2023-24 Edition

Mathematics, B.S.

The Department offers a B.S. in Mathematics. Within this program there are seven tracks; besides the standard track, there are six specializations or concentrations (in Mathematical Biology, Mathematical Finance, Data Science, Applied and Computational Mathematics, Mathematics for Education, and Mathematics for Education/Secondary Teaching Certification). In addition, the Department offers 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 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 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 3A Introduction to Linear Algebra
MATH 3D Elementary Differential Equations
MATH 13 Introduction to Abstract Mathematics
B. Computing skills:
MATH 9 Introduction to Programming for Numerical Analysis
C. Select one three-quarter lecture course sequence from the following:
General Chemistry
and General Chemistry
and General Chemistry
Classical Physics
and Classical Physics
and Classical Physics
Basic Statistics
and Introduction to Programming for Data Science
and Classical Physics
Upper-Division Requirements:
A. Complete:
MATH 120A Introduction to Abstract Algebra: Groups
MATH 121A Linear Algebra I
MATH 130A Probability I
MATH 140A- 140B Elementary Analysis I
and Elementary Analysis II

Requirements for the Pure Mathematics Major

Core requirements for all Mathematics majors plus:
Lower-Division Requirements:
A. Complete:
MATH 2E Multivariable Calculus II
Upper-Division Requirements:
A. Complete:
MATH 120B Introduction to Abstract Algebra: Rings and Fields
MATH 121B Linear Algebra II
MATH 147 Complex Analysis
B. Five additional four-unit MATH lecture courses numbered 100–189.
Sample Program — Pure Mathematics
Freshman
Fall Winter Spring
MATH 2AMATH 2BMATH 2D
PHYSICS 7C- 7LC (or CHEM 1A)PHYSICS 7D- 7LD (or CHEM 1B)PHYSICS 7E or CHEM 1C
General Education/ElectiveMATH 13General Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Sophomore
Fall Winter Spring
General Education/ElectiveMATH 3AMATH 3D
MATH 2EMATH 9General Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Junior
Fall Winter Spring
MATH 130AMATH 140AMATH 140B
MATH 120AMATH 120BMATH 141
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Senior
Fall Winter Spring
MATH 121AMATH 121BMATH 115
MATH 150MATH 147General Education/Elective
MATH 112AMATH 180AGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective

The Department offers two concentrations and three specializations. 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 Mathematics along with the lower- and upper-division requirements specified for each concentration and specialization.

Requirements for Mathematics Major with a Concentration in Data Science

Admission to this specialization 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 and must maintain the GPA to remain and graduate in the concentration. The admissions process begins with completing a form at the Department office, and includes an interview with the Department’s advisor for the specialization. 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 2E Multivariable Calculus II
B. Replace item C in the Core Requirements with the following:
MATH 10 Introduction to Programming for Data Science
STATS 7 Basic Statistics
PHYSICS 7C Classical Physics
Upper-Division Requirements
A. Complete:
MATH 105A- 105B Numerical Analysis I
and Numerical Analysis II
MATH 105LA- 105LB Numerical Analysis Laboratory
and Numerical Analysis Laboratory
MATH 121B Linear Algebra II
MATH 130B Probability II
MATH 110A- 110B Optimization I
and Optimization II
MATH 120B Introduction to Abstract Algebra: Rings and Fields
MATH 147 Complex Analysis
B. Select three electives from the following: 1
Mathematical Modeling
Dynamical Systems
The Theory of Differential Equations
Stochastic Processes
Fixed Income
and Mathematics of Financial Derivatives
Analysis in Several Variables
Introduction to Differential Geometry I
and Introduction to Differential Geometry II
Introduction to Cryptology I
and Introduction to Cryptology II
Combinatorics
Mathematics of Finance
Statistical Methods for Data Analysis I
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
and Computational Systems Biology
Sample Program - Mathematics Major Concentrating in Data Science
Freshman
Fall Winter Spring
MATH 2AMATH 2BMATH 3A
STATS 7PHYSICS 7CMATH 9
Sophomore
Fall Winter Spring
MATH 2DMATH 2EMATH 3D
MATH 13MATH 10 
Junior
Fall Winter Spring
MATH 105A- 105LAMATH 105B- 105LBMATH 120A
MATH 121AMATH 121BUpper-division elective
MATH 130AMATH 130B 
Senior
Fall Winter Spring
MATH 120BMATH 110AMATH 110B
MATH 140AMATH 140BMATH 147
Upper-Division ElectiveUpper-Division Elective 

