Department of Mathematics
Karl Rubin, Department Chair
340 Rowland Hall
9498245503
http://www.math.uci.edu/
Overview
The Department of Mathematics is engaged in teaching and in fundamental research in a wide variety of basic mathematical disciplines, and offers undergraduate and graduate students the opportunity to fashion a thorough program of study leading to professional competence in mathematical research or in an area of application.
The curriculum in mathematics includes opportunities for supervised individual study and research and is augmented by seminars and colloquia. It is designed to be compatible with curricular structures at other collegiate institutions in California in order to enable students transferring to UCI to continue their programs of mathematics study.
Undergraduate Program
The Department offers a B.S. degree in Mathematics. Within this program there are six tracks; besides the standard track, there are five specializations or concentrations (in Mathematical Biology, Mathematical Finance, 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.
Admission to the Major
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.
Requirements for the B.S. Degree in Mathematics (including Concentrations and Specializations)
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 

Introduction to Mathematical Methods for Physics and Classical Physics and Classical Physics 

Introduction to Mathematical Methods for Physics and Classical Physics and Classical Physics 

Classical Physics and Classical Physics and Classical Physics 

UpperDivision Requirements:  
A. Complete:  
MATH 120A  Introduction to Abstract Algebra: Groups 
MATH 121A  Linear Algebra 
MATH 130A  Probability and Stochastic Processes 
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 2  PHYSICS 7C 7LC  PHYSICS 7D 7LD 
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. 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 Mathematical Finance
Admission to this concentration 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 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 
UpperDivision Requirements:  
A. Complete:  
MATH 130B  Probability and Stochastic Processes 
MATH 133A  Statistical Methods with Applications to Finance 
MATH 176  Mathematics of Finance 
B. Select three elective lecture courses from the following:  
Numerical Analysis and Numerical Analysis (plus MATH 105LA105LB) 

Numerical Differential Equations (plus MATH 107L)  
Introduction to Partial Differential Equations and Applications and Introduction to Partial Differential Equations and Applications and Introduction to Partial Differential Equations and Applications 

Mathematical Modeling  
Dynamical Systems  
The Theory of Differential Equations  
Linear Algebra  
Probability and Stochastic Processes  
Statistical Methods with Applications to Finance  
Analysis in Several Variables  
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 
Sample Program — Mathematics Major Concentrating in Mathematical Finance
Freshman  

Fall  Winter  Spring 
MATH 2A  MATH 2B  MATH 2D 
PHYSICS 2  PHYSICS 7C 7LC  PHYSICS 7D 7LD 
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  MATH 9  General Education/Elective 
General Education/Elective  General Education/Elective  
Junior  
Fall  Winter  Spring 
MATH 130A  MATH 130B  ECON 122A 
MATH 140A  MATH 140B  MATH 140C 
ECON 105A  ECON 105B  ECON 105C 
General Education/Elective  General Education/Elective  General Education/Elective 
Senior  
Fall  Winter  Spring 
MATH 120A  MATH 133A  MATH 133B 
MATH 118  MATH 176  MATH 115 
ECON 134A  ECON 132A  MATH 121A 
General Education/Elective  General Education/Elective  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 and Numerical Analysis (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 and Stochastic Processes and Probability and Stochastic Processes 

Statistical Methods with Applications to Finance and Statistical Methods with Applications to Finance 

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 2  PHYSICS 7C 7LC  MATH 13 
General Education/Elective  General Education/Elective  PHYSICS 7D 7LD 
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 and Numerical Analysis (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 in Biology  
or MATH 115 
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 113C 
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 and Numerical Analysis Laboratory 
MATH 120B  Introduction to Abstract Algebra: Rings and Fields 
MATH 130B  Probability and Stochastic Processes 
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 2  PHYSICS 7C 7LC  PHYSICS 7D 7LD 
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 and Numerical Analysis Laboratory 
MATH 120B  Introduction to Abstract Algebra: Rings and Fields 
MATH 130B  Probability and Stochastic Processes 
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 Secondary Mathematics and Science Classrooms 
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 2  PHYSICS 7C 7LC  PHYSICS 7D 7LD 
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 
Additional Information
Honors Program in Mathematics
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 and 121B  
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 H120A  Honors Introduction to Graduate Algebra I 
MATH H120B  Honors Introduction to Graduate Algebra II 
MATH H120C  Honors Introduction to Graduate Algebra III 
or  
(MATH 120C or MATH 140C) and MATH 133A  MATH 133B  
or  
(MATH 120C or MATH 140C) and MATH 180A  MATH 180B  
or  
(MATH 120C or MATH 140C) and MATH 113A  MATH 113B  
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. 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 2  PHYSICS 7C 7LC  PHYSICS 7D 7LD 
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 
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:
Planning a Program of Study
For all Mathematics majors, or prospective majors, assistance in planning a program of study is available from the Mathematics Department Undergraduate Advisor and the advisors for the various tracks, as well as from the academic counselors for the School of Physical Sciences. The application process for the specializations and concentrations requires students to plan a program of study with the assistance of a faculty advisor. The following sample programs are only examples.
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.
Requirements for the Minor in Mathematics
A. Complete:  
MATH 13  Introduction to Abstract Mathematics 
MATH 120A  Introduction to Abstract Algebra: Groups 
or MATH 140A  Elementary Analysis 
B. Select five additional fourunit courses in MATH (plus the associated lab, where applicable) numbered 77–189. 
NOTE: Nearly all upperdivision courses in Mathematics have MATH 2AMATH 2B as prerequisites, and many courses have additional prerequisites such as MATH 2D, MATH 2E, MATH 3A, and/or MATH 3D.
Requirements for the Minor in Mathematics for Biology
A. Complete:  
MATH 13  Introduction to Abstract Mathematics 
MATH 113A 113B 113C  Mathematical Modeling in Biology and Mathematical Modeling in Biology and Mathematical Modeling in Biology 
B. Select two of the following:  
Numerical Analysis (plus MATH 105LA)  
Introduction to Partial Differential Equations and Applications  
Dynamical Systems  
The Theory of Differential Equations  
Linear Algebra  
Elementary Analysis  
C. One additional fourunit upperdivision lecture course in MATH numbered 100–189. 
NOTE: Nearly all upperdivision courses in Mathematics have MATH 2AMATH 2B as prerequisites, and many courses have additional prerequisites such as MATH 2D, MATH 2E, MATH 3A, and/or MATH 3D.
On This Page:
 Master of Science in Mathematics
 Master of Science with Teaching Credential
 Advancement to M.S. Candidacy
 Doctor of Philosophy in Mathematics
 Graduate Program in Mathematical, Computational, and Systems Biology
Graduate Program
Graduate courses are designed to meet the needs of students doing graduate work in mathematics and in those disciplines that require graduatelevel mathematics for their study. Among the fields covered are analysis, algebra, applied and computational mathematics, mathematical biology, geometry and topology, probability, ordinary and partial differential equations, and mathematical logic.
In addition to formal courses, there are seminars for advanced study toward the Ph.D. in various fields of mathematics. Topics will vary from year to year. Each seminar is conducted by a faculty member specializing in the subject studied. Enrollment will be subject to the approval of the instructor in charge.
Master of Science in Mathematics
To earn the Master of Science degree, the student must satisfy course and residency requirements, and achieve two passes at the M.S. level among three exams in Real Analysis, Complex Analysis, and Algebra prior to the beginning of the second year.
The total number of required courses for the M.S. degree is 12, completed with satisfactory performance, that is, with a grade of B or better. Students are required to complete at least one series of the following courses:
MATH 210A 210B 210C  Real Analysis and Real Analysis and Real Analysis 
or


MATH 220A 220B 220C  Analytic Function Theory and Analytic Function Theory and Analytic Function Theory 
or


MATH 230A 230B 230C  Algebra and Algebra and Algebra 
At most one undergraduate course may count as an elective course, provided it is sponsored by rank faculty and approved by the Graduate Advisor. At most one elective course (at least three units) is allowed outside the Department.
To satisfy exam requirements, students may take the Core Assessment Exam (offered in the spring of every year), the Comprehensive Exams (offered in the spring of every year), or the Qualifying Exams (offered before the start of each fall quarter) in Real Analysis, Complex Analysis, and Algebra. Students may not attempt to pass an exam in any particular area more than three times. Some students may require additional background before entering MATH 210 or MATH 230. This will be determined by assessment prior to the start of the students' first year by the Vice Chair of Graduate Studies, upon consultation with the Graduate Studies Committee. Such students will be directed into MATH 205 and/or MATH 206 during their first year. They may pass one Comprehensive Exam in the areas of Analysis or Algebra in lieu of achieving an M.S. pass in one of the Core Assessment or Qualifying Exams that must be obtained prior to the start of their second year.
Students who fail to pass the required examinations satisfactorily within the period specified will be recommended for academic disqualification by the Graduate Dean.
MATH 199, MATH 297, MATH 298, MATH 299, and may not be used to fulfill course requirements.
