Courses
Course descriptions and schedules offered below are a helpful guide to find courses offered by the department.
This listing is not meant to replace the official course catalog maintained by the University Registrar.
MATH 1050
Precollege Mathematics I
Fractions and decimals, basic algebra, graphing lines, factoring, systems of equations. Credit for this course will not count toward graduation in any degree program.
Prereq: 1040 (040) or 050, or Math Placement Level T, or permission of department. Not open to students with credit for any Math course above 1050 (050). This course is available for EM credit.
MATH 1060
Supplementary Pre-College Mathematics
Math 1060 is a terminal math course designed to satisfy the Quantitative Reasoning: Basic Computation category of the General Education Requirement (GE). Students may follow-up with Math 1116 to satisfy the Mathematical or Logical Analysis category of the General Education Requirement (GE). Students who wish to take math courses higher than Math 1116 should take Math 1075 rather than Math 1060.
Prereq: C- or better in 1050, or Math placement level S. Not open to students with credit for any higher numbered math class, or for any quarter class numbered higher than 50. GE quant reason basic computation course.
MATH 1075
Precollege Mathematics II
Algebraic, rational, and radical expressions; functions and graphs; quadratic equations; absolute value; inequalities; and applications. Credit for this course will not count toward graduation in any degree program.
Prereq: 1074 or 075; or a grade of C- or above in 1050; or Math Skills Assessment Level R or S; or ACT math subscore of 22 or higher that is less than 2 years old. Not open to students with credit for any Math course above 1075, except for 1116; or for any quarter-system course above 075, except for 116. This course is available for EM credit. GE quant reason basic computation course.
MATH 1116
Excursions in Mathematics
Critical thinking and problem solving, with relevant topics met in everyday life. Appropriate for non-science majors.
Prereq: 1073, 1074, 1075, 75, or 104; or Math Placement Level R or above; or ACT math subscore of 22 or higher that is less than 2 years old. Not open to students with credit for 1152 (153) or above. GE quant reason math and logical anly course. GE foundation math and quant reasoning or data anyl course.
MATH 1118
Mathematics for Architects
Topics in geometry for architecture majors.
Prereq: A grade of C- or above in 1148 or 1150, or credit for 148 or 150, or Math Placement Level M or L; and enrollment in School of Architecture.
MATH 1120
Precalculus with Review I
The purpose of this sequence is to accelerate students who need to complete Math 1151 Calculus I or beyond. Enrollment priority will be given to STEM majors. This is the first course of a two course sequence covering precalculus. In this first course, topics covered will include an introduction to functions (linear, polynomial and rational), equations and inequalities along with appropriate review. This course is designed with an emphasis on reviewing these fundamental basic algebra skills as they apply to precalculus in a just-in-time manner.
MATH 1121
Precalculus with Review II
The purpose of this sequence is to accelerate students who need to complete Math 1151 Calculus I or beyond. Enrollment priority will be given to STEM majors. This is the second course of a two-course sequence covering precalculus. In this course, topics covered will include systems of equations, trigonometry, inverse functions, and applications of functions (including previews of some calculus topics) along with appropriate review. This course is designed with an added emphasis on conceptual understanding of these topics as a preparation for Calculus.
MATH 1125
Mathematics for Elementary Teachers I
Sequence 1125-1126 involves numbers, geometry, measurement, and mathematical reasoning, for prospective elementary school teachers.
Prereq: A grade of C- or above in 1075; or credit for 1074, 75, or 104; or Math Placement Level R or above; or ACT math subscore of 22 or higher that is less than 2 years old; and enrollment in Early Childhood or Special Education major, or in Middle Childhood major or pre-major with area of concentration different than Math.
MATH 1126
Mathematics for Elementary Teachers II
Continuation of 1125: numbers, geometry, measurement, and mathematical reasoning, for prospective elementary school teachers.
Prereq: A grade of C- or above in 1125; and enrollment in Early Childhood or Special Education major, or in Middle Childhood major or pre-major with area of concentration different than Math.
MATH 1130
College Algebra for Business
Algebraic, exponential, and logarithmic functions. Matrix algebra. Applications to business.
Prereq: A grade of C- or above in 1075, or credit for 104, or Math Placement Level M or N, or ACT math subscore of 22 or higher that is less than 2 years old. Not open to students with credit for 1131 (131), or for any Math course numbered 1149 (150) or above. This course is available for EM credit. GE quant reason math and logical anly course. GE foundation math and quant reasoning or data anyl course.
MATH 1131
Calculus for Business
Survey of calculus of one and several variables; applications to business.
Prereq: A grade of C- or above in 1130, 1144, 1148, or 1150, or credit for 130, 148, or 150, or Math Placement Level L. Not open to students with credit for 1151 (151) or above, or 1134 (132). This course is available for EM credit. GE quant reason math and logical anly course. GE foundation math and quant reasoning or data anyl course.
MATH 1135
Number and Operations for Teachers
The first course in a two semester sequence for teachers of elementary and middle grade students. This course focuses on concepts of numbers and arithmetic operations, including modern and historical perspectives.
Prereq: A grade of C- or above in 1075; or credit for 1074, 75, or 104; or Math Placement Level R or above; or ACT math subscore of 22 or higher that is less than 2 years old. Not open to students with credit for 106.
MATH 1136
Measurement and Geometry for Teachers
This course is the second in a two semester sequence for teachers of elementary and middle grade students. This course focuses on concepts of measurement and geometry, including modern and historical perspectives.
Prereq: A grade of C- or above in 1135.
MATH 1140
Calculus with Review I
This is the first of a two semester course sequence. The topics covered in Math 1140 will include differential calculus of one real variable, with review of important algebra and pre-calculus concepts. Calculus with Review I is a course designed with an emphasis on reviewing these fundamental pre-calculus skills as they apply to calculus.
Prereq: A grade of C- or above in 1148 and 1149, or in 1144, 1150, or 150, or Math Placement Level L. Not open to students with credit for 1141, or 1151 or above, or 151.xx or above. GE quant reason math and logical anyl course. GE foundation math and quant reasoning or data anyl course.
MATH 1141
Calculus with Review II
This is the second of a two semester course sequence. The topics covered in Math 1141 will include differential calculus of one real variable, with review of important algebra and pre-calculus concepts. Math 1141 is a course designed with an emphasis on reviewing these fundamental pre-calculus skills as they apply to calculus.
Prereq: A grade of C- or above in 1140. Not open to students with credit for 1151 or above (151.xx, or above). GE quant reason math and logical anyl course. GE foundation math and quant reasoning or data anyl course.
MATH 1148
College Algebra
Functions: polynomial, rational, radical, exponential, and logarithmic. Introduction to right-angle trigonometry. Applications.
Prereq: A grade of C- or above in 1075, or credit for 104 or 148, or Math Placement Level N, or ACT math subscore of 22 or higher that is less than 2 years old, or permission of department. Not open to students with credit for 1144, or for Math courses numbered 1150 (150) or above. This course is available for EM credit. GE quant reason math and logical anly course. GE foundation math and quant reasoning or data anyl course.
MATH 1149
Trigonometry
Trigonometric functions and their properties. Vectors, polar coordinates and complex numbers.
Prereq: A grade of C- or above in 1148, or permission of department. Not open to students with credit for 1144, or for any Math course numbered 1150 (150) or above. This course is available for EM credit. GE quant reason math and logical anly course. GE foundation math and quant reasoning or data anyl course.