Requirements for Mathematics Major with a Concentration in Mathematical Finance

Admission to this concentration requires approval in advance by the Mathematics Department. Students need a GPA of 3.0 in university mathematics courses to be admitted to the concentration and must maintain the GPA to remain and graduate in 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 at the Department office and includes an interview with the Department’s advisor for the concentration. 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 2E Multivariable Calculus II
B. Replace item C in the Core Requirements with the following:
MATH 10 Introduction to Programming for Data Science
STATS 7 Basic Statistics
PHYSICS 7C Classical Physics
Upper-Division Requirements:
A. Complete:
MATH 120B Introduction to Abstract Algebra: Rings and Fields
MATH 121B Linear Algebra II
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 147 Complex Analysis
B. Select one elective lecture course from the following:
Numerical Analysis I
and Numerical Analysis II (plus MATH 105LA-105LB)
Optimization I
Introduction to Cryptology I
Mathematics of Finance
Introduction to Artificial Intelligence
Neural Networks and Deep Learning
Applications of Probability in Computer Science
Machine Learning and Data-Mining
C. Complete the following eight required Economics courses:
ECON 20A- 20B Basic Economics I
and Basic Economics II
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 — Mathematics Major Concentrating in Mathematical Finance
Freshman
Fall Winter Spring
MATH 2AMATH 2BMATH 2D
STATS 7MATH 9MATH 10
General Education/ElectiveMATH 13General Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Sophomore
Fall Winter Spring
MATH 2EMATH 3AMATH 3D
ECON 20AECON 20BGeneral Education/Elective
General Education/ElectivePHYSICS 7CGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Junior
Fall Winter Spring
MATH 130AMATH 130BMATH 130C
MATH 140AMATH 140BMATH 140C
ECON 105AECON 105BECON 105C
MATH 121AMATH 121BGeneral Education/Elective
Senior
Fall Winter Spring
MATH 134AMATH 134BMATH 134C
MATH 120AMATH 176MATH 121A
ECON 134AECON 132AGeneral Education/Elective
MATH 147General Education/Elective 

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

Admission to this specialization requires approval in advance by the Mathematics Department. The admissions process begins with completing a form at the Department office, and includes an interview with the Department’s advisor for the specialization. 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 2E Multivariable Calculus II
Upper-Division Requirements:
A. Six required lecture courses:
MATH 105A- 105B Numerical Analysis I
and Numerical Analysis II (plus MATH 105LA-LB)
MATH 112A- 112B Introduction to Partial Differential Equations and Applications I
and Introduction to Partial Differential Equations and Applications II
MATH 115 Mathematical Modeling
MATH 121B Linear Algebra II
B. Select three additional Mathematics courses from the following:
Numerical Differential Equations (plus MATH 107L)
Optimization I
and Optimization II
Introduction to Partial Differential Equations and Applications III
Dynamical Systems
The Theory of Differential Equations
Probability II
and Stochastic Processes
Fixed Income
and Mathematics of Financial Derivatives
Analysis in Several Variables
Mathematics of Finance
C. Two approved upper-division courses in an area of application outside of Mathematics. Approval must be obtained in advance from the advisor for this specialization. The student is responsible for satisfying any prerequisites for these courses.
Sample Program — Mathematics Major Specializing in Applied and Computational Mathematics
Freshman
Fall Winter Spring
MATH 2AMATH 2BMATH 2D
PHYSICS 7C- 7LC (or CHEM 1A)PHYSICS 7D- 7LD (or CHEM 1B)PHYSICS 7E or CHEM 1C
General Education/ElectiveGeneral Education/ElectiveMATH 13
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Sophomore
Fall Winter Spring
MATH 2EMATH 3AMATH 3D
MATH 9General Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Junior
Fall Winter Spring
MATH 112AMATH 112BMATH 115
MATH 121AMATH 121BMATH 140B
MATH 130AMATH 140AGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Senior
Fall Winter Spring
MATH 105A- 105LAMATH 105B- 105LBMATH 107- 107L
MATH 117MATH 118Technical Elective
MATH 120ATechnical ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective

Requirements for Mathematics Major with a Specialization in Mathematical Biology

Admission to this specialization requires approval in advance by the Mathematics Department. The admissions process begins with completing a form at the Department Office, and includes an interview with the Department’s advisor for the specialization. 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 2E Multivariable Calculus II
B. Replace item C in the Core Requirements with the following:
BIO SCI 93 From DNA to Organisms
BIO SCI 94 From Organisms to Ecosystems
and two courses selected from the following:
Genetics
General Chemistry
General Chemistry
Introduction to Mathematical Methods for Physics
Classical Physics
Classical Physics
Upper-Division Requirements:
A. Complete the following seven required upper-division lecture courses:
Numerical Analysis I
and Numerical Analysis II (plus MATH 105LA-LB)
Introduction to Partial Differential Equations and Applications I
and Introduction to Partial Differential Equations and Applications II
Mathematical Modeling in Biology I
and Mathematical Modeling in Biology II
Mathematical Modeling
B. Two additional elective courses, at least one from MATH courses numbered 100–189. The second elective may be either an upper-division MATH course or a four-unit upper-division Biological Sciences course with the advanced approval by the advisor for this specialization.
Sample Program — Mathematics Major Specializing in Mathematical Biology
Freshman
Fall Winter Spring
MATH 2AMATH 2BMATH 2D
BIO SCI 93BIO SCI 94MATH 13
General EducationGeneral EducationGeneral Education
General EducationGeneral EducationGeneral Education
Sophomore
Fall Winter Spring
MATH 2EMATH 3AMATH 3D
CHEM 1ACHEM 1BGeneral Education/Elective
MATH 9General Education/ElectiveGeneral Education/Elective
General Education/Elective  
Junior
Fall Winter Spring
MATH 113AMATH 113BMATH 115
MATH 105A- 105LAMATH 105B- 105LBMATH 121A
General Education/ElectiveMATH 140AMATH 140B
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Senior
Fall Winter Spring
MATH 112AMATH 112BMATH 115
MATH 130AMATH 120AMATH Elective
Bio. ElectiveGeneral Education/ElectiveGeneral Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective

Requirements for Mathematics Major with a Specialization in Mathematics for Education

Admission to this specialization requires approval in advance by the Mathematics Department. The admission process begins with completing a form at the Department office, and includes an interview with the Department’s advisor for the specialization. This approval should be applied for no later than the end of the junior year.

This specialization is designed to help prepare students for teaching mathematics. Students wishing to go on and teach at the intermediate and high school levels should also consult with an academic advisor in the School of Education. A Commission on Teacher Credentialing (CTC)-approved subject-matter program (SMP) in Mathematics can be easily satisfied in tandem with this specialization, and enables students to waive a subject matter exam for teachers. Specific SMP requirements and enrollment procedures are available from the School of Education.

Core requirements for all Mathematics majors plus:
Lower-Division Requirements:
A. Complete:
MATH 8 Explorations in Functions and Modeling
Upper-Division Requirements:
A. Complete:
MATH 105A- 105LA Numerical Analysis I
and Numerical Analysis Laboratory
MATH 120B Introduction to Abstract Algebra: Rings and Fields
MATH 130B Probability II
MATH 150 Introduction to Mathematical Logic
MATH 161 Modern Geometry
MATH 180A Number Theory I
MATH 184- 184L History of Mathematics
and History of Mathematics Lesson Lab
Plus one additional four-unit MATH course numbered 100–189.
B. Complete:
PHY SCI 5 California Teach 1: Introduction to Science and Mathematics Teaching
PHY SCI 105 California Teach 2: Middle School Science and Mathematics Teaching
Sample Program — Mathematics Major Specializing in Mathematics for Education
Freshman
Fall Winter Spring
MATH 2AMATH 2BMATH 2D
PHYSICS 7C- 7LC (or CHEM 1A)PHYSICS 7D- 7LD (or CHEM 1B)PHYSICS 7E or CHEM 1C
General EducationMATH 13General Education
General Education/ElectiveGeneral Education 
Sophomore
Fall Winter Spring
MATH 3AMATH 3DMATH 8
PHY SCI 5PHY SCI 105MATH 121A
General EducationGeneral EducationMATH 9
General Education  
Junior
Fall Winter Spring
MATH 130AMATH 130BMATH 161
MATH 140AMATH 120AMATH 120B
General EducationMATH 140BGeneral Education/Elective
Senior
Fall Winter Spring
MATH 105A- 105LAMATH 180AMATH 184- 184L
MATH 150General Education/ElectiveGeneral Educaton
General Education/ElectiveMath. ElectiveGeneral Education

Requirements for Mathematics Major with a Concentration in Mathematics for Education/Secondary Teaching Certification

Admission to this concentration requires approval in advance. The admission process begins with completing an Intent form at the Cal Teach Resource and Advising Center.

Following completion of the Intent form, students must complete an application in the Mathematics Department office and an interview with the Department’s advisor for the concentration. These approvals should be applied for no later than the end of the sophomore year.