The residency requirement ordinarily is satisfied by fulltime enrollment for three quarters immediately preceding the award of the M.S. degree. When appropriate, a leave of absence may be granted between matriculation and the final quarters of study.
If the candidate is not advanced before the beginning of the quarter in which all requirements are completed, the degree will not be conferred until the end of the following quarter. Deadlines for submission of the Application for Advancement to Candidacy are published on the Graduate Division website under filing fees and deadlines.
Master of Science in Mathematics with a Teaching Credential
In cooperation with the UCI School of Education, the Department of Mathematics sponsors a coordinated program for the M.S. degree in Mathematics and the California Single Subject Teaching Credential. The requirements for this option are the same as the Master of Science in Mathematics requirements listed above.
The student will complete the requirements for the Master's degree with the Mathematics Department (generally a twoyear commitment) and then will petition with the UCI School of Education to take the School of Education's credential courses (generally a oneyear commitment). The student must meet the requirements of the School of Education for the CBEST, CSET, TB test, and Certificate of Clearance. Prospective graduate students interested in this program should so indicate on their applications. A detailed description of the program can be requested from the School of Education.
Advancement to M.S. Candidacy
All Master’s students must be advanced to candidacy for the degree prior to the beginning of their final quarter of enrollment. An application for Advancement to Candidacy must be completed by the student and submitted for approval to the Department. The approved application must be submitted to the Graduate Division by the deadline published on the Graduate Division website. Advancement to M.S.Candidacy must occur one quarter prior to the degree conferral quarter.
Filing fee information can be located on the Graduate Division website.
Doctor of Philosophy in Mathematics
When accepted into the doctoral program, the student embarks on a program of formal courses, seminars, and individual study courses to prepare for the Ph.D. written examinations, Advancement to Candidacy examination, and dissertation.
Upon entering the program, students are expected to take MATH 210A, MATH 210B, MATH 210C, MATH 220A, MATH 220B, MATH 220C, MATH 230A, MATH 230B, and MATH 230C, which must be passed with a grade of B or better. Students must complete these sequences by the end of the second year.
By the start of the second year, students must achieve at least two passes at the M.S. level among three exams in Real Analysis, Complex Analysis, and Algebra. By the start of the third year, students must achieve two Ph.D. level passes among three exams in Real Analysis, Complex Analysis, and Algebra.
To satisfy the exam requirements, students may take the Core Assessment Exams (offered in spring of every year) or the Qualifying Exams (offered before the start of the fall quarter) in these areas. Students may not attempt to take an exam in a particular subject area more than three times. A student who passes a Qualifying Examination at the Ph.D. level prior to taking the corresponding course will be exempted from taking the course.
Some students may require additional background prior to entering MATH 210A, MATH 210B, MATH 210C, MATH 230A, MATH 230B, and MATH 230C. This will be determined by assessment prior to the start of the students’ first year by the Vice Chair for Graduate Studies, upon consultation with the Graduate Studies Committee. Such students will be directed into MATH 205 and/or MATH 206, or equivalent, during their first year. These students may pass one Comprehensive Exam in the areas of Algebra or Analysis in lieu of achieving an M.S. pass on one Core Assessment or Qualifying Exam that must be obtained prior to the start of the students’ second year. Comprehensive Exams in Analysis and Algebra will be offered once per year in the spring quarter.
By the end of their second year, students must declare a major specialization from the following areas: Algebra, Analysis, Applied and Computational Mathematics, Geometry and Topology, Logic, or Probability. Students are required to take two series of courses from their chosen area. (Students who later decide to change their area must also take two series of courses from the new area.) Additionally, all students must take two series outside their declared major area of specialization. Special topics courses within certain areas of specialization and courses counted toward the M.S. degree, other than MATH 205AMATH 205BMATH 205C and MATH 206AMATH 206BMATH 206C, will count toward the fulfillment of the major specialization requirement.
By the beginning of their third year, students must have an advisor specializing in their major area. With the advisor’s aid, the student forms a committee for the Advancement to Candidacy oral examination. This committee will be approved by the Department on behalf of the Dean of the Graduate Division and the Graduate Council and will consist of five faculty members. At least one, and at most two, of the members must be faculty from outside the Department. Before the end of the third year, students must have a written proposal, approved by their committee, for the Advancement to Candidacy examination. The proposal should explain the role of at least two series of courses from the student’s major area of specialization that will be used to satisfy the Advancement to Candidacy requirements. The proposal should also explain the role of additional research reading material as well as providing a plan for investigating specific topics under the direction of the student’s advisor(s). Only one of the courses MATH 210AMATH 210BMATH 210C, MATH 220AMATH 220BMATH 220C, and MATH 230AMATH 230BMATH 230C may count for the course requirement for Advancement to Candidacy Examinations. After the student meets the requirements, the Graduate Studies Committee recommends to the Dean of the Graduate Division the advancement to candidacy for the Ph.D. degree. Students should advance to candidacy by the beginning of their fourth year.
After advancing to candidacy, students are expected to be fully involved in research toward writing their Ph.D. dissertation. Ideally, students should keep in steady contact/interaction with their Doctoral Committee.
Teaching experience and training is an integral part of the Ph.D. program. All doctoral students are expected to participate in the Department’s teaching program.
The candidate must demonstrate independent, creative research in Mathematics by writing and defending a dissertation that makes a new and valuable contribution to mathematics in the candidate’s area of concentration. Upon Advancement to Candidacy a student must form a Thesis Committee, a subcommittee of the Advancement Examination Committee, consisting of at least three faculty members and chaired by the student’s advisor. The committee guides and supervises the candidate’s research, study, and writing of the dissertation; conducts an oral defense of the dissertation; and recommends that the Ph.D. be conferred upon approval of the Doctoral Dissertation. The normative time for completion of the Ph.D. is five years, and the maximum time permitted is seven years. Completion of the Ph.D. degree must occur within nine quarters of Advancement to Ph.D. candidacy.
Examinations
Ph.D. examinations are given in Algebra, Complex Analysis, and Real Analysis. All students seeking the Ph.D. degree must successfully complete two examinations before the end of the third year of entering the graduate program. Only two attempts are allowed for a Ph.D. student on each exam.
Area Requirements
Ph.D. students will choose from one of six areas of specialization in the Mathematics Department, which determines course work requirements. Each area of specialization will have a core course, which the Department will do its best to offer each year. The Department will offer other courses every other year, or more frequently depending on student demands and other Department priorities.
Algebra  
MATH 230A 230B 230C  Algebra and Algebra and Algebra (core) 
MATH 232A 232B 232C  Algebraic Number Theory and Algebraic Number Theory and Algebraic Number Theory 
MATH 233A 233B 233C  Algebraic Geometry and Algebraic Geometry and Algebraic Geometry 
MATH 234B 234C  Topics in Algebra and Topics in Algebra 
MATH 235A 235B 235C  Mathematics of Cryptography and Mathematics of Cryptography and Mathematics of Cryptography 
MATH 239A 239B 239C  Analytic Methods in Arithmetic Geometry and Analytic Methods in Arithmetic Geometry and Analytic Methods in Arithmetic Geometry 
Analysis  
MATH 210A 210B 210C  Real Analysis and Real Analysis and Real Analysis (core) 
MATH 211A 211B 211C  Topics in Analysis and Topics in Analysis and Topics in Analysis 
MATH 220A 220B 220C  Analytic Function Theory and Analytic Function Theory and Analytic Function Theory (core) 
MATH 260A 260B 260C  Functional Analysis and Functional Analysis and Functional Analysis 
MATH 295A 295B 295C  Partial Differential Equations and Partial Differential Equations and Partial Differential Equations 
MATH 296  Topics in Partial Differential Equations 
Applied and Computational Mathematics  
MATH 290A 290B 290C  Methods in Applied Mathematics and Methods in Applied Mathematics and Methods in Applied Mathematics (core) 
MATH 225A 225B 225C  Introduction to Numerical Analysis and Scientific Computing and Introduction to Numerical Analysis and Scientific Computing and Introduction to Numerical Analysis and Scientific Computing 
MATH 226A 226B 226C  Computational Differential Equations and Computational Differential Equations and Computational Differential Equations 
MATH 227A 227B  Mathematical and Computational Biology and Mathematical and Computational Biology 
MATH 291C  Topics in Applied and Computational Math 
MATH 295A 295B 295C  Partial Differential Equations and Partial Differential Equations and Partial Differential Equations 
Geometry and Topology  
MATH 218A 218B 218C  Introduction to Manifolds and Geometry and Introduction to Manifolds and Geometry and Introduction to Manifolds and Geometry (core) 
MATH 222A 222B 222C  Several Complex Variables and Complex Geometry and Several Complex Variables and Complex Geometry and Several Complex Variables and Complex Geometry 
MATH 240A 240B 240C  Differential Geometry and Differential Geometry and Differential Geometry 
MATH 245A 245C 245C  Topics in Differential Geometry and Topics in Differential Geometry and Topics in Differential Geometry 
MATH 250A 250B 250C  Algebraic Topology and Algebraic Topology and Algebraic Topology 
Logic  
MATH 280A 280B 280C  Mathematical Logic and Mathematical Logic and Mathematical Logic (core) 
MATH 281A 281B 281C  Set Theory and Set Theory and Set Theory 
MATH 282A 282B 282C  Model Theory and Model Theory and Model Theory 
MATH 285A 285B 285C  Topics in Mathematical Logic and Topics in Mathematical Logic and Topics in Mathematical Logic 
Probability  
MATH 210A 210B 210C  Real Analysis and Real Analysis and Real Analysis 
MATH 211A 211B 211C  Topics in Analysis and Topics in Analysis and Topics in Analysis 
MATH 270A 270B 270C  Probability and Probability and Probability (core) 
MATH 271A 271B 271C  Stochastic Processes and Stochastic Processes and Stochastic Processes (core) 
MATH 272A 272B 272C  Probability Models and Probability Models and Probability Models (core) 
MATH 274  Topics in Probability 
Graduate Program in Mathematical, Computational, and Systems Biology
The graduate program in Mathematical, Computational, and Systems Biology (MCSB) is designed to meet the interdisciplinary training challenges of modern biology and function in concert with selected department programs, including the Ph.D. in Mathematics. Detailed information is available at the Mathematical, Computational, and Systems Biology website and in the Interdisciplinary Studies section of the Catalogue.
