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 juniorlevel 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
LowerDivision Requirements:  
A. Complete the following:  
MATH 2A 2B  SingleVariable Calculus and SingleVariable Calculus 
MATH 2D  Multivariable Calculus 
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 threequarter 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  
UpperDivision Requirements:  
A. Complete:  
MATH 120A  Introduction to Abstract Algebra: Groups 
MATH 121A  Linear Algebra 
MATH 130A  Probability I 
MATH 140A 140B  Elementary Analysis and Elementary Analysis 
Requirements for the Pure Mathematics Major
Core requirements for all Mathematics majors plus:  
LowerDivision Requirements:  
A. Complete:  
MATH 2E  Multivariable Calculus 
UpperDivision Requirements:  
A. Complete:  
MATH 120B  Introduction to Abstract Algebra: Rings and Fields 
MATH 121B  Linear Algebra 
MATH 147  Complex Analysis 
B. Five additional fourunit MATH lecture courses numbered 100–189. 
Sample Program — Pure Mathematics
Freshman  

Fall  Winter  Spring 
MATH 2A  MATH 2B  MATH 2D 
PHYSICS 7C 7LC (or CHEM 1A)  PHYSICS 7D 7LD (or CHEM 1B)  PHYSICS 7E or CHEM 1C 
General Education/Elective  MATH 13  General Education/Elective 
General Education/Elective  General Education/Elective  General Education/Elective 
Sophomore  
Fall  Winter  Spring 
General Education/Elective  MATH 3A  MATH 3D 
MATH 2E  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 
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 upperdivision 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 lowerdivision and upperdivision 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:  
LowerDivision Requirements:  
A. Complete:  
MATH 2E  Multivariable Calculus 
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 
UpperDivision Requirements  
A. Complete:  
MATH 105A 105B  Numerical Analysis I and Numerical Analysis II 
MATH 121B  Linear Algebra 
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  
Statistical Methods with Applications to Finance and Statistical Methods with Applications to Finance  
Fixed Income and Mathematics of Financial Derivatives  
Analysis in Several Variables  
Introduction to Differential Geometry and Introduction to Differential Geometry  
Introduction to Cryptology and Introduction to Cryptology  
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 DataMining  
Algorithms for Probabilistic and Deterministic Graphical Models  
Introduction to Computational Biology  
Artificial Intelligence in Biology and Medicine and Computational Systems Biology  
Digital Information Systems 
^{1}  At least one of the electives must be from outside the Mathematics department. Other upperdivision elective courses may be chosen with the approval of the faculty advisor. 
Sample Program  Mathematics Major Concentrating in Data Science
Freshman  

Fall  Winter  Spring 
MATH 2A  MATH 2B  MATH 3A 
STATS 7  PHYSICS 7C  MATH 9 
Sophomore  
Fall  Winter  Spring 
MATH 10  MATH 2D  MATH 2E 
MATH 13  MATH 3D  
Junior  
Fall  Winter  Spring 
MATH 105A  MATH 105B  MATH 120A 
MATH 121A  MATH 121B  
MATH 130A  MATH 130B  
Senior  
Fall  Winter  Spring 
MATH 110A  MATH 110B  UpperDivision Elective 
MATH 140A  MATH 140B  
UpperDivision Elective  UpperDivision 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 20AECON 20B, but no later than the end of the junior year.