MATH 1150
Precalculus
Functions: polynomial, rational, radical, exponential, logarithmic, trigonometric, and inverse trigonometric. Applications.
Prereq: Math Placement Level M. Not open to students with credit for 1144, 1148, or for 1149 or above, or for any quarter Math course numbered 150 or above. This course is available for EM credit. GE quant reason math and logical anly course. GE foundation math and quant reasoning or data anyl course.
MATH 1151
Calculus I
Differential and integral calculus of one real variable.
Prereq: A grade of C- or above in 1148 and 1149, or in 1144, 1150, or 150, or Math Placement Level L. Not open to students with credit for 1152 or 152.xx, or above. This course is available for EM credit. GE quant reason math and logical anly course. GE foundation math and quant reasoning or data anyl course.
MATH 1152
Calculus II
Integral calculus, sequences and series, parametric curves, polar coordinates, (optional: vectors).
Prereq: A grade of C- or above in 1114 (114), 1151, 1156, 1161.xx, 152.xx, 161.xx, or 161.01H. Not open to students with credit for 1172, 1181H or any Math class numbered 1500 or above, or with credit for 153.xx, or Math courses numbered 162.xx or above. This course is available for EM credit. GE quant reason math and logical anly course. GE foundation math and quant reasoning or data anyl course.
MATH 1154
Calculus I for Engineering Technology
Calculus I for Engineering Technology is the first in a two-course calculus sequence specifically designed for Engineering Technology. It covers standard Calculus topics including limits, differentiation, integration, optimization, and approximation with an emphasis on building mathematical intuition, problem solving ability and using appropriate technology to find solutions.
Prereq: A grade of C- or above in 1148 and 1149, or grade of C- or above in 1144 or 1150, or Math Placement Level L. Not open to students with credit for 2153 or above.
MATH 1155
Calculus II for Engineering Technology
Calculus II for Engineering Technology is the second in a two-course calculus sequence specifically for Engineering Technology. It covers standard Calculus topics including related rates, Taylor Polynomial approximations, differential equations and functions of several variables with an emphasis on building mathematical intuition, problem solving and using appropriate technology to find solutions.
Prereq: A grade of C- or above in 1154.
MATH 1156
Calculus for the Biological Sciences
Differential calculus and mathematical modeling in the life sciences.
Prereq: A grade of C- or above in 1148 and 1149, or a grade of C- or above in 1150, or credit for 150, or Math Placement Level L. Not open to students with credit for 1151 (151.xx) or above. GE quant reason math and logical anly course. GE foundation math and quant reasoning or data anyl course.
MATH 1157
Mathematical Modeling for the Biological Sciences
Models in life sciences using integral calculus, linear algebra, dynamical systems, and ordinary differential equations.
Prereq: A grade of C- or above in 1151, 1156, 1161.xx, or 1181H, or credit for 152.xx. Not open to students with credit for 1152, or for any Math course numbered 2000 or above, or for a quarter-system Math course numbered 254.xx or above.
MATH 1161.01
Accelerated Calculus I
Differential and integral calculus of one real variable. Intended for students having prior experience with calculus.
Prereq: Math Placement Level L, and previous calculus experience. Not open to students with credit for any Math course numbered 1152 or above, or for the quarter-system Math courses 151.xx and 152.xx, or for any quarter-system course numbered 162 or above. GE quant reason math and logical anly course.
MATH 1161.02
Accelerated Calculus I for Honors Engineers
Differential and integral calculus of one real variable. Intended for students in Fundamentals of Engineering for Honors (FEH).
Prereq: Math Placement Level L, and previous calculus experience. Not open to students with credit for 1152, or 151.xx and 152.xx, or 162 or above. GE quant reason math and logical anly course.
MATH 1165
Math for Middle School Teachers I
Algebra and reasoning for middle school teachers.
Prereq: A grade of C- or above in 1148 and 1149, or in 1150, or credit for 150, or Math Placement Level L; and major or pre-major in Middle Childhood Education, within either ASC or EHE.
MATH 1166
Math for Middle School Teachers II
Geometry for middle school teachers.
Prereq: A grade of C- or above in 1165, and major or pre-major in Middle Childhood Education either within ASC or within EHE.
MATH 1172
Engineering Mathematics A
Techniques of integration, Taylor series, differential calculus of several variables. Applications.
Prereq: A grade of C- or above in 1114 (114), 1151, 1156, 1161.xx, 152.xx, 161.xx, or 161.01H. Not open to students with credit for 1152, 1534 (153.xx), or 1544 (154), or for any Math class numbered 1172 or above, or for any quarter-system Math class numbered 254.xx or above. Not open to students majoring in Math, pre-Actuarial Science, or Actuarial Science. This course is available for EM credit.
MATH 1181H
Honors Calculus I
Single variable calculus treated in depth.
Prereq: 1151 or 151.xx, and permission of department. GE quant reason math and logical anly course. GE foundation math and quant reasoning or data anyl course.
MATH 1187
Problem Solving
Problem solving involving topics in college algebra and calculus.
Prereq: Permission of department. Repeatable to a maximum of 8 cr hrs or 4 completions. This course is graded S/U.
MATH 1187H
Honors Problem Solving
Problem solving beyond what is encountered in standard programs.
Prereq: Permission of department. Repeatable to a maximum of 8 cr hrs or 4 completions. This course is graded S/U.
MATH 1193
Individual Studies in Mathematics
Individual studies.
Prereq: Permission of department. Repeatable to a maximum of 6 cr hrs or 2 completions. This course is graded S/U.
MATH 1194
Group Studies in Mathematics
Designed to give groups of undergraduate students an opportunity to pursue special studies not otherwise offered.
Prereq: Permission of department. Repeatable to a maximum of 6 cr hrs or 2 completions.
MATH 1194H
Honors Group Studies in Mathematics
Designed to give groups of honors undergraduate students an opportunity to pursue special studies not otherwise offered.
Prereq: Permission of department. Repeatable to a maximum of 6 cr hrs or 2 completions.
MATH 1295
Introductory Seminar
Seminar on mathematical topics for beginning math majors.
Prereq: Enrollment in Math major, or permission of department. This course is graded S/U.
MATH 2010S
Intersections of Mathematics and Society: Hidden Figures
This course examines the intersections of race, gender, and mathematics as it relates to the accomplishments of the African-American mathematicians featured in the book. We analyze how mathematics and the advancement of American society were intertwined from WWII to the Space Race and focus on understanding the mathematical tools used by human computers and scientists at Langley during this time.
Prereq: A grade of C- or above in 1148 and 1149; or a grade of C- or above in 1150; or Math Placement Level L. GE cultures and ideas and diversity soc div in the US and service learning course.
MATH 2137
Algebra and Coordinate Geometry for Teachers
This is one of two independent courses which follow Math 1136 to provide necessary content for middle grade teachers. This course focuses on algebra, coordinate geometry, and their connections through equations in one or more unknowns. Modern and historical perspectives are woven throughout.
Prereq: A grade of C- or above in 1136; and a grade of C- or above in 1149 or 1150, or credit for 150, or math placement level L.
MATH 2138
Calculus and its History for Teachers
This is one of two independent courses which follow Math 1136 to provide necessary content for middle grade teachers. This course focuses on functions and calculus, including modern and historical perspectives.
Prereq: A grade of C- or above in 1136; and a grade of C- or above in 1149 or 1150, or credit for 150, or math placement level L.
MATH 2153
Calculus III
Multivariable differential and integral calculus.