Courses
MATH 1A. PreCalculus. 4 Workload Units.
Basic equations and inequalities, linear and quadratic functions, and systems of simultaneous equations. Course may be offered online.
MATH 1B. PreCalculus. 4 Units.
Preparation for calculus and other mathematics courses. Exponentials, logarithms, trigonometry, polynomials, and rational functions. Satisfies no requirements other than contribution to the 180 units required for graduation. Course may be offered online.
Prerequisite: MATH 1A or placement into MATH 1B via the Calculus Placement exam, or a score of 450 or higher on the Mathematics section of the SAT Reasoning Test.
Restriction: MATH 1B may not be taken for credit if taken after MATH 2A.
MATH 2A. SingleVariable Calculus. 4 Units.
Introduction to derivatives, calculation of derivatives of algebraic and trigonometric functions; applications including curve sketching, related rates, and optimization. Exponential and logarithm functions.
Prerequisite: MATH 1B or placement into MATH 2A via the Calculus Placement exam (fee required), or a score of 3 on the AP Calculus AB exam, or a score of 650 or higher on the Mathematics section of the SAT Reasoning Test, or a composite score of 29 or higher on the ACT Test. MATH 1B with a grade of C or better.
Overlaps with MATH 5A.
Restriction: School of Physical Sciences, School of Engineering, and School of Information and Computer Sciences majors have first consideration for enrollment.
(Vb)
MATH 2B. SingleVariable Calculus. 4 Units.
Definite integrals; the fundamental theorem of calculus. Applications of integration including finding areas and volumes. Techniques of integration. Infinite sequences and series. Parametric and polar equations.
Prerequisite: MATH 2A, or a score of 4 or higher on the AP Calculus AB Exam, or a score of 3 or higher on the AP Calculus BC Exam, or MATH 5A.
Restriction: School of Physical Sciences, School of Engineering, and School of Information and Computer Sciences majors have first consideration for enrollment.
(Vb)
MATH 2D. Multivariable Calculus. 4 Units.
Differential and integral calculus of realvalued functions of several real variables, including applications. Polar coordinates.
Prerequisite: MATH 2B or MATH 5B, or a score of 4 or higher on the AP Calculus BC exam.
Restriction: School of Physical Sciences, School of Engineering, School of Information and Computer Sciences and Undecided/Undeclared majors have first consideration for enrollment.
(Vb)
MATH 2E. Multivariable Calculus. 4 Units.
The differential and integral calculus of vectorvalued functions. Implicit and inverse function theorems. Line and surface integrals, divergence and curl, theorems of Greens, Gauss, and Stokes.
Prerequisite: MATH 2D.
Restriction: School of Physical Sciences and School of Engineering majors have first consideration for enrollment.
MATH 3A. Introduction to Linear Algebra. 4 Units.
Systems of linear equations, matrix operations, determinants, eigenvalues and eigenvectors, vector spaces, subspaces, and dimension.
Prerequisite: MATH 2B or MATH 5B or a score of 4 or higher on the AP Calculus BC exam.
Overlaps with MATH 6G, I&C SCI 6N.
Restriction: School of Physical Sciences, School of Engineering, and Undecided/Undeclared majors have first consideration for enrollment.
(Vb)
MATH 3D. Elementary Differential Equations. 4 Units.
Linear differential equations, variation of parameters, constant coefficient cookbook, systems of equations, Laplace tranforms, series solutions.
Prerequisite: MATH 3A and MATH 2D and (MATH 2B or a score of 4 or higher on the AP Calculus BC exam).
Restriction: School of Physical Sciences and School of Engineering majors have first consideration for enrollment.
MATH 4. Mathematics for Economists. 4 Units.
Topics in linear algebra and multivariable differential calculus suitable for economic applications.
Prerequisite: MATH 2B or MATH 5B or a score of 4 or higher on the AP Calculus BC exam.
Overlaps with MATH 2D, MATH 2J, MATH 3A.
Restriction: MATH 4 may not be taken for credit if taken after MATH 2D and either MATH 2J or MATH 3A.
(Vb)
MATH 5A. Calculus for Life Sciences. 4 Units.
Differential calculus with applications to life sciences. Exponential, logarithmic, and trigonometric functions. Limits, differentiation techniques, optimization and difference equations.
Prerequisite: MATH 1B or placement into MATH 5A via the Calculus Placement exam (fee required), or a score of 3 on the AP Calculus AB exam, or a score of 650 or higher on the Mathematics section of the SAT Reasoning Test, or a composite score of 29 or higher on the ACT Test. MATH 1B with a grade of C or better.
Overlaps with MATH 2A.
Restriction: School of Biological Sciences majors have first consideration for enrollment
(Vb)
MATH 5B. Calculus for Life Sciences. 4 Units.
Integral calculus and multivariable calculus with applications to life sciences. Integration techniques, applications of the integral, phase plane methods and basic modeling, basic multivariable methods.
Prerequisite: MATH 5A or MATH 2A, or a score of 4 or higher on the AP Calculus AB Exam, or a score of 3 or higher on the AP Calculus BC Exam.
Restriction: Cannot be taken for credit after MATH 2B. School of Biological Sciences majors have first consideration for enrollment.
(Vb)
MATH 8. Explorations in Functions and Modeling. 4 Units.
Explorations of applications and connections in topics in algebra, geometry, calculus, and statistics for future secondary math educators. Emphasis on nonstandard modeling problems.
Corequisite: MATH 2A.
MATH 9. Introduction to Programming for Numerical Analysis. 4 Units.
Introduction to computers and programming using MATLAB and MATHEMATICA. Representation of numbers and precision, basic data types, input/output, functions and modules, custom data types, testing/debugging, reading exceptions, plotting data, simple numerical linear algebra, numerical differentiation, and integration.
Prerequisite: MATH 2A.
Restriction: Mathematics majors have first consideration for enrollment.
(II and Vb ).
MATH 13. Introduction to Abstract Mathematics. 4 Units.
Introduction to formal definition and rigorous proof writing in mathematics. Topics include basic logic, set theory, equivalence relations, and various proof techniques such as direct, induction, contradiction, contrapositive, and exhaustion.
Prerequisite: MATH 2A or I&C SCI 6D.
Restriction: Mathematics majors have first consideration for enrollment.
MATH 105A. Numerical Analysis. 4 Units.
Introduction to the theory and practice of numerical computation. Floating point arithmetic, roundoff; solving transcendental equations; quadrature; linear systems, eigenvalues, power method.
Corequisite: MATH 105LA.
Prerequisite: MATH 3A or MATH 6G. Some acquaintance with computer programming.
Overlaps with ENGRMAE 185.
MATH 105B. Numerical Analysis. 4 Units.
Introduction to the theory and practice of numerical computation. Lagrange interpolation, finite differences, splines, Padé approximations; Gaussian quadrature; Fourier series and transforms.
Corequisite: MATH 105LB.
Prerequisite: MATH 105A.
MATH 105LA. Numerical Analysis Laboratory. 1 Unit.
Provides practical experience to complement the theory developed in Mathematics 105A.
Corequisite: MATH 105A.
MATH 105LB. Numerical Analysis Laboratory. 1 Unit.
Provides practical experience to complement the theory developed in Mathematics 105B.
Corequisite: MATH 105B.
MATH 107. Numerical Differential Equations. 4 Units.
Theory and applications of numerical methods to initial and boundaryvalue problems for ordinary and partial differential equations.
Corequisite: MATH 107L.
Prerequisite: MATH 3D and MATH 105A and MATH 105B.