Core requirements for all Mathematics majors plus:  
LowerDivision Requirements:  
A. Complete:  
MATH 2E  Multivariable Calculus 
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 
UpperDivision Requirements:  
A. Complete:  
MATH 120B  Introduction to Abstract Algebra: Rings and Fields 
MATH 121B  Linear Algebra 
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 105LA105LB)  
Optimization I  
Introduction to Cryptology  
Mathematics of Finance  
Introduction to Artificial Intelligence  
Neural Networks and Deep Learning  
Applications of Probability in Computer Science  
Machine Learning and DataMining  
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 2A  MATH 2B  MATH 2D 
STATS 7  MATH 9  MATH 10 
General Education/Elective  MATH 13  General Education/Elective 
General Education/Elective  General Education/Elective  General Education/Elective 
Sophomore  
Fall  Winter  Spring 
MATH 2E  MATH 3A  MATH 3D 
ECON 20A  ECON 20B  General Education/Elective 
General Education/Elective  PHYSICS 7C  General Education/Elective 
General Education/Elective  General Education/Elective  General Education/Elective 
Junior  
Fall  Winter  Spring 
MATH 130A  MATH 130B  MATH 130C 
MATH 140A  MATH 140B  MATH 140C 
ECON 105A  ECON 105B  ECON 105C 
MATH 121A  MATH 121B  General Education/Elective 
Senior  
Fall  Winter  Spring 
MATH 134A  MATH 134B  MATH 134C 
MATH 120A  MATH 176  MATH 121A 
ECON 134A  ECON 132A  General Education/Elective 
MATH 147  General 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:  
LowerDivision Requirements:  
A. Complete:  
MATH 2E  Multivariable Calculus 
UpperDivision Requirements:  
A. Six required lecture courses:  
MATH 105A 105B  Numerical Analysis I and Numerical Analysis II (plus MATH 105LALB) 
MATH 112A 112B  Introduction to Partial Differential Equations and Applications and Introduction to Partial Differential Equations and Applications 
MATH 115  Mathematical Modeling 
MATH 121B  Linear Algebra 
B. Select three additional Mathematics courses from the following:  
Numerical Differential Equations (plus MATH 107L)  
Introduction to Partial Differential Equations and Applications  
Dynamical Systems  
The Theory of Differential Equations  
Probability II and Stochastic Processes  
Statistical Methods with Applications to Finance and Statistical Methods with Applications to Finance  
Fixed Income and Mathematics of Financial Derivatives  
Analysis in Several Variables  
Mathematics of Finance  
C. Two approved upperdivision 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 2A  MATH 2B  MATH 2D 
PHYSICS 7C 7LC (or CHEM 1A)  PHYSICS 7D 7LD (or CHEM 1B)  PHYSICS 7E or CHEM 1C 
General Education/Elective  General Education/Elective  MATH 13 
General Education/Elective  General Education/Elective  General Education/Elective 
Sophomore  
Fall  Winter  Spring 
MATH 2E  MATH 3A  MATH 3D 
MATH 9  General Education/Elective  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 112A  MATH 112B  MATH 115 
MATH 121A  MATH 121B  MATH 140B 
MATH 130A  MATH 140A  General Education/Elective 
General Education/Elective  General Education/Elective  General Education/Elective 
Senior  
Fall  Winter  Spring 
MATH 105A 105LA  MATH 105B 105LB  MATH 107 107L 
MATH 117  MATH 118  Technical Elective 
MATH 120A  Technical Elective  General Education/Elective 
General Education/Elective  General Education/Elective  General 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:  
LowerDivision Requirements:  
A. Complete:  
MATH 2E  Multivariable Calculus 
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  
UpperDivision Requirements:  
A. Complete the following seven required upperdivision lecture courses:  
Numerical Analysis I and Numerical Analysis II (plus MATH 105LALB)  
Introduction to Partial Differential Equations and Applications and Introduction to Partial Differential Equations and Applications  
Mathematical Modeling in Biology and Mathematical Modeling in Biology  
Mathematical Modeling  
B. Two additional elective courses, at least one from MATH courses numbered 100–189. The second elective may be either an upperdivision MATH course or a fourunit upperdivision 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 2A  MATH 2B  MATH 2D 
BIO SCI 93  BIO SCI 94  MATH 13 
General Education  General Education  General Education 
