D Elementary Differential Equations
MATH 9 Introduction to Programming for Numerical Analysis
MATH 13 Introduction to Abstract Mathematics
Upper-Division Requirements:
A. Complete the following:
MATH 105A- 105LA Numerical Analysis I
and Numerical Analysis Laboratory
MATH 105B- 105LB Numerical Analysis II
and Numerical Analysis Laboratory
MATH 121A- 121B Linear Algebra I
and Linear Algebra II
MATH 130A Probability I
MATH 140A- 140B Elementary Analysis I
and Elementary Analysis II

Requirements for the Applied and Computational Mathematics Major

Core requirements for all Applied and Computational Mathematics majors plus:
Lower-Division Requirements:
A. Select three lower-division courses from the following:
From DNA to Organisms
and DNA to Organisms - Introduction to Biology Research
From Organisms to Ecosystems
and Organisms to Ecosystems - Introduction to Biology Research Analysis
Genetics
General Chemistry
General Chemistry
General Chemistry
Introduction to Programming for Data Science
Classical Physics
Classical Physics
Classical Physics
Basic Statistics
Upper-Division Requirements:
A. Complete:
MATH 112A- 112B Introduction to Partial Differential Equations and Applications I
and Introduction to Partial Differential Equations and Applications II
MATH 115 Mathematical Modeling
B. Select three additional upper-division MATH courses from the following:
Numerical Differential Equations
and Numerical Differential Equations Laboratory
Optimization I
Optimization II
Introduction to Partial Differential Equations and Applications III
Mathematical Modeling in Biology I
Mathematical Modeling in Biology II
Mathematical Modeling
Dynamical Systems
The Theory of Differential Equations
Introduction to Abstract Algebra: Groups
Probability II
Stochastic Processes
Fixed Income
Mathematics of Financial Derivatives
Analysis in Several Variables
Complex Analysis
Mathematics of Finance
Mathematical Machine Learning
C. Select two 4-unit upper-division courses in an area outside of mathematics from the below list or obtain advanced approval from an Applied and Computational Mathematics advisor for courses outside of this list:
Introduction to Data Management
Design and Analysis of Algorithms
Introduction to Artificial Intelligence
Neural Networks and Deep Learning
Machine Learning and Data-Mining
Introduction to Computational Biology
Intermediate Economics I
Intermediate Quantitative Economics I
Intermediate Quantitative Economics II
Management Science
Introduction to Marketing
Introduction to Management Information Systems
Introduction to Logic
Introduction to Set Theory and Mathematical Reasoning
Metalogic
Computational Methods
Classical Mechanics
Classical Mechanics
Relativity and Black Holes
Mathematical Physics
Mathematical Physics
Statistical Methods for Data Analysis I
Statistical Methods for Data Analysis II
Statistical Methods for Data Analysis III
Introduction to Probability and Statistics II
Sample Program — Applied and Computational Mathematics
Freshman
Fall Winter Spring
MATH 2AMATH 2BMATH 2D
PHYSICS 7C or CHEM 1APHYSICS 7D or CHEM 1BPHYSICS 7E or CHEM 1C
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Sophomore
Fall Winter Spring
MATH 2EMATH 3AMATH 3D
MATH 9MATH 13General Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Junior
Fall Winter Spring
MATH 105A- 105LAMATH 105B- 105LBMATH 121B
MATH 130AMATH 121AUpper-Division Math Elective
General Education/ElectiveUpper-Division Math ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Senior
Fall Winter Spring
MATH 112AMATH 112BMATH 115
MATH 140AMATH 140BNon-Math Elective
Upper-Division Math ElectiveNon-Math ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective

The Applied and Computational Mathematics major offers two concentrations and one specialization. Note that all require the completion of an application and an interview with the faculty advisor for that concentration or specialization. Admission into a concentration or specialization is not guaranteed. Students must complete the basic "Core" requirements for the B.S. in Applied and Computational Mathematics along with the lower- and upper-division requirements specified for each concentration and specialization. Students choosing to specialize or concentrate can only do so with a single specialization/concentration.

Requirements for Applied and Computational Mathematics Major with a Concentration in Data Science

Admission to this concentration requires approval in advance by the Mathematics Department. Students need a GPA of 3.0 in all lower-division and upper-division MATH courses to be admitted to the concentration. Before applying, students should have finished all lower-division requirements for the Data Science concentration. The admissions process begins with completing a Data Science concentration advising form and includes an interview with the Department's advisor for the concentration. This approval should be applied for no later than the end of the junior year.