Prereq: A grade of C- or above in 1152, 1172, 1534, 1544, 1181H, or 4181H, or credit for 153.xx, 154, 162.xx, or 162.01H. Not open to students with credit for any course 2153 or above, or for any quarter-system class 254.xx or above. This course is available for EM credit.
MATH 2162.01
Accelerated Calculus II
Vectors, multivariable calculus, integral theorems.
Prereq: A grade of C- or above in 1161.xx, 1181H, or 4181H. Not open to students with credit for semester Math course above 2162.01, or for any quarter Math course numbered 254.xx or above.
MATH 2162.02
Accelerated Calculus II for Honors Engineers
Accelerated multivariable calculus. Intended for students in Fundamentals of Engineering for Honors (FEH).
Prereq: A grade of C- or above in 1161.xx, 1181H, or 4181H. Not open to students with credit for 2153, or for a semester Math course numbered 2162 or above, or for a quarter Math course numbered 263.xx or above.
MATH 2167
Calculus for Middle School Teachers
Concepts of Calculus for Middle School teachers.
Prereq: A grade of C- or above in 1165, or credit for 1164 (110); and enrollment in Middle Childhood Education major or pre-major, within ASC or EHE. Not open to students with credit for 111.
MATH 2168
History of Mathematics for Middle School Teachers
Historical and mathematical discussion of topics in the middle school math curriculum.
Prereq: A grade of C- or above in 2167, or credit for 111; and enrollment as a major or pre-major in Middle Childhood Education (within either ASC or EHE). Not open to students with credit for 212.
MATH 2173
Engineering Mathematics B
Multiple integrals, line integrals, vector fields, second order ordinary differential equations.
Prereq: 1172 or 1544 (154). Not open to students with credit for 2153, or for any Math course 2173 or above, or for any quarter-system Math course 254.xx or above.
MATH 2174
Linear Algebra and Differential Equations for Engineers
Matrix theory, eigenvectors and eigenvalues, ordinary and partial differential equations.
Prereq: 2173, and enrollment in Engineering, Physics, or Chemistry major; or permission of Math department. Not open to students with credit for both 2415 (415.xx) and 2568 (568 or 571), or with credit for 5520H (520H and 521H).
MATH 2177
Mathematical Topics for Engineers
Multiple integrals, line integrals; matrix algebra; linear (ordinary and partial) differential equations.
Prereq: 1172, 1544 (154), 2153, 2162.xx, 2182H, 4182H, 254.xx, 263.xx, 263.01H, or 264H; and a major or minor in Biochem, BiomedE, Chem, CEEGS, FABEng, MatScEn, CBE, Physics or WeldEng. Not open to students with credit for 2174 or 5520H, or with credit for both (i) 2415 (415), 2255 (255), or 4512 (512) and (ii) 2568 (568 or 571).
MATH 2182H
Honors Calculus II
Multivariable calculus treated in depth.
Prereq: A grade of C or above in 1181H or 4181H. Not open to students with credit for both 162.01H and 263.01H.
MATH 2193
Individual Studies in Mathematics
Individual studies.
Prereq: Permission of department. Repeatable to a maximum of 6 cr hrs or 2 completions. This course is graded S/U.
MATH 2194
Group Studies in Mathematics
Designed to give groups of able undergraduate students an opportunity to pursue special studies not otherwise offered.
Prereq: Permission of department. Repeatable to a maximum of 6 cr hrs or 2 completions.
MATH 2255
Differential Equations and Their Applications
Ordinary differential equations, their series solutions, numerical methods, Laplace transforms, physical applications.
Prereq: A grade of C- or above in 2153, 2162.xx, 2173, 2182H, or 4182H, or credit for 254.xx, 263.xx, 263.01H, or 264H. Not open to students with credit for 2415, 5520H, 255, 415.xx, or 521H.
MATH 2366
Introduction to Discrete Mathematics
Mathematical reasoning, logic, sets, functions, recursive definitions, elementary counting principles.
Prereq: C- or better in 1131, 1151, 1161.xx, or 1181H; or credit for 132, 152.xx, 161.xx, 161.01H; or permission of department. Open only to majors in MIS (Management Information Systems). Not open to students with credit for 366.
MATH 2415
Ordinary and Partial Differential Equations
Ordinary and partial differential equations: Fourier series, boundary and initial value problems.
Prereq: 2153, 2162.xx, 2173, 2182H, 4182H, 254.xx, 263.xx, 263.01H, or 264H; or 2568 and either 1172 or 1544 (154). Not open to students with credit for 2255 (255), 5520H (521H), 2174, or 415.xx.
MATH 2568
Linear Algebra
Matrix algebra, vector spaces and linear maps, bases and dimension, eigenvalues and eigenvectors, applications.
Prereq: A grade of C- or above in 1172, 1544, 2153, 2162.xx, 2182H, or 4182H; or a grade of C- or above in both 1152 and CSE 2321. Not open to students with credit for 4568 or 5520H.
MATH 2568H
Honors Linear Algebra
This course, an introduction to linear algebra, is aimed at math majors who want a rigorous background in finite-dimensional linear algebra and exposure to applications of modern relevance, including some practice in implementing ideas from this course on a computer.
Prereq: A grade of C- or above in 2153, 2162.xx, 2182H, or 4182H; and permission of department. Not open to students with credit for 2568, 4568, or 5520H.
MATH 3295
Senior Seminar
Seminar on mathematical topics and career possibilities for senior math majors and actuarial science majors.
Prereq: Enrollment in Math or Actuarial Science major, and permission of department. This course is graded S/U.
MATH 3345
Foundations of Higher Mathematics
Introduction to logic, proof techniques, set theory, number theory, real numbers.
Prereq: Major or minor in Math, CSE, CIS, ECE, IMME, STAT, STEMED-PRE or STEMED-BS, and:
If Math, IMME, STAT, STEMED-PRE or STEMED-BS:
Prereq: A grade of C- or above in 2153, 2162.xx, 2173, or 2182H.
If CIS, CSE or ECE:
Prereq: A grade of C- or above in CSE 2321; and a grade of C- or above in 1161.xx, 1172, 1181H, 1534, 1544, 1152, or 4181H.
MATH 3345H
Honors Foundations of Higher Mathematics
A systematic introduction to problem solving and proof-writing through interesting, non-trivial mathematics. This class serves as a bridge between a problem-oriented Calculus class and the more conceptual classes in the math major. Additionally, this class exposes students to some of math's greatest intellectual successes.
Prereq: A grade of C- or above in 2153, 2162.xx, 2173, or 2182H; and permission of department. Not open to students with credit for 3345.
MATH 3350
Introduction to Mathematical Biology
Introduction to quantitative and qualitative analysis of several mathematical models for biological systems.
Prereq: C- or better in Math 2255, 2415, 5520H; or credit for 255, 415.xx, or 521H. Not open to students with credit for 350.
MATH 3532
Mathematical Foundations of Actuarial Science
Problem workshop for applications of calculus and probability to actuarial science and risk management.
Prereq: C- or better in 4530, 5530H, or Stat 4201; or credit for Math 530, 531H, or Stat 420. Not open to students with credit for 532.
MATH 3588
Practicum in Actuarial Science
Presentations by practicing actuaries on topics drawn from their fields of expertise; oral presentations by students on selected topics in actuarial science.
Prereq: Completion of second writing course. Jr standing. Open only to actuarial science majors. Not open to students with credit for 588.
MATH 3589
Introduction to Financial Mathematics
Introduction to mathematics used in financial asset pricing, based on the binomial asset pricing model. Prepares students for further study of stochastic calculus in continuous time.