General Education  General Education  General Education 
Sophomore  
Fall  Winter  Spring 
MATH 2E  MATH 3A  MATH 3D 
CHEM 1A  CHEM 1B  General Education/Elective 
MATH 9  General Education/Elective  General Education/Elective 
General Education/Elective  
Junior  
Fall  Winter  Spring 
MATH 113A  MATH 113B  MATH 115 
MATH 105A 105LA  MATH 105B 105LB  MATH 121A 
General Education/Elective  MATH 140A  MATH 140B 
General Education/Elective  General Education/Elective  General Education/Elective 
Senior  
Fall  Winter  Spring 
MATH 112A  MATH 112B  MATH 115 
MATH 130A  MATH 120A  MATH Elective 
Bio. Elective  General Education/Elective  General Education/Elective 
General Education/Elective  General Education/Elective  General 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 subjectmatter 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:  
LowerDivision Requirements:  
A. Complete:  
MATH 8  Explorations in Functions and Modeling 
UpperDivision 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 
MATH 184 184L  History of Mathematics and History of Mathematics Lesson Lab 
Plus one additional fourunit 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 2A  MATH 2B  MATH 2D 
PHYSICS 7C 7LC (or CHEM 1A)  PHYSICS 7D 7LD (or CHEM 1B)  PHYSICS 7E or CHEM 1C 
General Education  MATH 13  General Education 
General Education/Elective  General Education  
Sophomore  
Fall  Winter  Spring 
MATH 3A  MATH 3D  MATH 8 
PHY SCI 5  PHY SCI 105  MATH 121A 
General Education  General Education  MATH 9 
General Education  
Junior  
Fall  Winter  Spring 
MATH 130A  MATH 130B  MATH 161 
MATH 140A  MATH 120A  MATH 120B 
General Education  MATH 140B  General Education/Elective 
Senior  
Fall  Winter  Spring 
MATH 105A 105LA  MATH 180A  MATH 184 184L 
MATH 150  General Education/Elective  General Educaton 
General Education/Elective  Math. Elective  General 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 subjectmatter 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:  
LowerDivision Requirements:  
A. Complete:  
MATH 8  Explorations in Functions and Modeling 
UpperDivision 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 
MATH 184 184L  History of Mathematics and History of Mathematics Lesson Lab 
Plus one addtional fourunit 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 2A  MATH 2B  MATH 2D 
PHYSICS 7C 7LC (or CHEM 1A)  PHYSICS 7D 7LD (or CHEM 1B)  PHYSICS 7E or CHEM 1C 
PHY SCI 5  MATH 13  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 
General Education  CHEM 193  General Education 
Junior  
Fall  Winter  Spring 
MATH 130A  MATH 130B  MATH 184 184L 
MATH 140A  MATH 120A  MATH 120B 
EDUC 55  MATH 140B  EDUC 148 
EDUC 143AW  Math. Elective  
Senior  
Fall  Winter  Spring 
MATH 105A 105LA  EDUC 109  EDUC 158 
MATH 150  EDUC 158  General Education 
EDUC 143BW  General Education  General 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 
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


Honors Introduction to Graduate Algebra I  
Honors Introduction to Graduate Algebra II  
Honors Introduction to Graduate Algebra III  
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 H120AMATH H120BMATH H120C in item C may be used to satisfy upperdivision electives or taken in place of MATH 120AMATH 120BMATH 120C and MATH 121AMATH 121B. Similarly, MATH H140AMATH H140BMATH H140C may be used to satisfy upperdivision electives or taken in place of MATH 140AMATH 140BMATH 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 7LC (or CHEM 1A)  PHYSICS 7D 7LD (or CHEM 1B)  PHYSICS 7E or CHEM 1C 
General Education/Elective  MATH 13  General Education/Elective 
General Education/Elective  General Education/Elective  General Education/Elective 
Sophomore  
Fall  Winter  Spring 
MATH 3A  MATH 3D  MATH 121B 
General Education/Elective  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 H120A  MATH H120B  MATH H120C 
MATH H140A  MATH H140B  MATH H140C 
MATH 130A  MATH 147  General Education/Elective 
General Education/Elective  General Education/Elective  General Education/Elective 
Senior  
Fall  Winter  Spring 
MATH 150  MATH 162A  MATH 162B 
General Education/Elective  MATH 199  General Education/Elective 
MATH 199 
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/undergraduatestudies/concentrationsandspecializations).
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.