MATH 107L. Numerical Differential Equations Laboratory. 1 Unit.
Provides practical experience to complement the theory developed in Mathematics 107.
Corequisite: MATH 107.
MATH 112A. Introduction to Partial Differential Equations and Applications. 4 Units.
Introduction to ordinary and partial differential equations and their applications in engineering and science. Basic methods for classical PDEs (potential, heat, and wave equations). Classification of PDEs, separation of variables and series expansions, special functions, eigenvalue problems.
MATH 112B. Introduction to Partial Differential Equations and Applications. 4 Units.
Introduction to partial differential equations and their applications in engineering and science. Basic methods for classical PDEs (potential, heat, and wave equations). Green functions and integral representations, method of characteristics.
Prerequisite: MATH 112A.
MATH 112C. Introduction to Partial Differential Equations and Applications. 4 Units.
Nonhomogeneous problems and Green's functions, SturmLiouville theory, general Fourier expansions, applications of partial differential equations in different areas of science.
Prerequisite: MATH 112B.
MATH 113A. Mathematical Modeling in Biology. 4 Units.
Discrete mathematical and statistical models; difference equations, population dynamics, Markov chains, and statistical models in biology.
MATH 113B. Mathematical Modeling in Biology. 4 Units.
Linear algebra; differential equations models; dynamical systems; stability; hysteresis; phase plane analysis; applications to cell biology, viral dynamics, and infectious diseases.
Prerequisite: MATH 2B.
MATH 113C. Mathematical Modeling in Biology. 4 Units.
Partial differential equations models in biology such as one dimensional blood flow, morphogen gradients, and tumor growth; stochastic models in cancer and epidemiology.
Prerequisite: MATH 113B.
MATH 115. Mathematical Modeling. 4 Units.
Mathematical modeling and analysis of phenomena that arise in engineering physical sciences, biology, economics, or social sciences.
Prerequisite: Corequisite or prerequisite: MATH 112A or ENGRMAE 140. MATH 2D and (MATH 3A or MATH 6G) and MATH 3D.
MATH 117. Dynamical Systems. 4 Units.
Introduction to the modern theory of dynamical systems including contraction mapping principle, fractals and chaos, conservative systems, Kepler problem, billiard models, expanding maps, Smale's horseshoe, topological entropy.
MATH 118. The Theory of Differential Equations. 4 Units.
Existence and uniqueness of solutions, continuous dependence of solutions on initial conditions and parameteres, Lyapunov and asymptotic stability, Floquet theory, nonlinear systems, and bifurcations.
MATH 120A. Introduction to Abstract Algebra: Groups. 4 Units.
Axioms for group theory; permutation groups, matrix groups. Isomorphisms, homomorphisms, quotient groups. Advanced topics as time permits. Special emphasis on doing proofs.
Prerequisite: (MATH 3A OR MATH 6G) AND MATH 13. MATH 13 with a grade of C or better.
Restriction: Mathematics majors have first consideration for enrollment.
MATH 120B. Introduction to Abstract Algebra: Rings and Fields. 4 Units.
Basic properties of rings; ideals, quotient rings; polynomial and matrix rings. Elements of field theory.
Prerequisite: MATH 120A. MATH 120A with a grade of C or better.
Restriction: Mathematics majors have first consideration for enrollment.
MATH 120C. Introduction to Abstract Algebra: Galois Theory. 4 Units.
Galois Theory: proof of the impossibility of certain rulerandcompass constructions (squaring the circle, trisecting angles); nonexistence of analogues to the "quadratic formula" for polynomial equations of degree 5 or higher.
Prerequisite: MATH 120B.
Restriction: Mathematics majors have first consideration for enrollment.
MATH H120A. Honors Introduction to Graduate Algebra I. 5 Units.
Introduction to abstract linear algebra, including bases, linear transformation, eigenvectors, canonical forms, inner products, and symmetric operators. Introduction to groups, rings, and fields, including examples of groups, group actions, Sylow theorems, modules over principal ideal domains, polynomials, and Galois groups.
Prerequisite: (MATH 3A OR MATH 6G) and MATH 13. MATH 13 with a grade of C or better.
Restriction: Mathematics Honors Program students have first consideration for enrollment.
Concurrent with MATH 206A.
MATH H120B. Honors Introduction to Graduate Algebra II. 5 Units.
Introduction to abstract linear algebra, including bases, linear transformation, eigenvectors, canonical forms, inner products, and symmetric operators. Introduction to groups, rings, and fields, including examples of groups, group actions, Sylow theorems, modules over principal ideal domains, polynomials, and Galois groups.
Prerequisite: MATH H120A.
Restriction: Mathematics Honors Program students have first consideration for enrollment.
Concurrent with MATH 206B.
MATH H120C. Honors Introduction to Graduate Algebra III. 5 Units.
Introduction to abstract linear algebra, including bases, linear transformation, eigenvectors, canonical forms, inner products, and symmetric operators. Introduction to groups, rings, and fields, including examples of groups, group actions, Sylow theorems, modules over principal ideal domains, polynomials, and Galois groups.
Prerequisite: MATH H120B.
Restriction: Mathematics Honors Program students have first consideration for enrollment.
Concurrent with MATH 206C.
MATH 121A. Linear Algebra. 4 Units.
Introduction to modern abstract linear algebra. Special emphasis on students doing proofs. Vector spaces, linear independence, bases, dimension. Linear transformations and their matrix representations. Theory of determinants.
Prerequisite: (MATH 3A OR MATH 6G) AND MATH 13. MATH 13 with a grade of C or better.
Restriction: Mathematics majors have first consideration for enrollment.
MATH 121B. Linear Algebra. 4 Units.
Introduction to modern abstract linear algebra. Special emphasis on students doing proofs. Canonical forms; inner products; similarity of matrices.
Prerequisite: MATH 121A.
Restriction: Mathematics majors have first consideration for enrollment.
MATH 130A. Probability and Stochastic Processes. 4 Units.
Basic concepts of random variables, distributions, independence, correlations, moments, limit theorems, conditional probability, Markov chains, gambler's ruin, branching process, birth and death processes, numerical simulations in Matlab.
Prerequisite: MATH 2A and MATH 2B and (MATH 3A or MATH 6G).
Overlaps with MATH 131A, MATH 132A, STATS 120A.
MATH 130B. Probability and Stochastic Processes. 4 Units.
Exponential distributions, Poisson processes, continuous time Markov chains, renewal theory, insurance ruin and claim problems, numerical simulations in Matlab.
Prerequisite: MATH 130A OR MATH 131A or STATS 120A.
MATH 130C. Probability and Stochastic Processes. 4 Units.
Martingales, Invariance Principle, Brownian motions and applications in option pricing, stationary processes and applications in Wiener filter, numerical simulations in Matlab.
Prerequisite: MATH 130B.
MATH 133A. Statistical Methods with Applications to Finance. 4 Units.
Overview of probability, statistics, and financial concepts: distribution, point estimation, confidence interval, linear regression, hypothesis testing, principal component analysis, financial applications.
Prerequisite: MATH 130A or MATH 131A or STATS 120A.
MATH 133B. Statistical Methods with Applications to Finance. 4 Units.
Overview of markets and options: asset modeling, Brownian motion, risk neutrality, option pricing, value at risk, MC simulations.
Prerequisite: MATH 133A.
MATH 140A. Elementary Analysis. 4 Units.
Introduction to real analysis, including convergence of sequence, infinite series, differentiation and integration, and sequences of functions. Students are expected to do proofs.
Prerequisite: MATH 2B and MATH 2D and MATH 3A and MATH 13. MATH 13 with a grade of C or better.
Restriction: Math majors have first consideration for enrollment.
MATH 140B. Elementary Analysis. 4 Units.
Introduction to real analysis including convergence of sequences, infinite series, differentiation and integration, and sequences of functions. Students are expected to do proofs.
Prerequisite: MATH 140A. MATH 140A with a grade of C or better.
Restriction: Mathematics majors have first consideration for enrollment.
MATH 140C. Analysis in Several Variables . 4 Units.
Rigorous treatment of multivariable differential calculus. Jacobians, Inverse and Implicit Function theorems.
Prerequisite: MATH 140B.
MATH H140A. Honors Introduction to Graduate Analysis I. 5 Units.
Construction of the real number system, topology of the real line, concepts of continuity, differential and integral calculus, sequences and series of functions, equicontinuity, metric spaces, multivariable differential and integral calculus, implicit functions, curves and surfaces.
Prerequisite: MATH 2D and MATH 3A and MATH 13. MATH 13 with a grade of C or better.
Restriction: Mathematics Honors Program students have first consideration for enrollment.
Concurrent with MATH 205A.
MATH H140B. Honors Introduction to Graduate Analysis II. 5 Units.
Construction of the real number system, topology of the real line, concepts of continuity, differential and integral calculus, sequences and series of functions, equicontinuity, metric spaces, multivariable differential and integral calculus, implicit functions, curves and surfaces.