Prereq: C- or better in 3345 or credit for 345; and either C- or better in 4530, 5530H, or Stat 4201; or credit for 530, 531H, or Stat 420; or permission of department. Not open to students with credit for 589.
MATH 3607
Beginning Scientific Computing
Introduction to mathematical theory of algorithms used to solve problems that typically arise in sciences, engineering, and finance.
Prereq: Both a C- or better in 2255, 2415, or 5520H, or credit for 255, 415.xx, or 521H; and also a C- or better in 2568 or 5520H, or credit for 568, 571, or 520H.
MATH 3618
Theory of Interest
Financial transactions involving interest: measurement of interest, force of interest, annuities-certain, introduction to financial derivatives.
Prereq: A grade of C- or above in 1152, 1172, 1181H, 1534, 1544, 2162.xx, 2153, or 4181H, or credit for 153, 154, 162, 162H, or 191H; and enrollment in Math major, or Actuarial Science major or pre-major. Not open to students with credit for 618.
MATH 4181H
Honors Analysis I
4181H - 4182H is an enriched honors sequence introducing students to mathematical underpinnings of calculus.
Prereq: Permission of department.
MATH 4182H
Honors Analysis II
4181H - 4182H is an enriched honors sequence introducing students to mathematical underpinnings of calculus.
Prereq: A grade of B- or above in 4181H, or permission of department. Not open to students with credit for 264H.
MATH 4193
Individual Studies in Mathematics
Individual studies.
Prereq: Permission of department. Repeatable to a maximum of 6 cr hrs or 2 completions. This course is graded S/U.
MATH 4194
Group Studies in Mathematics
Designed to give groups of able undergraduate students an opportunity to pursue special studies not otherwise offered.
Prereq: Permission of department. Repeatable to a maximum of 6 cr hrs or 2 completions.
MATH 4350
Quantitative Neuroscience
Introduction to mathematical modeling and computational analysis of neuronal systems, Hodgkin-Huxley model, dynamical systems methods, neuronal networks, models for neurological disease.
Prereq: 1152 (152) or 1157, or permission of instructor.
MATH 4407
Geometry for Teaching
Algebra connections between school mathematics and undergraduate mathematics, focusing on the algebra in the Common Core State Standards for Mathematics.
Prereq: Enrollment in the M.Ed. program for secondary mathematics. Prereq or concur: 4507; or permission of instructor.
MATH 4420
Capstone Course for Integrated Major in Mathematics and English
Students combine the Mathematics and English knowledge and skills they have acquired in the integrated major through a capstone experience.
Prereq: Sr standing in Integrated Major in Mathematics and English (IMME) Program, or permission of instructor. Not open to students with credit for English 4420. Cross-listed in English.
MATH 4480
Algebra for Teaching
Algebra connections between school mathematics and undergraduate mathematics, focusing on the algebra in the Common Core State Standards for Mathematics.
Prereq: Enrollment in the M.Ed. program for secondary mathematics. Prereq or concur: 4580; or permission of instructor.
MATH 4504
History of Mathematics
Development of mathematics from primitive origins to present forms. Topics include development of arithmetic, algebra, geometry, trigonometry, and calculus.
Prereq: A grade of C- or above in 2568, 4507, or 5520H, or credit for 568, 571, 507, 580, or 520H, and enrollment in Math major or Grad standing in EduTL; or permission of department. Not open to students with credit for 504.
MATH 4507
Geometry
Topics in Euclidean, spherical, and hyperbolic geometries.
Prereq: A grade of C- or above in 3345, and in 2568 or 5520H; or credit for 345, and credit for 568, 571, or 520H. Not open to students with credit for 507.
MATH 4512
Partial Differential Equations for Science and Engineering
Second order ordinary differential equations via Laplace transforms and series solutions; Fourier series; three archetypical partial differential equations; boundary value problems; Sturm-Liouville theory. Intended for Engineering students.
Prereq: A grade of C- or above in 2153, 2162.xx, 2173, 2182H, or 4182H, or credit for 254.xx, 263.xx, 263.01H, or 264H. Not open to students with credit for 4557 (557) or 512.
MATH 4530
Probability
Combinatorial probability, random variables, independence, expectation, variance.
Prereq: A grade of C- or above in 2153, 2162.xx, 2173, 2177, 2182H, or 4182H, or credit for 254.xx, 263.xx, 263.01H, or 264H. Not open to students with credit for 5530H (531H), 530, or Stat 4201 (420).
MATH 4545
Analysis Overview
Topics in calculus and analysis.
Prereq: A grade or C- or above in 2153, 2162.xx, 2173, 2182H, or 4182H, or credit for 254, 263.xx, 263.01H, 264H, or equiv; and a grade of C- or above in 2568 or 5520H, or equiv; and Grad standing in Statistics or Biostatistics; and permission of department (Statistics or Biostatistics).
MATH 4547
Introductory Analysis I
4547 - 4548 involves advanced calculus: sequences, limits, continuity, differentiation, Riemann integral, sequences and series of functions, Taylor series, improper integrals.
Prereq: C- or better in 3345; or credit for 345. Not open to students with credit for 548.
MATH 4548
Introductory Analysis II
Continuation of Math 4547. Advanced calculus: sequences, limits, continuity, differentiation, Riemann integral, sequences and series of functions, Taylor series, improper integrals.
Prereq: C- or better in 4547, or credit for 548. Not open to students with credit for 549.
MATH 4551
Vector Analysis
Vector operations; Jacobian and change of variables; divergence, gradient, and curl; Green's, Stokes', and divergence theorems; applications.
Prereq: C- or better in 2153, 2162.xx, 2173, or 2182H; or credit for 254.xx, 263.xx, or 263.01H. Not open to students with credit for 4182H (264H), 513, or 551.
MATH 4552
Complex Analysis
Introduction to analytic functions of a complex variable, integral theorems, power series, residues, conformal mapping.
Prereq: A grade of C- or above in 2153, 2162.xx, 2173, 2182H, or 4182H, or credit for 254.xx, 263.xx, 263.01H, or 264H. Not open to students with credit for 5522H (522H), 514, or 552.
MATH 4556
Dynamical Systems
Systems of linear, first-order differential equations; existence and uniqueness theorems; numerical methods; qualitative theory; and physical applications.
Prereq: A grade of C- or above in 2153, 2162.xx, 2173, 2182H, or 4182H, or credit for 254.xx, 263.xx, 263.01H, or 264H. Not open to students with credit for 556.
MATH 4557
Partial Differential Equations
First and second-order PDE's; existence and uniqueness, initial and boundary value problems, Fourier series; Green's functions; wave, heat and Laplace equations; nonlinear PDE's; applications.
Prereq: C- or better in 2255, 2415, 4556, or 5520H; or credit for 255, 415.xx, or 521H. Intended for Math majors. Not open to students with credit for 4512 (512), or 557.
MATH 4568
Linear Algebra for Engineering Graduate Students
Systems of linear equations, vector spaces, bases and dimension, linear maps and matrices, eigenvalues and eigenvectors, applications.
Prereq: A grade of C- or above in 1172, 2153, 2162.xx, 2182H, or 4182H, or credit for 254, 263.xx, 263.01H, or 264H, or equiv; and Grad standing. Not open to students with credit for 2568 (568), 5101 (601), 5520H (520H), or 572.