This concentration allows students pursuing the B.S. in Mathematics to earn a bachelor’s degree and complete the required course work and field experience for a California Preliminary Single Subject Teaching Credential at the same time. With careful, early planning, it is possible for students to complete both in four years. For additional information about teacher certification requirements and enrollment procedures, see Preparation for Teaching Science and Mathematics or contact the Cal Teach Resource and Advising Center. A Commission on Teacher Credentialing (CTC)-approved subject-matter program (SMP) in Mathematics can be satisfied in tandem with this concentration, and enables students to waive a subject matter exam for teachers. Specific SMP requirements and enrollment procedures are available from the Cal Teach Resource and Advising Center or the School of Education.

Core requirements for all Mathematics majors plus:
Lower-Division Requirements:
A. Complete:
MATH 8 Explorations in Functions and Modeling
Upper-Division Requirements:
A. Complete:
MATH 105A- 105LA Numerical Analysis I
and Numerical Analysis Laboratory
MATH 120B Introduction to Abstract Algebra: Rings and Fields
MATH 130B Probability II
MATH 150 Introduction to Mathematical Logic
MATH 161 Modern Geometry
MATH 180A Number Theory I
MATH 184- 184L History of Mathematics
and History of Mathematics Lesson Lab
Plus one addtional four-unit MATH course numbered 100–189.
B. Complete:
CHEM 193 Research Methods
or PHYSICS 193 Research Methods
EDUC 55 Knowing and Learning in Mathematics and Science
EDUC 109 Reading and Writing in Mathematics and Science
EDUC 143AW Classroom Interactions I
EDUC 143BW Classroom Interactions II
EDUC 148 Complex Pedagogical Design
EDUC 158 Student Teaching Mathematics and Science in Middle/High School (two quarters)
PHY SCI 5 California Teach 1: Introduction to Science and Mathematics Teaching
PHY SCI 105 California Teach 2: Middle School Science and Mathematics Teaching

NOTE: Students may pursue either the concentration in Mathematics for Education/Secondary Teaching Certification or the specialization in Mathematics for Education, but not both.

Sample Program - Concentration in Mathematics for Education/Secondary Teaching Certification
Freshman
Fall Winter Spring
MATH 2AMATH 2BMATH 2D
PHYSICS 7C- 7LC (or CHEM 1A)PHYSICS 7D- 7LD (or CHEM 1B)PHYSICS 7E or CHEM 1C
PHY SCI 5MATH 13MATH 8
General EducationGeneral EducationMATH 9
Sophomore
Fall Winter Spring
MATH 3AMATH 3DMATH 161
PHY SCI 105MATH 180AMATH 121A
General EducationCHEM 193General Education
Junior
Fall Winter Spring
MATH 130AMATH 130BMATH 184- 184L
MATH 140AMATH 120AMATH 120B
EDUC 55MATH 140BEDUC 148
 EDUC 143AWMath. Elective
Senior
Fall Winter Spring
MATH 105A- 105LAEDUC 109EDUC 158
MATH 150EDUC 158General Education
EDUC 143BWGeneral EducationGeneral Education
 

The Honors Program in Mathematics is designed for students contemplating graduate work in 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 Mathematics (in any one of its tracks)
B. Complete:
MATH 120B Introduction to Abstract Algebra: Rings and Fields
MATH 121B Linear Algebra II
C. Complete one of the following series:
Honors Introduction to Graduate Analysis I
Honors Introduction to Graduate Analysis II
Honors Introduction to Graduate Analysis III
or
or
or
or
or
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 Mathematics major requirements and the requirements for any specialization/concentration. However, MATH H120A-MATH H120B-MATH H120C in item C may be used to satisfy upper-division electives or taken in place of MATH 120A-MATH 120B-MATH 120C and MATH 121A-MATH 121B. Similarly, 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 — Mathematics Major Honors Program

Freshman
Fall Winter Spring
MATH 2BMATH 2DMATH 2E
PHYSICS 7C- 7LC (or CHEM 1A)PHYSICS 7D- 7LD (or CHEM 1B)PHYSICS 7E or CHEM 1C
General Education/ElectiveMATH 13General Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Sophomore
Fall Winter Spring
MATH 3AMATH 3DMATH 121B
General Education/ElectiveMATH 121AGeneral Education/Elective
General Education/ElectiveMATH 9General Education/Elective
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Junior
Fall Winter Spring
MATH 121AMATH 121BMATH 199
MATH H140AMATH H140BMATH H140C
MATH 130AMATH 162AMATH 162B
General Education/ElectiveGeneral Education/ElectiveGeneral Education/Elective
Senior
Fall Winter Spring
MATH 120AMATH 120BMATH 120C
General Education/ElectiveMATH 147General Education/Elective
MATH 199General ElectiveMATH 141

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).

Those in the specialization for Education should note that MATH 184 may not be offered more than once every other year and thus should be taken when offered.