Prerequisite: MATH H140A.
Restriction: Mathematics Honors Program students have first consideration for enrollment.
Concurrent with MATH 205B.
MATH H140C. Honors Introduction to Graduate Analysis III. 5 Units.
Construction of the real number system; topology of the real line; concepts of continuity, differential, and integral calculus; sequences and series of functions, equicontinuity, metric spaces, multivariable differential, and integral calculus; implicit functions, curves and surfaces.
Prerequisite: MATH H140B.
Restriction: Mathematics Honors Program students have first consideration for enrollment.
Concurrent with MATH 205C.
MATH 141. Introduction to Topology. 4 Units.
The elements of naive set theory and the basic properties of metric spaces. Introduction to topological properties.
Prerequisite: MATH 140A.
MATH 147. Complex Analysis. 4 Units.
Rigorous treatment of basic complex analysis: analytic functions, Cauchy integral theory and its consequences, power series, residue calculus, harmonic functions, conformal mapping. Students are expected to do proofs.
Corequisite: MATH 140B.
Prerequisite: MATH 140A.
Overlaps with MATH 114A.
Restriction: MATH 114A may not be taken for credit after MATH 147.
MATH 150. Introduction to Mathematical Logic. 4 Units.
First order logic through the Completeness Theorem for predicate logic.
Prerequisite: MATH 13 or (I&C SCI 6B and I&C SCI 6D). MATH 13 with a grade of C or better.
Overlaps with LPS 105B, PHILOS 105B.
MATH 161. Modern Geometry. 4 Units.
Euclidean Geometry; Hilbert's Axioms; Absolute Geometry; Hyperbolic Geometry; the Poincare Models; and Geometric Transformations.
Prerequisite: MATH 13 or (I&C SCI 6B and I&C SCI 6D). MATH 13 with a C or better.
Restriction: Math majors have first consideration for enrollment.
MATH 162A. Introduction to Differential Geometry. 4 Units.
Applications of advanced calculus and linear algebra to the geometry of curves and surfaces in space.
MATH 162B. Introduction to Differential Geometry. 4 Units.
Applications of advanced calculus and linear algebra to the geometry of curves and surfaces in space.
Prerequisite: MATH 162A.
MATH 173A. Introduction to Cryptology. 4 Units.
Introduction to some of the mathematics used in the making and breaking of codes, with applications to classical ciphers and public key systems. The mathematics which is covered includes topics from number theory, probability, and abstract algebra.
Prerequisite: MATH 2B and (MATH 3A or MATH 6G) and (MATH 13 or (I&C SCI 6B and I&C SCI 6D)). MATH 13 with a grade of C or better.
MATH 173B. Introduction to Cryptology. 4 Units.
Introduction to some of the mathematics used in the making and breaking of codes, with applications to classical ciphers and public key systems. The mathematics which is covered includes topics from number theory, probability, and abstract algebra.
Prerequisite: MATH 173A.
MATH 174A. Modern Graph Theory I. 4 Units.
An introductory course emphasizing the fundamental concepts of graph theory by developing abilities to produce examples, following and devising simple proofs, and current applications of graph theory. Topics include graph types; matching in graphs; Menger's Theorem; Kuratowski's Theorem.
Prerequisite: MATH 2B and (MATH 3A or MATH 6G) and (MATH 13 or (I&C SCI 6B and I&C SCI 6D)). MATH 13 with a grade of C or better.
MATH 175. Combinatorics . 4 Units.
Introduction to combinatorics including basic counting principles, permutations, combinations, binomial coefficients, inclusionexclusion, derangements, ordinary and exponential generating functions, recurrence relations, Catalan numbers, Stirling numbers, and partition numbers. Course may be offered online.
Prerequisite: MATH 2B and MATH 13. MATH 13 with a grade of C or better.
MATH 176. Mathematics of Finance. 4 Units.
After reviewing tools from probability, statistics, and elementary differential and partial differential equations, concepts such as hedging, arbitrage, Puts, Calls, the design of portfolios, the derivation and solution of the BlacScholes, and other equations are discussed.
Prerequisite: MATH 3A.
Same as ECON 135.
Restriction: Mathematics, Economics, Quantitative Economics, and Business Economics majors have first consideration for enrollment.
MATH 180A. Number Theory. 4 Units.
Introduction to number theory and applications. Divisibility, prime numbers, factorization. Arithmetic functions. Congruences. Quadratic residue. Diophantine equations. Introduction to cryptography.
Prerequisite: MATH 3A and MATH 13. MATH 13 with a grade of C or better.
Restriction: Math majors have first consideration for enrollment.
MATH 180B. Number Theory. 4 Units.
Introduction to number theory and applications. Analytic number theory, character sums, finite fields, discrete logarithm, computational complexity. Introduction to coding theory. Other topics as time permits.
Prerequisite: MATH 180A.
Restriction: Mathematics majors have first consideration for enrollment.
MATH 184. History of Mathematics. 4 Units.
Topics vary from year to year. Some possible topics: mathematics in ancient times; the development of modern analysis; the evolution of geometric ideas. Students will be assigned individual topics for term papers.
Prerequisite: MATH 120A and MATH 140A.
Restriction: Math majors have first consideration for enrollment.
MATH 184L. History of Mathematics Lesson Lab. 1 Unit.
Aspiring math teachers research, design, present, and peer review middle school or high school math lessons that draw from history of mathematics topics.
MATH 189. Special Topics in Mathematics. 4 Units.
Offered from time to time, but not on a regular basis. Content and prerequisites vary with the instructor.
Prerequisite: Prerequisites vary.
Repeatability: Unlimited as topics vary.
MATH 192. Studies in the Learning and Teaching of Secondary Mathematics. 2 Units.
Focus is on historic and current mathematical concepts related to student learning and effective math pedagogy, with fieldwork in grades 614.
Prerequisite: MATH 2D and MATH 2J and MATH 3D and (MATH 13 or MATH 120A or MATH 140A).
Grading Option: Pass/no pass only.
Repeatability: May be taken for credit 2 times.
Restriction: Upperdivision students only. Math majors with specialization in Mathematics for Education only.
MATH 194. Problem Solving Seminar. 2 Units.
Develops ability in analytical thinking and problem solving, using problems of the type found in the Mathematics Olympiad and the Putnam Mathematical Competition. Students taking the course in fall will prepare for and take the Putnam examination in December.
Grading Option: Pass/no pass only.
Repeatability: May be taken for credit 2 times.
MATH 199A. Special Studies in Mathematics. 24 Units.
Supervised reading. For outstanding undergraduate Mathematics majors in supervised but independent reading or research of mathematical topics.
Repeatability: Unlimited as topics vary.
MATH 199B. Special Studies in Mathematics. 24 Units.
Supervised reading. For outstanding undergraduate Mathematics majors in supervised but independent reading or research of mathematical topics.
Repeatability: Unlimited as topics vary.
MATH 199C. Special Studies in Mathematics. 24 Units.
Supervised reading. For outstanding undergraduate Mathematics majors in supervised but independent reading or research of mathematical topics.
Repeatability: Unlimited as topics vary.
MATH 205A. Introduction to Graduate Analysis. 5 Units.
Construction of the real number system, topology of the real line, concepts of continuity, differential and integral calculus, sequences and series of functions, equicontinuity, metric spaces, multivariable differential and integral calculus, implicit functions, curves and surfaces.
Prerequisite: MATH 2E and MATH 3A and MATH 13.
Concurrent with MATH H140A.
MATH 205B. Introduction to Graduate Analysis. 5 Units.
Construction of the real number system, topology of the real line, concepts of continuity, differential and integral calculus, sequences and series of functions, equicontinuity, metric spaces, multivariable differential and integral calculus, implicit functions, curves and surfaces.
Prerequisite: MATH 205A.
Concurrent with MATH H140B.
MATH 205C. Introduction to Graduate Analysis. 5 Units.
Construction of the real number system, topology of the real line, concepts of continuity, differential and integral calculus, sequences and series of functions, equicontinuity, metric spaces, multivariable differential and integral calculus, implicit functions, curves and surfaces.
Prerequisite: MATH 205B.
Concurrent with MATH H140C.
MATH 206A. Introduction to Graduate Algebra. 5 Units.
Introduction to abstract linear algebra, including bases, linear transformation, eigenvectors, canonical forms, inner products, symmetric operators. Introduction to groups, rings, and fields including examples of groups, group actions, Sylow theorems, modules over principal ideal domains, polynomials, and Galois groups.
Prerequisite: MATH 3A.
Concurrent with MATH H120A.
MATH 206B. Introduction to Graduate Algebra. 5 Units.
Introduction to abstract linear algebra, including bases, linear transformation, eigenvectors, canonical forms, inner products, symmetric operators. Introduction to groups, rings, and fields including examples of groups, group actions, Sylow theorems, modules over principal ideal domains, polynomials, and Galois groups.
Prerequisite: MATH 206A.
Concurrent with MATH H120B.