Core requirements for all Mathematics majors plus:
Lower-Division Requirements:
A. Complete:
MATH 10 Introduction to Programming for Data Science
STATS 7 Basic Statistics
PHYSICS 7C Classical Physics
Upper-Division Requirements:
A. Complete:
MATH 110A- 110B Optimization I
and Optimization II
MATH 130B Probability II
B. Complete five electives from the list below, with at least one course outside of MATH. Other options may be chosen in consultation with the Data Science concentration advisor
Mathematical Modeling
Dynamical Systems
The Theory of Differential Equations
Introduction to Abstract Algebra: Rings and Fields
Stochastic Processes
Fixed Income
Mathematics of Financial Derivatives
Analysis in Several Variables
Complex Analysis
Introduction to Differential Geometry I
Introduction to Differential Geometry II
Introduction to Cryptology I
Introduction to Cryptology II
Combinatorics
Mathematics of Finance
Mathematical Machine Learning
Statistical Methods for Data Analysis I
Statistical Methods for Data Analysis II
Introduction to Artificial Intelligence
Neural Networks and Deep Learning
Applications of Probability in Computer Science
Machine Learning and Data-Mining
Algorithms for Probabilistic and Deterministic Graphical Models
Introduction to Computational Biology
Artificial Intelligence in Biology and Medicine
Computational Systems Biology
Sample Program — Applied and Computational Mathematics Major Concentrating in Data Science
Freshman
Fall Winter Spring
MATH 2AMATH 2BMATH 3A
STATS 7PHYSICS 7CMATH 9
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Sophomore
Fall Winter Spring
MATH 2DMATH 2EMATH 3D
MATH 13MATH 10General Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Junior
Fall Winter Spring
MATH 105A- 105LAMATH 105B- 105LBMATH 121B
MATH 130AMATH 121AUpper-Division Math Elective
General Education/ElectiveMATH 130BUpper-Division Math Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Senior
Fall Winter Spring
MATH 140AMATH 110AMATH 110B
Non-Math ElectiveMATH 140BUpper-Division Math Elective
General Education/ElectiveUpper-Division Math ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective

Requirements for Applied and Computational Mathematics Major with a Concentration in Mathematical Finance

Admission to this concentration requires approval in advance by the Mathematical Finance advisor. Students need a GPA of 3.0 in lower-division and upper-division mathematics courses to be admitted to the concentration. The department may limit the number of students admitted into this concentration during impacted years. The admissions process begins with completing a form and submitting it to the Mathematical Finance advisor, followed by an interview. This approval should be applied for after the student has completed ECON 20A-ECON 20B, but no later than the end of the junior year.

Core requirements for all Mathematics majors plus:
Lower-Division Requirements:
A. Complete:
MATH 10 Introduction to Programming for Data Science
STATS 7 Basic Statistics
PHYSICS 7C Classical Physics
ECON 20A- 20B Basic Economics I
and Basic Economics II
Upper-Division Requirements:
A. Complete the following upper-division MATH courses:
MATH 130B Probability II
MATH 130C Stochastic Processes
MATH 134A Fixed Income
MATH 134B Mathematics of Financial Derivatives
MATH 134C Mathematical Models for Finance
MATH 176 Mathematics of Finance
B. Complete the following six required upper-division ECON courses:
ECON 105A- 105B- 105C Intermediate Quantitative Economics I
and Intermediate Quantitative Economics II
and Intermediate Quantitative Economics III
ECON 122A Applied Econometrics I
or ECON 123A Econometrics I
ECON 132A Introduction to Financial Investments
ECON 134A Corporate Finance
or ECON 161A Money and Banking
Sample Program - Applied and Computational Mathematics Major Concentrating in Mathematical Finance
Freshman
Fall Winter Spring
MATH 2AMATH 2BMATH 2D
STATS 7MATH 9MATH 10
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Sophomore
Fall Winter Spring
MATH 2EMATH 3AMATH 3D
ECON 20AECON 20BMATH 13
PHYSICS 7CGeneral Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Junior
Fall Winter Spring
MATH 130AMATH 130BMATH 130C
MATH 121AMATH 121BMATH 134A
ECON 105AECON 105BECON 105C
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Senior
Fall Winter Spring
MATH 105A- 105LAMATH 105B- 105LBMATH 134C
ECON 134AMATH 140AMATH 140B
ECON 132AMATH 134BECON 122A
General Education/ElectiveMATH 176General Education/Elective
 

Requirements for Applied and Computational Mathematics Major with a Specialization in Mathematical Biology

Admission to this specialization requires approval in advance by the Mathematical Biology advisor. The admissions process begins with completing a form at the Mathematical Biology advisor and includes and interview. This approval should be applied for no later than the end of the junior year.
 
