Mathematics
B.S. Department of Mathematics · UC Irvine · 2026-2027 Catalog
The Department offers a B.S. in Mathematics. Within this program there are three tracks; besides the pure track, there is a specialization in Mathematics for Education and a Concentration in Mathematics for Education/Secondary Teaching certification. In addition, the Department offers a B.S. in Applied and Computational Mathematics (with concentrations in Data Science and Mathematical Finance and a specialization in Mathematical Biology) and a minor 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.
Admission
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.
Requirements
All students must meet the University Requirements. School Requirements: None.
Core Requirements for all Mathematics Majors
| Course | Title | Units |
|---|---|---|
| A. Complete: | ||
| MATH 2A & MATH 2B | Single-Variable Calculus Iand Single-Variable Calculus II | |
| MATH 2D | Multivariable Calculus I | |
| 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 | |
| MATH 120A | Introduction to Abstract Algebra: Groups | |
| MATH 121A | Linear Algebra I | |
| MATH 130A | Probability I | |
| MATH 140A & MATH 140B | Elementary Analysis Iand Elementary Analysis II | |
| B. Select one three-quarter lecture course sequence from the following: | ||
| CHEM 1A & CHEM 1B & CHEM 1C | General Chemistryand General Chemistryand General Chemistry | |
| PHYSICS 7C & PHYSICS 7D & PHYSICS 7E | Classical Physicsand Classical Physicsand Classical Physics | |
| STATS 7 & MATH 10 & PHYSICS 7C | Basic Statisticsand Introduction to Programming for Data Scienceand Classical Physics | |
Requirements for the Pure Mathematics Major
| Course | Title | Units |
|---|---|---|
| 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. | ||
The Department offers one concentration and one specialization. Note that both 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 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.
| Course | Title | Units |
|---|---|---|
| A. Complete Core Requirement A | ||
| B. Replace item B in the Core Requirements with the following: | ||
| STATS 7 & PHYSICS 7C & MATH 10 | Basic Statisticsand Classical Physicsand Introduction to Programming for Data Science | |
| C. Complete: | ||
| MATH 8 | Explorations in Functions and Modeling | |
| MATH 105A & MATH 105LA | Numerical Analysis Iand Numerical Analysis Laboratory | |
| MATH 120B | Introduction to Abstract Algebra: Rings and Fields | |
| MATH 150 | Introduction to Mathematical Logic | |
| MATH 161 | Modern Geometry | |
| MATH 180A | Number Theory I | |
| MATH 184 & MATH 184L | Topics in the History of Mathematicsand History of Mathematics Lesson Lab | |
| MATH 192 | Studies in the Learning and Teaching of Secondary Mathematics | |
| Plus two additional four-unit MATH courses numbered 100–189. | ||
| D. 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 | |
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.
| Course | Title | Units |
|---|---|---|
| A. Complete Core Requirement A | ||
| B. Replace item B in the Core Requirements with the following: | ||
| STATS 7 & PHYSICS 7C & MATH 10 | Basic Statisticsand Classical Physicsand Introduction to Programming for Data Science | |
| C. Complete: | ||
| MATH 8 | Explorations in Functions and Modeling | |
| MATH 105A & MATH 105LA | Numerical Analysis Iand Numerical Analysis Laboratory | |
| MATH 120B | Introduction to Abstract Algebra: Rings and Fields | |
| MATH 150 | Introduction to Mathematical Logic | |
| MATH 161 | Modern Geometry | |
| MATH 180A | Number Theory I | |
| MATH 184 & MATH 184L | Topics in the History of Mathematicsand History of Mathematics Lesson Lab | |
| Plus two additional four-unit MATH courses numbered 100–189. | ||
| D. Complete: | ||
| MATH 192 | Studies in the Learning and Teaching of Secondary Mathematics (Two quarters) | |
| orPHYSICS 193 | Research Methods | |
| orCHEM 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 Programs
Sample Program — Pure Mathematics
Freshman
| Fall | Winter | Spring |
|---|---|---|
| MATH 2A | MATH 2B | MATH 2D |
| General Education/Elective | MATH 13 | PHYSICS 7D or CHEM 1B |
| General Education/Elective | PHYSICS 7C or CHEM 1A | General Education/Elective |
| General Education/Elective | General Education/Elective | General Education/Elective |
Sophomore
| Fall | Winter | Spring |
|---|---|---|
| MATH 2E | MATH 3A | MATH 3D |
| PHYSICS 7E or CHEM 1C | MATH 9 | General Education/Elective |
| General Education/Elective | General Education/Elective | General Education/Elective |