MATH 206C. Introduction to Graduate Algebra. 5 Units.
Introduction to abstract linear algebra, including bases, linear transformation, eigenvectors, canonical forms, inner products, symmetric operators. Introduction to groups, rings, and fields including examples of groups, group actions, Sylow theorems, modules over principal ideal domains, polynomials, and Galois groups.
Prerequisite: MATH 206B.
Concurrent with MATH H120C.
MATH 210A. Real Analysis. 4 Units.
Measure theory, Lebesgue integral, signed measures, RadonNikodym theorem, functions of bounded variation and absolutely continuous functions, classical Banach spaces, Lp spaces, integration on locally compact spaces and the RieszMarkov theorem, measure and outer measure, product measure spaces.
Prerequisite: MATH 140C.
MATH 210B. Real Analysis. 4 Units.
Measure theory, Lebesgue integral, signed measures, RadonNikodym theorem, functions of bounded variation and absolutely continuous functions, classical Banach spaces, Lp spaces, integration on locally compact spaces and the RieszMarkov theorem, measure and outer measure, product measure spaces.
Prerequisite: MATH 210A.
MATH 210C. Real Analysis. 4 Units.
Measure theory, Lebesgue integral, signed measures, RadonNikodym theorem, functions of bounded variation and absolutely continuous functions, classical Banach spaces, Lp spaces, integration on locally compact spaces and the RieszMarkov theorem, measure and outer measure, product measure spaces.
Prerequisite: MATH 210B.
MATH 211A. Topics in Analysis . 4 Units.
Studies in selected areas of Real Analysis, a continuation of MATH 210AMATH 210BMATH 210C. Topics addressed vary each quarter.
Prerequisite: MATH 210C.
MATH 211B. Topics in Analysis . 4 Units.
Studies in selected areas of Real Analysis, a continuation of MATH 210AMATH 210BMATH 210C. Topics addressed vary each quarter.
Prerequisite: MATH 211A.
MATH 211C. Topics in Analysis . 4 Units.
Studies in selected areas of Real Analysis, a continuation of MATH 210AMATH 210BMATH 210C. Topics addressed vary each quarter.
Prerequisite: MATH 211B.
MATH 218A. Introduction to Manifolds and Geometry. 4 Units.
General topology and fundamental groups, covering space; Stokes theorem on manifolds, selected topics on abstract manifold theory.
Prerequisite: MATH 205C.
MATH 218B. Introduction to Manifolds and Geometry. 4 Units.
General topology and fundamental groups, covering space; Stokes theorem on manifolds, selected topics on abstract manifold theory.
Prerequisite: MATH 218A.
MATH 218C. Introduction to Manifolds and Geometry. 4 Units.
General topology and fundamental groups, covering space; Stokes theorem on manifolds, selected topics on abstract manifold theory.
Prerequisite: MATH 218B.
MATH 220A. Analytic Function Theory. 4 Units.
Standard theorems about analytic functions. Harmonic functions. Normal families. Conformal mapping.
Prerequisite: MATH 140C.
MATH 220B. Analytic Function Theory. 4 Units.
Standard theorems about analytic functions. Harmonic functions. Normal families. Conformal mapping.
Prerequisite: MATH 220A.
MATH 220C. Analytic Function Theory. 4 Units.
Standard theorems about analytic functions. Harmonic functions. Normal families. Conformal mapping.
Prerequisite: MATH 220B.
MATH 222A. Several Complex Variables and Complex Geometry. 4 Units.
Several Complex variables, dbar problems, mappings, Kaehler geometry, de Rham and Dolbeault Theorems, Chern Classes, Hodge Theorems, Calabi conjecture, KahlerEinstein geometry, MongeAmpere.
MATH 222B. Several Complex Variables and Complex Geometry. 4 Units.
Several Complex variables, dbar problems, mappings, Kaehler geometry, Le Rham and Dolbeault Theorems, Chern Classes, Hodge Theorems, Calabi conjecture, KahlerEinstein geometry, MongeAmpere.
Prerequisite: MATH 222A.
MATH 222C. Several Complex Variables and Complex Geometry. 4 Units.
Several Complex variables, dbar problems, mappings, Kaehler geometry, Le Rham and Dolbeault Theorems, Chern Classes, Hodge Theorems, Calabi conjecture, KahlerEinstein geometry, MongeAmpere.
Prerequisite: MATH 222B.
MATH 225A. Introduction to Numerical Analysis and Scientific Computing. 4 Units.
Introduction to fundamentals of numerical analysis from an advanced viewpoint. Error analysis, approximation of functions, nonlinear equations.
Prerequisite: MATH 3D and ((MATH 105A and MATH 105B) or (MATH 140A and MATH 140B)) and MATH 121A and (MATH 112A or ENGRMAE 140).
Restriction: Graduate students only.
MATH 225B. Introduction to Numerical Analysis and Scientific Computing. 4 Units.
Introduction to fundamentals of numerical analysis from an advanced viewpoint. Numerical linear algebra, numerical solutions of differential equations; stability.
Prerequisite: MATH 225A.
Restriction: Graduate students only.
MATH 225C. Introduction to Numerical Analysis and Scientific Computing. 4 Units.
Introduction to fundamentals of numerical analysis from an advanced viewpoint. Numerical linear algebra, numerical solutions of differential equations; stability.
Prerequisite: MATH 225B.
Restriction: Graduate students only.
MATH 226A. Computational Differential Equations. 4 Units.
Finite difference and finite element methods. Quick treatment of functional and nonlinear analysis background: weak solution, Lp spaces, Sobolev spaces. Approximation theory. Fourier and PetrovGalerkin methods; mesh generation. Elliptic, parabolic, hyperbolic cases in 226ABC, respectively.
Prerequisite: MATH 3D and (MATH 112A or ENGRMAE 140) and (MATH 140B or MATH 105B).
MATH 226B. Computational Differential Equations. 4 Units.
Finite difference and finite element methods. Quick treatment of functional and nonlinear analysis background: weak solution, Lp spaces, Sobolev spaces. Approximation theory. Fourier and PetrovGalerkin methods; mesh generation. Elliptic, parabolic, hyperbolic cases in 226ABC, respectively.
Prerequisite: MATH 226A.
MATH 226C. Computational Differential Equations. 4 Units.
Finite difference and finite element methods. Quick treatment of functional and nonlinear analysis background: weak solution, Lp spaces, Sobolev spaces. Approximation theory. Fourier and PetrovGalerkin methods; mesh generation. Elliptic, parabolic, hyperbolic cases in 226ABC, respectively.
Prerequisite: MATH 226B.
MATH 227A. Mathematical and Computational Biology. 4 Units.
Analytical and numerical methods for dynamical systems, temporalspatial dynamics, steady state, stability, stochasticity. Application to life sciences: genetics, tissue growth and patterning, cancers, ion channels gating, signaling networks, morphogen gradients. Analytical methods.
MATH 227B. Mathematical and Computational Biology. 4 Units.
Analytical and numerical methods for dynamical systems, temporalspatial dynamics, steady state, stability, stochasticity. Application to life sciences: genetics, tissue growth and patterning, cancers, ion channels gating, signaling networks, morphogen gradients. Numerical simulations.
Prerequisite: MATH 227A.
MATH 227C. Mathematical and Computational Biology . 4 Units.
Analytical and numerical methods for dynamical systems, temporalspatial dynamics, steady state, stability, stochasticity. Application to life sciences: genetics, tissue growth and patterning, cancers, ion channels gating, signaling networks, morphogen gradients. Probabilistic methods.
Prerequisite: MATH 227A.
Same as COMPSCI 285.
MATH 230A. Algebra. 4 Units.
Elements of the theories of groups, rings, fields, modules. Galois theory. Modules over principal ideal domains. Artinian, Noetherian, and semisimple rings and modules.
MATH 230B. Algebra. 4 Units.
Elements of the theories of groups, rings, fields, modules. Galois theory. Modules over principal ideal domains. Artinian, Noetherian, and semisimple rings and modules.
Prerequisite: MATH 230A.
MATH 230C. Algebra. 4 Units.
Elements of the theories of groups, rings, fields, modules. Galois theory. Modules over principal ideal domains. Artinian, Noetherian, and semisimple rings and modules.
Prerequisite: MATH 230B.
MATH 232A. Algebraic Number Theory. 4 Units.
Algebraic integers, prime ideals, class groups, Dirichlet unit theorem, localization, completion, Cebotarev density theorem, Lfunctions, Gauss sums, diophantine equations, zeta functions over finite fields. Introduction to class field theory.
Prerequisite: MATH 230C.
MATH 232B. Algebraic Number Theory. 4 Units.
Algebraic integers, prime ideals, class groups, Dirichlet unit theorem, localization, completion, Cebotarev density theorem, Lfunctions, Gauss sums, diophantine equations, zeta functions over finite fields. Introduction to class field theory.
Prerequisite: MATH 232A.
MATH 232C. Algebraic Number Theory. 4 Units.