MATH 4570
Applied Algebraic Topology
This course will serve as an introduction to algebraic topology, with a view toward persistent homology of point clouds for applications to data analysis. Homology of simplicial complexes over a field with a focus on building up intuition about homology moving to a specialized notion of persistent homology of persistence modules. Real-world applications to data analysis will be provided.
Prereq: A grade of C- or above in 2568 and 3345.
MATH 4573
Elementary Number Theory
Prime numbers, modular arithmetic, Diophantine equations, combinatorial analysis; introduction to concepts of abstract algebra.
Prereq: A grade of C- or above in 3345 or 4181H, or credit for 264H or 345. Not open to students with credit for 5576H or 573.
MATH 4575
Combinatorial Mathematics
Classic puzzles of recreational mathematics; matching theory and graph theory; enumeration techniques; combinatorial analysis.
Prereq: C- or better in 2568 or 5520H; or credit for 568, 571, or 520H. Not open to students with credit for 5529H or 575.
MATH 4578
Discrete Mathematical Models
Homogeneous and non-homogeneous difference equations of one or several variables, Markov chains, graph theory, network flows.
Prereq: Both a C- or better in 2568 or 5520H; and also a C- or better in 4530, 5530H or Stat 4201; or both credit for 568, 571, or 520H; and also credit for 530, 531H, or Stat 420. Not open to students with credit for 578.
MATH 4580
Abstract Algebra I
Topics in number theory, group theory, vector spaces and linear transformation, field theory, and field extensions.
Prereq: A grade of C- or above in 3345, or credit for 345; and a grade of C- or above in 2568 or 5520H, or credit for 568, 571, or 520H. Not open to students with credit for 581 or 591H.
MATH 4581
Abstract Algebra II
Continuation of Math 4580: topics in number theory, group theory, vector spaces and linear transformations, field theory, and field extensions.
Prereq: A grade of C- or above in 4580, or credit for 5590H or 581. Not open to students with credit for 582 or 592H.
MATH 4990
Undergraduate Seminar in Mathematical Biology Research
Seminar on research in mathematical biology and its applications, with an emphasis on evolutionary biology, ecology, neuroscience, and cell biology.
Prereq: Permission of instructor. Repeatable to a maximum of 3 cr hrs. This course is graded S/U. Cross-listed in EEOB 4990.
MATH 4998
Undergraduate Research
Opportunity for undergraduate students to do mathematical research.
Prereq: Permission of department. Repeatable to a maximum of 6 cr hrs or 2 completions. This course is graded S/U.
MATH 4998H
Honors Undergraduate Research
Opportunity for honors undergraduate students to do mathematical research.
Prereq: Honors standing and permission of department. Repeatable to a maximum of 6 cr hrs or 2 completions. This course is graded S/U.
MATH 4999
Undergraduate Thesis
Opportunity for undergraduate students to write a thesis.
Prereq: Permission of department. Repeatable to a maximum of 6 cr hrs or 2 completions. This course is graded S/U.
MATH 4999H
Honors Undergraduate Thesis
Opportunity for honors undergraduate students to write a thesis.
Prereq: Honors standing and permission of department. Not open to students with credit for 783H. Repeatable to a maximum of 6 cr hrs or 2 completions. This course is graded S/U.
MATH 5001
Introduction to Set Theory
Axioms of set theory, transfinite induction and recursion, cardinal numbers, cardinal arithmetic, ordinal numbers, ordinal arithmetic, Axiom of Choice, equivalent principles, closed unbounded and stationary sets, infinitary combinatorics.
Prereq: 4547 (547), 4580 (580), Grad standing or permission of department. Not open to students with credit for 647
MATH 5051
Introduction to Mathematical Logic
Syntax and semantics of sentential logic, syntax and semantics of first-order logic, compactness of first-order logic, Goedel's completeness theorem, theories and models of theories, Goedel's incompleteness theorems; computability.
Prereq: 4547 (547), 4580 (580), Grad standing, or permission of department. Not open to students with credit for 648 or 649.
MATH 5101
Linear Mathematics in Finite Dimensions
Vector spaces; linear transformations; inner product spaces; eigenvalues and eigenvectors; Hermitian, unitary and normal matrices; quadratic forms; constraints; Rayleigh quotients; singular value decomposition; pseudo-inverse.
Prereq: 2568 (568), 571, or grad standing. Not open to students with credit for 601.
MATH 5102
Linear Mathematics in Infinite Dimensions
Sturm-Liouville systems, Hilbert spaces, Fourier and wavelet theory, Green's functions, Helmholtz's equation, cylinder and spherical harmonic solutions, interior and exterior boundary value problems, method of steepest descent and stationary phase.
Prereq: 5101 (602). Not open to students with credit for 603.02.
MATH 5111
Algebra I
Groups and homomorphisms, group actions and Sylow's theorems, direct and semidirect products, rings and homomorphisms, factorizations in rings, polynomial rings.
Prereq: Grad standing, or permission of department. Not open to students with credit for 670.
MATH 5112
Algebra II
Modules and vector spaces, modules over a principal ideal domain, applications to linear algebra, field theory, Galois theory.
Prereq: 5111 (671) or 591H. Not open to students with credit for 672.
MATH 5152
Introduction to Number Theory with Applications
Divisibility, fundamental theorem of arithmetic, Fermat's theorem, congruences, Euler's formula, prime numbers, Euler's phi-function, counting primes, powers and roots mod m, quadratic reciprocity theorem, Diophantine approximation, Pell's theorem.
Prereq: Both 5101 (602) and 4581 (582); or Grad standing. Not open to students with credit for 683.
MATH 5168
Introduction to the Finite Element Method
Basic concepts, formulation, and application of finite element techniques for numerical solution of problems of engineering and scientific interest.
Prereq: 2568 (568) or CivilEn 2060 (406), and CSE 1221. Not open to students with credit for both CivilEn 768 and MechEng 7068. Cross-listed in MechEng and CivilEn.
MATH 5194
Group Studies in Mathematics
Designed to give groups of advanced undergraduate and beginning graduate students an opportunity to pursue special studies not otherwise offered.
Prereq: Permission of department. Repeatable.
MATH 5194H
Honors Group Studies in Mathematics
Gives groups of honors undergraduate students an opportunity to pursue special studies not otherwise offered.
Prereq: Permission of department. Repeatable to a maximum of 6 cr hrs or 2 completions.
MATH 5201
Introduction to Real Analysis I
Basic metric topology, sequences and series, continuous functions, differentiable functions of one variable, Riemann integration, uniform convergence, Fourier series.
Prereq: Grad standing, or permission of department. Not open to students with credit for 651.
MATH 5202
Introduction to Real Analysis II
Continuation of Fourier series, differentiable functions of several variables, implicit function theorem and inverse function theorem, introduction to Lebesgue measure and Lebesgue integration, introduction to Hilbert spaces.
Prereq: 5201 (652). Not open to students with credit for 653.
MATH 5221
Introduction to Complex Analysis
Calculus of functions of a complex variable, series expansion and singularities of complex analytic functions, Cauchy's integral theorem, maximum principle, harmonic functions, differentials and residue theory, Weierstrass theorem.
Prereq: 4547 (548). Not open to students with credit for 5251 (654).
MATH 5251
Complex Variables and Applications
Complex numbers and complex differentiable functions, elementary analytic functions, complex integration, series, poles and residues, conformal mapping, applications of conformal mapping.
Prereq: Both 2153.xx (254) and 4547 (548); or permission of department. Not open to students with credit for 4552 (552), 514, or 654.