| General Education/Elective | General Education/Elective | General Education/Elective |
Junior
| Fall | Winter | Spring |
|---|---|---|
| MATH 130A | MATH 140A | MATH 140B |
| MATH 120A | MATH 120B | MATH 141 |
| General Education/Elective | General Education/Elective | General Education/Elective |
| General Education/Elective | General Education/Elective | General Education/Elective |
Senior
| Fall | Winter | Spring |
|---|---|---|
| MATH 121A | MATH 121B | MATH 115 |
| MATH 150 | MATH 147 | General Education/Elective |
| MATH 112A | MATH 180A | General Education/Elective |
| General Education/Elective | General Education/Elective | General Education/Elective |
Sample Program — Mathematics Major Specializing in Mathematics for Education
Freshman
| Fall | Winter | Spring |
|---|---|---|
| MATH 2A | MATH 2B | MATH 2D |
| STATS 7 | PHYSICS 7C | MATH 9 |
| General Education | General Education | General Education |
| General Education/Elective | General Education | MATH 3A |
Sophomore
| Fall | Winter | Spring |
|---|---|---|
| MATH 192 | MATH 3D | MATH 8 |
| PHY SCI 5 | PHY SCI 105 | MATH 121A |
| MATH 13 | General Education | MATH 10 |
| General Education |
Junior
| Fall | Winter | Spring |
|---|---|---|
| MATH 130A | Math Elective (100-189) | MATH 161 |
| MATH 140A | MATH 120A | MATH 120B |
| General Education | MATH 140B | General Education/Elective |
Senior
| Fall | Winter | Spring |
|---|---|---|
| MATH 105A& MATH 105LA | MATH 180A | MATH 184& 184L |
| MATH 150 | General Education/Elective | General Educaton |
| General Education/Elective | Math. Elective | General Education |
Sample Program - Concentration in Mathematics for Education/Secondary Teaching Certification
Freshman
| Fall | Winter | Spring |
|---|---|---|
| MATH 2A | MATH 2B | MATH 2D |
| STATS 7 | PHYSICS 7C | General Education |
| PHY SCI 5 | General Education | MATH 8 |
| General Education | General Education | MATH 9 |
Sophomore
| Fall | Winter | Spring |
|---|---|---|
| MATH 3A | MATH 3D | MATH 161 |
| PHY SCI 105 | MATH 180A | MATH 121A |
| MATH 13 | CHEM 193, PHYSICS 193, or MATH 192 (two quarters) | MATH 10 |
Junior
| Fall | Winter | Spring |
|---|---|---|
| MATH 130A | Math Elective (100-189) | MATH 184& 184L |
| MATH 140A | MATH 120A | MATH 120B |
| EDUC 55 | MATH 140B | EDUC 148 |
| EDUC 143AW | Math Elective (100-189) |
Senior
| Fall | Winter | Spring |
|---|---|---|
| MATH 105A& MATH 105LA | EDUC 109 | EDUC 158 |
| MATH 150 | EDUC 158 | General Education |
| EDUC 143BW | General Education | General Education |
Honors
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:
| Course | Title | Units |
|---|---|---|
| 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: | ||
| 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 120C or MATH 140C) and MATH 180A - MATH 180B | ||
| or | ||
| (MATH 120C or MATH 140C) and MATH 162A - MATH 162B | ||
| 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. 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 2B | MATH 2D | MATH 2E |
| PHYSICS 7C& PHYSICS 7LC (or CHEM 1A) | PHYSICS 7D& PHYSICS 7LD (or CHEM 1B) | PHYSICS 7E or CHEM 1C |
| General Education/Elective | General Education/Elective | General Education/Elective |
| General Education/Elective | General Education/Elective | General Education/Elective |
Sophomore
| Fall | Winter | Spring |
|---|---|---|
| MATH 3A | MATH 3D | MATH 121B |
| MATH 13 | MATH 121A | General Education/Elective |
| General Education/Elective | MATH 9 | General Education/Elective |
| General Education/Elective | General Education/Elective | General Education/Elective |
Junior
| Fall | Winter | Spring |
|---|---|---|
| MATH 121A | MATH 121B | MATH 199 |
| MATH H140A | MATH H140B | MATH H140C |
| MATH 130A | MATH 162A | MATH 162B |
| General Education/Elective | General Education/Elective | General Education/Elective |
Senior
| Fall | Winter | Spring |
|---|---|---|
| MATH 120A | MATH 120B | MATH 120C |
| General Education/Elective | MATH 147 | General Education/Elective |
| MATH 199 | General Elective | MATH 141 |
Research in Mathematics
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:
- Algebra: MATH 120A-MATH 120B-MATH 120C
- Probability and Statistics: MATH 130A-MATH 130B-MATH 130C
- Analysis: MATH 140A-MATH 140B-MATH 140C
- Logic: MATH 150
- Geometry: MATH 162A-MATH 162B
- Number Theory: MATH 180A-MATH 180B
Program of Study
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 in Mathematics for Education should note that MATH 184 may not be offered more than once every other year and thus should be taken when offered.