Algebraic integers, prime ideals, class groups, Dirichlet unit theorem, localization, completion, Cebotarev density theorem, Lfunctions, Gauss sums, diophantine equations, zeta functions over finite fields. Introduction to class field theory.
Prerequisite: MATH 232B.
MATH 233A. Algebraic Geometry. 4 Units.
Basic commutative algebra and classical algebraic geometry. Algebraic varieties, morphisms, rational maps, blow ups. Theory of schemes, sheaves, divisors, cohomology. Algebraic curves and surfaces, RiemannRoch theorem, Jocobian classification of curves and surfaces.
Prerequisite: MATH 230C.
MATH 233B. Algebraic Geometry. 4 Units.
Basic commutative algebra and classical algebraic geometry. Algebraic varieties, morphisms, rational maps, blow ups. Theory of schemes, sheaves, divisors, cohomology. Algebraic curves and surfaces, RiemannRoch theorem, Jocobian classification of curves and surfaces.
Prerequisite: MATH 233A.
MATH 233C. Algebraic Geometry. 4 Units.
Basic commutative algebra and classical algebraic geometry. Algebraic varieties, morphisms, rational maps, blow ups. Theory of schemes, sheaves, divisors, cohomology. Algebraic curves and surfaces, RiemannRoch theorem, Jocobian classification of curves and surfaces.
Prerequisite: MATH 233B.
MATH 234B. Topics in Algebra. 4 Units.
Group theory, homological algebra, and other selected topics.
Prerequisite: MATH 230C.
Repeatability: May be repeated for credit unlimited times.
MATH 234C. Topics in Algebra. 4 Units.
Group theory, homological algebra, and other selected topics.
Prerequisite: MATH 234B.
Repeatability: May be repeated for credit unlimited times.
MATH 235A. Mathematics of Cryptography. 4 Units.
Mathematics of public key cryptography: encryption and signature schemes; RSA; factoring; primality testing; discrete log based cryptosystems, elliptic and hyperelliptic curve cryptography and additional topics as determined by the instructor.
Prerequisite: MATH 230C.
MATH 235B. Mathematics of Cryptography. 4 Units.
Mathematics of public key cryptography: encryption and signature schemes; RSA; factoring; primality testing; discrete log based cryptosystems, elliptic and hyperelliptic curve cryptography and additional topics as determined by the instructor.
Prerequisite: MATH 235A.
MATH 235C. Mathematics of Cryptography. 4 Units.
Mathematics of public key cryptography: encryption and signature schemes; RSA; factoring; primality testing; discrete log based cryptosystems, elliptic and hyperelliptic curve cryptography and additional topics as determined by the instructor.
Prerequisite: MATH 235B.
MATH 239A. Analytic Methods in Arithmetic Geometry. 4 Units.
Riemann zeta function, Dirichlet Lfunctions, prime number theorem, zeta functions over finite fields, sieve methods, zeta functions of algebraic curves, algebraic coding theory, LFunctions over number fields, Lfunctions of modular forms, Eisenstein series.
MATH 239B. Analytic Methods in Arithmetic Geometry. 4 Units.
Riemann zeta function, Dirichlet Lfunctions, prime number theorem, zeta functions over finite fields, sieve methods, zeta functions of algebraic curves, algebraic coding theory, LFunctions over number fields, Lfunctions of modular forms, Eisenstein series.
Prerequisite: MATH 239A.
MATH 239C. Analytic Methods in Arithmetic Geometry. 4 Units.
Riemann zeta function, Dirichlet Lfunctions, prime number theorem, zeta functions over finite fields, sieve methods, zeta functions of algebraic curves, algebraic coding theory, LFunctions over number fields, Lfunctions of modular forms, Eisenstein series.
Prerequisite: MATH 239B.
MATH 240A. Differential Geometry. 4 Units.
Riemannian manifolds, connections, curvature and torsion. Submanifolds, mean curvature, Gauss curvature equation. Geodesics, minimal submanifolds, first and second fundamental forms, variational formulas. Comparison theorems and their geometric applications. Hodge theory applications to geometry and topology.
MATH 240B. Differential Geometry. 4 Units.
Riemannian manifolds, connections, curvature and torsion. Submanifolds, mean curvature, Gauss curvature equation. Geodesics, minimal submanifolds, first and second fundamental forms, variational formulas. Comparison theorems and their geometric applications. Hodge theory applications to geometry and topology.
Prerequisite: MATH 240A.
MATH 240C. Differential Geometry. 4 Units.
Riemannian manifolds, connections, curvature and torsion. Submanifolds, mean curvature, Gauss curvature equation. Geodesics, minimal submanifolds, first and second fundamental forms, variational formulas. Comparison theorems and their geometric applications. Hodge theory applications to geometry and topology.
Prerequisite: MATH 240B.
MATH 245A. Topics in Differential Geometry. 4 Units.
Studies in selected areas of differential geometry, a continuation of MATH 240AMATH 240BMATH 240C. Topics addressed vary each quarter.
Prerequisite: MATH 240C.
Repeatability: Unlimited as topics vary.
MATH 245B. Topics in Differential Geometry. 4 Units.
Studies in selected areas of differential geometry, a continuation of MATH 240AMATH 240BMATH 240C. Topics addressed vary each quarter.
Prerequisite: MATH 245A.
Repeatability: Unlimited as topics vary.
MATH 245C. Topics in Differential Geometry. 4 Units.
Studies in selected areas of differential geometry, a continuation of MATH 240AMATH 240BMATH 240C. Topics addressed vary each quarter.
Prerequisite: MATH 245B.
Repeatability: Unlimited as topics vary.
MATH 250A. Algebraic Topology. 4 Units.
Provides fundamental materials in algebraic topology: fundamental group and covering space, homology and cohomology theory, and homotopy group.
Prerequisite: MATH 230A.
MATH 250B. Algebraic Topology. 4 Units.
Provides fundamental materials in algebraic topology: fundamental group and covering space, homology and cohomology theory, and homotopy group.
Prerequisite: MATH 250A.
MATH 250C. Algebraic Topology. 4 Units.
Provides fundamental materials in algebraic topology: fundamental group and covering space, homology and cohomology theory, and homotopy group.
Prerequisite: MATH 250B.
MATH 260A. Functional Analysis. 4 Units.
Normed linear spaces, Hilbert spaces, Banach spaces, StoneWeierstrass Theorem, locally convex spaces, bounded operators on Banach and Hilbert spaces, the GelfandNeumark Theorem for commutative C*algebras, the spectral theorem for bounded selfadjoint operators, unbounded operators on Hilbert spaces.
MATH 260B. Functional Analysis. 4 Units.
Normed linear spaces, Hilbert spaces, Banach spaces, StoneWeierstrass Theorem, locally convex spaces, bounded operators on Banach and Hilbert spaces, the GelfandNeumark Theorem for commutative C*algebras, the spectral theorem for bounded selfadjoint operators, unbounded operators on Hilbert spaces.
Prerequisite: MATH 260A.
MATH 260C. Functional Analysis. 4 Units.
Normed linear spaces, Hilbert spaces, Banach spaces, StoneWeierstrass Theorem, locally convex spaces, bounded operators on Banach and Hilbert spaces, the GelfandNeumark Theorem for commutative C*algebras, the spectral theorem for bounded selfadjoint operators, unbounded operators on Hilbert spaces.
Prerequisite: MATH 260B.
MATH 270A. Probability. 4 Units.
Probability spaces, distribution and characteristic functions. Strong limit theorems. Limit distributions for sums of independent random variables. Conditional expectation and martingale theory. Stochastic processes.
MATH 270B. Probability. 4 Units.
Probability spaces, distribution and characteristic functions. Strong limit theorems. Limit distributions for sums of independent random variables. Conditional expectation and martingale theory. Stochastic processes.
Prerequisite: MATH 270A.
MATH 270C. Probability. 4 Units.
Probability spaces, distribution and characteristic functions. Strong limit theorems. Limit distributions for sums of independent random variables. Conditional expectation and martingale theory. Stochastic processes.
Prerequisite: MATH 270B.
MATH 271A. Stochastic Processes. 4 Units.
Processes with independent increments, Wiener and Gaussian processes, function space integrals, stationary processes, Markov processes.
Prerequisite: MATH 210C.
Overlaps with STATS 270.
MATH 271B. Stochastic Processes. 4 Units.
Processes with independent increments, Wiener and Gaussian processes, function space integrals, stationary processes, Markov processes.
Prerequisite: MATH 271A.
Overlaps with STATS 270.
MATH 271C. Stochastic Processes. 4 Units.
Processes with independent increments, Wiener and Gaussian processes, function space integrals, stationary processes, Markov processes.
Prerequisite: MATH 271B.
Overlaps with STATS 270.
MATH 272A. Probability Models. 4 Units.
Spin systems, Ising models, contact process, exclusion process, percolation, increasing events, critical probabilities, sub and supercritical phases, scaling theory, oriented percolation, concentration of measure, Gaussian fields, Borell's inequality, chaining, entropy.