MATH 5401
Applied Differential Equations I
Existence and uniqueness, linear ODE systems, 2x2, phase plane analysis, conservative and reversible systems, bifurcation analysis, limit cycles, perturbation theory.
Prereq: 2255 (255) and 2568 (568 or 572). Not open to students with credit for 615.
MATH 5402
Applied Differential Equations II
Steady state, heat equation, wave equation, PDEs in two dimensions, the Dirichlet problem, nonlinear evolution equations, wave equations by method of characteristic curve.
Prereq: 5401 (616). Not open to students with credit for 617.
MATH 5421
Mathematics of Infectious Disease Dynamics
Provides an introduction to mathematical modeling of infectious diseases, including techniques for building and analyzing disease models, and discussions of calibration and comparison of models with data. This course is intended for graduate students in public health or other related disciplines and for upper level undergraduate and graduate mathematics students.
Prereq: 1152, 1172, or 153; or permission of instructor. Cross-listed in PubHEpi.
MATH 5451
Calculus of Variations and Tensor Calculus
Euler-Lagrange equations, Hamilton's Principle, Lagrangian mechanics, Hamiltonian dynamics, Hamilton-Jacobi integration theory of dynamical systems, direct methods, tensor calculus, curvature and geometry of continuum mechanics.
Prereq: 2415.xx (415) and 2568 (568 or 572). Not open to students with credit for 701.
MATH 5520H
Honors Linear Algebra and Differential Equations
Linear transformations and matrices, spectral theorem, ordinary differential equations, existence and uniqueness theorems, phase space, stability, oscillations.
Prereq: A grade of C or above in 4182H, or in both 2182H and 3345; or credit for 264H, or in both 263H and 345; or permission of department. Not open to students with credit for 520H and 521H.
MATH 5522H
Honors Complex Analysis
Theoretical treatment of complex analysis.
Prereq: A grade of C or above in 5520H, or credit for 521H, or permission of department. Not open to students with credit for 4552, 522H, 514, or 552
MATH 5529H
Honors Combinatorics
Combinatorial mathematics and its connections with geometry, algebra, analysis, and probability.
Prereq: A grade of C or above in 4182H, or in both 2182H and 3345; or credit for 264H, or for both 263H and 345; or permission of department. Not open to students with credit for 594H taken in Au10.
MATH 5530H
Honors Probability
Theoretical treatment of probability, with applications within and outside mathematics.
Prereq: A grade of C or above in 5529H, or permission of department. Not open to students with credit for 531H or 594H in Au08 or Au07.
MATH 5540H
Honors Differential Geometry
Geometry of curves and surfaces in 3-dimensional space, curvature, geodesics, Gauss-Bonnet Theorem, Riemannian metrics.
Prereq: A grade of C or above in 5520H, or in both 2182H and 2568; or credit for 520H, or in both 263.01H and 568; or permission of department. Not open to students with credit for 541H.
MATH 5576H
Honors Number Theory
Elementary analytic and algebraic number theory, tracing its unifying role in the development of mathematics through history.
*Au Sem (odd years). Prereq: A grade of C or above in 4182H, or in both 2182H and 3345; or credit for 264H, or for both 263H and 345; or permission of department. Not open to students with credit for 577H.
MATH 5588
Practicum in Actuarial and Quantitative Risk Management
This course introduces students to the real world practice relative to advanced Actuarial Science topics and more specifically to the MAQRM program.
Prereq: CSE 1222, 1223, 1224, or 2111; and Math 2153; and Math 3618; and Math 4530, or Stat 4201; and Stat 4202; and Math 2568; or permission of department; or graduate standing.
MATH 5590H
Honors Abstract Algebra I
5590H - 5591H includes elementary number theory, group theory, ring theory, abstract linear algebra, field theory, and Galois theory.
Prereq: A grade of C or above in 5520H or in 520H, or permission of department. Not open to students with credit for 591H.
MATH 5591H
Honors Abstract Algebra II
Continuation of 5590H: elementary number theory, group theory, ring theory, abstract linear algebra, field theory, and Galois theory.
Prereq: A grade of C or above in 5590H or in 591H, or permission of department. Not open to students with credit for 592H.
MATH 5601
Essentials of Numerical Methods
Systems of linear equations, linear least squares, eigenvalue problems, nonlinear equations and optimization, interpolation, numerical integration and differentiation, numerical solution for ODEs, IVPs and BVPs.
Prereq: 4556 (556) and either 2568 (568) or 572. Not open to students with credit for 607.
MATH 5602
Computational Partial Differential Equations
Parabolic PDEs: method of lines, stability and convergence; hyperbolic PDEs: shock capturing, flux limiters; elliptic PDEs: direct solvers and iterative methods.
Prereq: Under semesters 5601 and either 4512 or 4557. Under quarters either 512 or 557; and 556; and either 568 or 572. Not open to students with credit for 606.
MATH 5603
Numerical Linear Algebra
Fundamentals of numerical linear algebra; solving square systems; QR factorization and least squares; calculation of eigenvalues; iterative methods for linear systems; iterative methods for eigenvalue problems.
Prereq: Under semesters 2568 and one of 3607, 5601 or 5602. Under quarters either 568 or 571 and either 606 or 607.
MATH 5630
Life Contingencies I
Introduction to the mathematical theory of contingencies. Includes material from examinations by the Society of Actuaries and the Casualty Actuarial Society.
Prereq: A grade of C- or above in 3618; and a grade of C- or above in 4530, 5530H, or Stat 4201; and enrollment in Actuarial Science major or the MMS program in Financial Math; or permission of department.
MATH 5631
Life Contingencies II
Continuation of 5630: Mathematical Theory of Contingencies. Includes material from examinations by the Society of Actuaries and the Casualty Actuarial Society.
Prereq: A grade of C- or above in 5630. Open only to Actuarial Science majors, and to MMS students specializing in Financial Math.
MATH 5632
Financial Economics for Actuaries
Introduction to the evaluation of options, futures, and other derivatives, interest models and risk management techniques. Includes material from examinations by the Society of Actuaries and the Casualty Actuarial Society.
Prereq: A grade of C- or above in 3618; and a grade of C- or above in 4530, 5530H, or Stat 4201; and enrollment in Math major or Actuarial Science major or Actuarial Science Pre-major, or Grad standing; or permission of department.
MATH 5633
Loss Models I
Introduction to the construction and evaluation of actuarial models, with topics covered by examinations of the Society of Actuaries and the Casualty Actuarial Society.
Prereq: A C- or above in Stat 4202; and a C- or above in 4530, 5530H, or Stat 4201. Open only to actuarial science majors, and to MMS students specializing in Financial Math.
MATH 5634
Loss Models II
Continuation of 5633: introduction to the construction and evaluation of actuarial models, with topics covered by examinations of the Society of Actuaries and the Casualty Actuarial Society.
Prereq: C- or better in 5633. Open only to actuarial science majors, and to MMS students specializing in Financial Math.
MATH 5635
Stochastic Calculus for Finance I
Mathematics used in financial asset pricing, based on Wiener (Brownian motion) processes, with applications. Overview of needed real analysis, stochastic processes, Ito Calculus, Risk-neutral measure, connections with PDEs.
Prereq: A grade of C- or above in 3589 or 3345; and a grade of C- or above in 4530, 5530H, or Stat 4201; and enrollment in Math major or Actuarial Science major; or Grad standing; or permission of department.
MATH 5636
Stochastic Calculus for Finance II
Continuation of 5635. Feynman-Kac theorem, diffusion with drift, applications to problems in financial mathematics.