Core requirements for all Mathematics majors plus:
Lower-Division Requirements:
A. Complete:
BIO SCI 93- 93L From DNA to Organisms
and DNA to Organisms - Introduction to Biology Research
BIO SCI 94- 94L From Organisms to Ecosystems
and Organisms to Ecosystems - Introduction to Biology Research Analysis
MATH 10 Introduction to Programming for Data Science
Upper-Division Requirements:
A. Complete the following upper-division MATH courses:
MATH 112A- 112B Introduction to Partial Differential Equations and Applications I
and Introduction to Partial Differential Equations and Applications II
MATH 113A- 113B Mathematical Modeling in Biology I
and Mathematical Modeling in Biology II
MATH 115 Mathematical Modeling
B. Complete three elective courses, at least two MATH courses numbered 100-189. The third elective may be either a MATH course numbered 100-189 or a 4-unit upper-division Biological Sciences courses with advanced approval by the Mathematical Biology advisor.
Sample Program - Applied and Computational Mathematics Major Specializing in Mathematical Biology
Freshman
Fall Winter Spring
MATH 2AMATH 2BMATH 2D
BIO SCI 93- 93LBIO SCI 94- 94LGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Sophomore
Fall Winter Spring
MATH 2EMATH 3AMATH 3D
MATH 9MATH 10MATH 13
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Junior
Fall Winter Spring
MATH 113AMATH 113BMATH 115
MATH 105A- 105LAMATH 105B- 105LBMATH 130A
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Senior
Fall Winter Spring
MATH 112AMATH 112BMATH 140B
MATH 121AMATH 121BUpper-Division Math Elective
Upper-Division Bio Sci ElectiveMATH 140AGeneral Education/Elective
General Education/ElectiveUpper-Division Math ElectiveGeneral Education/Elective
NOTE: Students majoring in Applied and Computational Mathematics may not minor in Mathematics or Mathematics for Biology and may not double major in Mathematics. Likewise, students majoring in Mathematics may not minor in Mathematics or Mathematics for Biology and may not double major in Applied and Computational Mathematics. Students wishing to specialize or concentrate within the Applied and Computational Mathematics major may only do so in one specialization/concentration.
 

The Honors Program in Applied and Computational Mathematics is designed for students contemplating graduate work in applied mathematics. The program is open to junior and senior Mathematics majors who meet the minimum academic qualifications of a 3.5 GPA in Mathematics courses and a 3.2 GPA overall. It is highly recommended that students meet with the Honors Advisor by the beginning of their junior year to begin planning courses. Students should officially apply for the Honors Program no later than the fall quarter of their senior year. Recognition for completing the program is conferred upon graduation.

Participants must meet the following requirements:

A. Complete the requirements for the major in Applied and Computational Mathematics (in any one of its tracks)
B. Complete:
MATH 130B- 130C Probability II
and Stochastic Processes
C. Complete one of the following series:
MATH H140A Honors Introduction to Graduate Analysis I
MATH H140B Honors Introduction to Graduate Analysis II
MATH H140C Honors Introduction to Graduate Analysis III
or
MATH 140C and MATH 134A-MATH 134B
or
MATH 140C and MATH 112A-MATH 112B
or
MATH 140C and MATH 113A-MATH 113B
or
MATH 140C and MATH 117-MATH 118
or
MATH 140C and MATH 110A-MATH 110B
D. Complete one quarter of MATH 199 or a research project and thesis approved by the Honors Program Advisor.

These requirements are in addition to the Applied and Computational Mathematics major requirements and the requirements for any specialization/concentration. MATH H140A-MATH H140B-MATH H140C may be used to satisfy upper-division electives or taken in place of MATH 140A-MATH 140B-MATH 140C and MATH 141.

NOTE: If all requirements are completed and the student's work and final GPA satisfies the program restrictions, the student will graduate with Honors in Mathematics, and this distinction is noted on the transcript.

Sample Program - Applied and Computational Mathematics Major Honors Program
Freshman
Fall Winter Spring
MATH 2AMATH 2BMATH 2D
STATS 7PHYSICS 7CMATH 13
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Sophomore
Fall Winter Spring
MATH 2EMATH 3DMATH 10
MATH 3AMATH 9General Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Junior
Fall Winter Spring
MATH 105A- 105LAMATH 105B- 105LBMATH 130C
MATH 130AMATH 130BMATH 121B
Upper-Division Math ElectiveMATH 121ANon-Math Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Senior
Fall Winter Spring
MATH H140AMATH H140BMATH H140C
MATH 112AMATH 112BMATH 115
MATH 199Upper-Division Math ElectiveUpper-Division Math Elective
Non-Math ElectiveGeneral Education/ElectiveGeneral Education/Elective

In order to prepare for independent study/independent research, it is highly recommended that students take at least one course sequence in the field they are interested in studying. The following list contains the major mathematical disciplines and the course work suggested for completion prior to doing independent study in that field:

For all Mathematics majors, or prospective majors, assistance in planning a program of study is available from the School of Physical Sciences academic counselors, as well as from the Mathematics Department Undergraduate Advisor for the various tracks. The application process for the specializations and concentrations requires students to plan a program of study with the assistance of a faculty advisor (https://www.math.uci.edu/undergraduate-studies/concentrations-and-specializations).