Prerequisite: MATH 271C.
MATH 272B. Probability Models. 4 Units.
Spin systems, Ising models, contact process, exclusion process, percolation, increasing events, critical probabilities, sub and supercritical phases, scaling theory, oriented percolation, concentration of measure, Gaussian fields, Borell's inequality, chaining, entropy.
Prerequisite: MATH 272A.
MATH 272C. Probability Models. 4 Units.
Spin systems, Ising models, contact process, exclusion process, percolation, increasing events, critical probabilities, sub and supercritical phases, scaling theory, oriented percolation, concentration of measure, Gaussian fields, Borell's inequality, chaining, entropy.
Prerequisite: MATH 272B.
MATH 274. Topics in Probability. 4 Units.
Selected topics, such as theory of stochastic processes, martingale theory, stochastic integrals, stochastic differential equations.
Prerequisite: MATH 270C.
Repeatability: Unlimited as topics vary.
MATH 277A. Topics in Mathematical Physics . 4 Units.
Studies in selected areas of mathematical physics. Topics addressed vary each quarter.
Repeatability: May be repeated for credit unlimited times.
MATH 277B. Topics in Mathematical Physics . 4 Units.
Studies in selected areas of mathematical physics. Topics addressed vary each quarter.
Prerequisite: MATH 277A.
Repeatability: May be repeated for credit unlimited times.
MATH 277C. Topics in Mathematical Physics . 4 Units.
Studies in selected areas of mathematical physics. Topics addressed vary each quarter.
Prerequisite: MATH 277B.
Repeatability: May be repeated for credit unlimited times.
MATH 280A. Mathematical Logic. 4 Units.
Basic set theory; models, compactness, and completeness; basic model theory; Incompleteness and Gödel's Theorems; basic recursion theory; constructible sets.
MATH 280B. Mathematical Logic. 4 Units.
Basic set theory; models, compactness, and completeness; basic model theory; Incompleteness and Gödel's Theorems; basic recursion theory; constructible sets.
Prerequisite: MATH 280A.
MATH 280C. Mathematical Logic. 4 Units.
Basic set theory; models, compactness, and completeness; basic model theory; Incompleteness and Gödel's Theorems; basic recursion theory; constructible sets.
Prerequisite: MATH 280B.
MATH 281A. Set Theory. 4 Units.
Ordinals, cardinals, cardinal arithmetic, combinatorial set theory, models of set theory, Gödel's constructible universe, forcing, large cardinals, iterate forcing, inner model theory, fine structure.
Prerequisite: MATH 280C.
MATH 281B. Set Theory. 4 Units.
Ordinals, cardinals, cardinal arithmetic, combinatorial set theory, models of set theory, Gödel's constructible universe, forcing, large cardinals, iterate forcing, inner model theory, fine structure.
Prerequisite: MATH 281A.
MATH 281C. Set Theory. 4 Units.
Ordinals, cardinals, cardinal arithmetic, combinatorial set theory, models of set theory, Gödel's constructible universe, forcing, large cardinals, iterate forcing, inner model theory, fine structure.
Prerequisite: MATH 281B.
MATH 282A. Model Theory. 4 Units.
Languages, structures, compactness and completeness. Modeltheoretic constructions. Omitting types theorems. Morley's theorem. Ranks, forking. Model completeness. Ominimality. Applications to algebra.
Prerequisite: MATH 280C.
MATH 282B. Model Theory. 4 Units.
Languages, structures, compactness and completeness. Modeltheoretic constructions. Omitting types theorems. Morley's theorem. Ranks, forking. Model completeness. Ominimality. Applications to algebra.
Prerequisite: MATH 282A.
MATH 282C. Model Theory. 4 Units.
Languages, structures, compactness and completeness. Modeltheoretic constructions. Omitting types theorems. Morley's theorem. Ranks, forking. Model completeness. Ominimality. Applications to algebra.
Prerequisite: MATH 282B.
MATH 285A. Topics in Mathematical Logic. 4 Units.
Studies in selected areas of mathematical logic, a continuation of MATH 280AMATH 280BMATH 280C. Topics addressed vary each quarter.
Prerequisite: MATH 280C.
Repeatability: Unlimited as topics vary.
MATH 285B. Topics in Mathematical Logic. 4 Units.
Studies in selected areas of mathematical logic, a continuation of MATH 280AMATH 280BMATH 280C. Topics addressed vary each quarter.
Prerequisite: MATH 285A.
Repeatability: Unlimited as topics vary.
MATH 285C. Topics in Mathematical Logic. 4 Units.
Studies in selected areas of mathematical logic, a continuation of MATH 280AMATH 280BMATH 280C. Topics addressed vary each quarter.
Prerequisite: MATH 285B.
Repeatability: Unlimited as topics vary.
MATH 290A. Methods in Applied Mathematics. 4 Units.
Introduction to ODEs and dynamical systems: existence and uniqueness. Equilibria and periodic solutions. Bifurcation theory. Perturbation methods: approximate solution of differential equations. Multiple scales and WKB. Matched asymptotic. Calculus of variations: direct methods, EulerLagrange equation. Second variation and Legendre condition.
MATH 290B. Methods in Applied Mathematics. 4 Units.
Introduction to ODEs and dynamical systems: existence and uniqueness. Equilibria and periodic solutions. Bifurcation theory. Perturbation methods: approximate solution of differential equations. Multiple scales and WKB. Matched asymptotic. Calculus of variations: direct methods, EulerLagrange equation. Second variation and Legendre condition.
Prerequisite: MATH 290A.
MATH 290C. Methods in Applied Mathematics. 4 Units.
Introduction to ODEs and dynamical systems: existence and uniqueness. Equilibria and periodic solutions. Bifurcation theory. Perturbation methods: approximate solution of differential equations. Multiple scales and WKB. Matched asymptotic. Calculus of variations: direct methods, EulerLagrange equation. Second variation and Legendre condition.
Prerequisite: MATH 290B.
MATH 291C. Topics in Applied and Computational Math. 4 Units.
Studies in selected areas of applied and computational mathematics. Topics addressed vary each quarter.
Repeatability: May be repeated for credit unlimited times.
MATH 295A. Partial Differential Equations. 4 Units.
Theory and techniques for linear and nonlinear partial differential equations. Local and global theory of partial differential equations: analytic, geometric, and functional analytic methods.
MATH 295B. Partial Differential Equations. 4 Units.
Theory and techniques for linear and nonlinear partial differential equations. Local and global theory of partial differential equations: analytic, geometric, and functional analytic methods.
Prerequisite: MATH 295A.
MATH 295C. Partial Differential Equations. 4 Units.
Theory and techniques for linear and nonlinear partial differential equations. Local and global theory of partial differential equations: analytic, geometric, and functional analytic methods.
Prerequisite: MATH 295B.
MATH 296. Topics in Partial Differential Equations. 4 Units.
Studies in selected areas of partial differential equations, a continuation of MATH 295AMATH 295BMATH 295C. Topics addressed vary each quarter.
Prerequisite: MATH 295C.
Repeatability: Unlimited as topics vary.
Restriction: Graduate students only.
MATH 297. Mathematics Colloquium. 1 Unit.
Weekly colloquia on topics of current interest in mathematics.
Grading Option: Satisfactory/unsatisfactory only.
Repeatability: May be repeated for credit unlimited times.
MATH 298A. Seminar . 13 Units.
Seminars organized for detailed discussion of research problems of current interest in the Department. The format, content, frequency, and course value are variable.
Grading Option: Satisfactory/unsatisfactory only.
Repeatability: Unlimited as topics vary.
MATH 298B. Seminar . 2 Units.
Seminars organized for detailed discussion of research problems of current interest in the Department. The format, content, frequency, and course value are variable.
Prerequisite: MATH 298A.
Grading Option: Satisfactory/unsatisfactory only.
Repeatability: Unlimited as topics vary.
MATH 298C. Seminar . 2 Units.
Seminars organized for detailed discussion of research problems of current interest in the Department. The format, content, frequency, and course value are variable.
Prerequisite: MATH 298B.
Grading Option: Satisfactory/unsatisfactory only.
Repeatability: Unlimited as topics vary.
MATH 299A. Supervised Reading and Research. 112 Units.
Supervised reading and research with Mathematics faculty.
Repeatability: May be repeated for credit unlimited times.
MATH 299B. Supervised Reading and Research. 112 Units.
Supervised reading and research with Mathematics faculty.
Prerequisite: MATH 299A.
Repeatability: May be repeated for credit unlimited times.
MATH 299C. Supervised Reading and Research. 112 Units.
Supervised reading and research with Mathematics faculty.
Prerequisite: MATH 299B.
Repeatability: May be repeated for credit unlimited times.
MATH 399. University Teaching. 14 Units.
Limited to Teaching Assistants.
Grading Option: Satisfactory/unsatisfactory only.
Repeatability: May be repeated for credit unlimited times.