Prereq: A grade of C- or above in 5635; and enrollment in Math major or Actuarial Science major, or Grad standing; or permission of department.
MATH 5637
Topics in Predictive Modeling
An introduction to some basic concepts and methods in statistical learning with emphasis on the mathematics behind these concepts and methods.
Prereq: A grade of C- or above in 2568 or 5520H, and a grade of C- or above in Stat 4202; or permission of department.
MATH 5651
Mathematical Modeling of Biological Processes
Enzyme dynamics, predator-prey and competition model, spread of diseases, plant growth, cell cycle and cell differentiation, reaction-diffusion with advection, cancer models and cancer therapy, wound healing.
Prereq: Grad standing; or either 4512 (512) or 557, and 4556 (556), and either 2568 (568) or 572. Not open to students with credit for 865.
MATH 5660
Integrated Molecular and Cellular Biology for Non-Biologists
Overview of molecular and cellular biology of single cells, tissues, organisms and their interactions, including genetics and biochemistry of single cells.
Prereq: Bio 1101 (101) or permission of instructor. Not open to students with credit for any one of MolGen 5660 (660), 4500 (500), 4606 (606), 605, or 661. Cross-listed in MolGen 5660.
MATH 5702
Curves and Surfaces in Euclidean Three Space
Parametrized curves, curvature of curves; Frenet frames, curves with prescribed curvatures, curves on hypersurfaces; principal, Gaussian, and mean curvatures; surfaces in R^3, triangulation and classification of surfaces, Gauss-Bonnet theorem.
Prereq: Grad standing or 2153.01 (254) and either 2568 (568) or 572. Not open to students with credit for 642.
MATH 5756
Mathematical Methods in Relativity Theory I
Special relativity as moving frames; tensors, exterior algebra and exterior calculus; differentiable manifolds and space time structures; parallel transport, torsion and curvatures, metric compatibility; structure equations of differential geometry.
Prereq: 2153.xx (254) and one of 2568 (568) or 5101 (601) or 572. Not open to students with credit for 665.
MATH 5757
Mathematical Methods in Relativity Theory II
Gravitation via geometry; stress energy tensor, fluid dynamics; energy momentum conservation; Einstein's field equations, geodesic world lines via Hamilton-Jacobi theory; Schwarzschild spacetime; gauge invariant perturbation theory.
Prereq: 5756 (665). Not open to students with credit for 666.
MATH 5801
General Topology and Knot Theory
Topological spaces; continuous maps and metric spaces; connectedness, compactness, countability axioms; metrization, compactification, and convergence; combinatorial, geometric, and algebraic techniques in knot theory; invariants of knots.
Prereq: Grad standing; or 4547 (547) and either 2568 (568) or 572. Not open to students with credit for 640.
MATH 6001
Advanced Mathematical Logic I: Proof Theory
Logical calculi; cut elimination and Herbrand's theorem; ordinal analysis; ordinal analysis of theories of sets; constructive and intuitionistic logics; realizability; proof mining.
Prereq: 5051 (649), or permission of department. Not open to students with credit for 747.
MATH 6002
Advanced Mathematical Logic II: Model Theory
Construction of models, compactness, Lowenheim-Skolem theorems, unions of elementary chains, omitting types; categoricity; saturation; model completeness, quantifier elimination; ultraproducts; definability.
Prereq: 5051 (649) or permission of department. Not open to students with credit for 747.
MATH 6003
Advanced Mathematical Logic III: Set Theory
Axioms of set theory; ordinal and cardinal numbers; transitive models of ZFC; the constructible universe L and HOD; forcing; large cardinals; descriptive set theory.
Prereq: 5051 (649) or permission of department. Not open to students with credit for 747.
MATH 6004
Advanced Mathematical Logic IV: Computability Theory
Relative recursion; Turing reducibility, structure of Turing degrees; structure of the recursively enumerable degrees and priority arguments; recursion in higher types; generalized recursion; Borel and projective sets; determinacy.
Prereq: 5051 (649) or permission of department. Not open to students with credit for 747.
MATH 6111
Abstract Algebra I
Group theory; series and actions of groups; ring theory; modules; UFDs and PIDs; polynomial and Noetherian rings; linear and multilinear algebra.
Prereq: 5112, or Grad standing.
MATH 6112
Abstract Algebra II
Introduction to category theory; elementary homological algebra; field theory; finite Galois Theory; infinite Galois Theory; algebraic spaces.
Prereq: 6111 (771). Not open to students with credit for 772.
MATH 6131
Introduction to Representation Theory
Finite groups and representations; Irreducible representations; Character theory; Symmetric groups; Symmetric functions; Associative algebras; Quivers.
Prereq: 5101 or 5111, or Grad standing, or permission of instructor.
MATH 6151
Commutative Algebra
Prime and primary ideals; rings and modules of fractions; integral dependence; chain conditions; valuation and Dedekind domains; completions; Dimension Theory.
Prereq: 6112 (772). Not open to students with credit for 978.
MATH 6152
Non-Commutative Algebra
Semisimple modules and rings and the Wedderburn Structure Theorem; Jacobson Radical; central simple algebras and the Noether-Skolem Theorem; Brauer Group; primitive rings, Density Theorem.
Prereq: 6112 (772). Not open to students with credit for 982.
MATH 6191
Internship in Mathematical Sciences
Internship and practical experiences, designed primarily for Master level students in the mathematical sciences.
Prereq: Permission of department. This course is graded S/U.
MATH 6193
Individual Studies in Mathematics
Individual studies.
Prereq: Permission of department. Repeatable. This course is graded S/U.
MATH 6194
Group Studies in Mathematics
Designed to give groups of PhD students an opportunity to pursue special studies not otherwise offered.
Prereq: Permission of department. Repeatable.
MATH 6211
Real Analysis I
Measures; integration; introduction to normed linear spaces; introduction to L^p spaces; Fourier analysis; signed measures and differentiation.
Prereq: 5202 (653). Not open to students with credit for 750.
MATH 6212
Real Analysis II
Elements of functional analysis; properties and relations of L^p spaces and Fourier analysis; elements of the theory of distributions; selected applications.
Prereq: 6211 (751). Not open to students with credit for 752.
MATH 6221
Complex Analysis I
Basic Cauchy theory; harmonic functions; Riemann mapping theorem, conformal maps; analytic continuation; applications of residue calculus; counting theorems for entire and meromorphic functions.
Prereq: 5202 (653). Not open to students with credit for 753.
MATH 6222
Complex Analysis II
Approximation theorems; applications to Fourier analysis and number theory; Jensen and Weierstrass Theorems; Basic SCV: Cauchy-Riemann equations in several variables; pseudoconvexity and extension phenomena; d-bar methods.
Prereq: 6221.
MATH 6251
Theory of Probability I
Review of measures and integration; independence for events and for random variables; covariance and correlation for random variables; weak and strong laws of large numbers; Borel-Cantelli lemmas; Central Limit Theorems.
Prereq: 5202 (653). Not open to students with credit for 722.
MATH 6252
Theory of Probability II
Central limit theorems; Poisson processes; random walks, Markov chains; martingales; Brownian motion; stochastic processes.
Prereq: 6251 (723). Not open to students with credit for 724.
MATH 6411
Ordinary Differential Equations I
Existence, uniqueness and smooth dependence; linear systems; periodic and homoclinic orbits; stability, hyperbolicity; stable, unstable, and center invariant manifolds; bifurcations of equilibria and periodic orbits; chaos, strange attractors.
Prereq: Both 5202 and either 2568 (568) or 572. Not open to students with credit for Math 715.
MATH 6451
Partial Differential Equations I
Second order linear equations; first order equations: conservation laws, Hamilton-Jacobi equations; Fourier and Laplace transform method, Hopf-Cole and Legendre transform, singular perturbation method; Cauchy-Kovalevskaya Theorem.
Prereq: 6411 (715). Not open to students with credit for 717.
MATH 6501
Combinatorics and Graph Theory I
Enumerative combinatorics: factorials, binomials and multinomials, Stirling approximation, recursion and generating functions, Catalan numbers. Graph theory: Kuratowksi's theorem, graph coloring, Ramsey theory, matrix-tree theorem, expander graphs.
Prereq: Grad standing in Math; or 4581 and 2568; or permission of instructor.
MATH 6502
Combinatorics and Graph Theory II
Ramsey theory, extremal graph theory. First moment method, second moment method, alterations. Concentration inequalities. Lovasz local lemma. Martingale methods. Correlation inequalities. Phase transitions. Random trees, random planar maps.
Prereq: 6501 or permission of instructor.
MATH 6601
Numerical Methods in Scientific Computing I
Numerical linear algebra: matrix operations, direct and iterative methods for systems of linear equations, eigenvalue problems; Nonlinear equations and systems; Numerical Integration.
Prereq: 5603, and permission of the Graduate School; or Grad standing.
MATH 6602
Numerical Methods in Scientific Computing II
Approximation theory: interpolation, projection, integration; Initial value problems: one- and multi-step methods, Runge-Kutta methods, stability analysis; PDEs: advection equation, diffusion equation, stability analysis.
Prereq: 6601.
MATH 6701
Differentiable Manifolds
Differentiable manifolds; vector bundles, existence theorem for ODE, flows, sprays; vector fields, differential operators, Lie and exterior derivatives; Poincare Lemma, Darboux's Theorem; Frobenius's Theorem, Lie groups; de Rham cohomology.
Prereq: Grad standing or all of 5201 (652), and either 2568 (568) or 572, and 2153.01 (254). Not open to students with credit for 765.
MATH 6702
Differential Geometry
Riemannian manifolds, distance, volume; covariant derivatives, Levi-Civita connection; geodesics, curvatures: sectional, Ricci, scalar; Jacobi fields, conjugate points; Rauch comparison, Hopf-Rinow, Hadamard, Preissman's and Berger's Sphere Theorems.
Prereq: 6701 (765). Not open to students with credit for 766.
MATH 6801
Algebraic Topology I
Simplicial and CW- complexes, operations on spaces; homotopy and homeomorphism type; fundamental group, Seifert Van-Kampen Theorem; classification of covering spaces; singular and simplicial homology, chain maps, homotopy invariance, functoriality.
Prereq: Grad standing or both 5801 (640) and 5111 (670). Not open to students with credit for 756.
MATH 6802
Algebraic Topology II
Homology of pairs, excision, axioms; Mayer-Vietoris, cellular homology; cohomology groups, Ext and Tor functors, universal coefficients; Kunneth Theorem; Orientation on manifolds; fundamental class; Poincare, Alexander, and Lefschetz duality.
Prereq: 6801 (756). Not open to students with credit for 758.
MATH 6998
Graduate Research
Graduate research, primarily for Masters and beginning PhD students participating in research projects other than their thesis work.
Prereq: Permission of department. Repeatable. This course is graded S/U.
MATH 6999
Graduate Thesis Research
Graduate research, primarily for students working on their master theses.
Prereq: Permission of department. Repeatable. This course is graded S/U.
MATH 7121.01
Algebraic Number Theory
Algebraic integers, Dedekind domains, ideal class group; Galois theory of prime ideals, Frobenius automorphisms; geometry of numbers; cyclotomic fields, class field theory over Q; quadratic fields; local fields; ideles and adeles.
Prereq: 6112. Not open to students with credit for 7121.02.
MATH 7121.02
Algebraic Number Theory
Algebraic integers, Dedekind domains, ideal class group; Galois theory of prime ideals, Frobenius automorphisms; geometry of numbers; cyclotomic fields, class field theory over Q; quadratic fields; local fields; ideles and adeles.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7122.01
Analytic Number Theory
Properties and examples of L-functions; primes in arithmetic progression; Riemann-Weil formula; non-vanishing theorem; analysis of L-functions on the critical line; principle of large sieve; Brauer-Siegel theorem, Ikehara-Tauberian theorem.
Prereq: 7121.01 and 6222. Not open to students with credit for 7122.02.
MATH 7122.02
Analytic Number Theory
Properties and examples of L-functions; primes in arithmetic progression; Riemann-Weil formula; non-vanishing theorem; analysis of L-functions on the critical line; principle of large sieve; Brauer-Siegel theorem, Ikehara-Tauberian theorem. This course section is open only to mathematics postcandidacy students.
Prereq: Permission of instructor. This course is graded S/U.
MATH 7141.01
Algebraic Geometry I
Affine and quasi-projective varieties; morphisms and rational maps; nonsingular varieties; sheaves and schemes; first properties of schemes; separated and proper maps of schemes.
Prereq: 6112 and 6151. Not open to students with credit for 7141.02.
MATH 7141.02
Algebraic Geometry I
Affine and quasi-projective varieties; morphisms and rational maps; nonsingular varieties; sheaves and schemes; first properties of schemes; separated and proper maps of schemes.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7142.01
Algebraic Geometry II
Sheaves of Modules, quasi-coherent and coherent sheaves; divisors, projective morphism; sheaf of differentials; derived functors and sheaf cohomology; coherent sheaf cohomology of schemes; Serre's Duality, higher direct images, flat and smooth maps.
Prereq: 7141.01. Not open to students with credit for 7142.02.
MATH 7142.02
Algebraic Geometry II
Sheaves of Modules, quasi-coherent and coherent sheaves; divisors, projective morphism; sheaf of differentials; derived functors and sheaf cohomology; coherent sheaf cohomology of schemes; Serre's Duality, higher direct images, flat and smooth maps.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7161.01
Lie Algebras
Nilpotent and solvable Lie algebras; structure and classification of simple Lie algebras; Levi-Malcev decomposition; root systems; Dynkin diagrams; introduction to representation of complex semi-simple Lie algebras; universal enveloping algebra.
Prereq: 6111, or instructor permission.
MATH 7161.02
Lie Algebras
Nilpotent and solvable Lie algebras; structure and classification of simple Lie algebras; Levi-Malcev decomposition; root systems; Dynkin diagrams; introduction to representation of complex semi-simple Lie algebras; universal enveloping algebra.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7162.01
Lie Groups and Representation Theory
Basic group theory constructions; passage between a Lie group and its Lie algebra; homogeneous spaces; maximal tori; unitary trick and complete reducibility; classification of irreducible unitary representations; Cartan-Weyl theory.
Prereq: 7161.01 and 6701. Not open to students with credit for 7162.02.
MATH 7162.02
Lie Groups and Representation Theory
Basic group theory constructions; passage between a Lie group and its Lie algebra; homogeneous spaces; maximal tori; unitary trick and complete reducibility; classification of irreducible unitary representations; Cartan-Weyl theory. This course section is open only to mathematics postcandidacy students.
Prereq: Permission of instructor. This course is graded S/U.
MATH 7193
Individual Studies in Mathematics
Individual studies.
Prereq: Permission of department. Repeatable. This course is graded S/U.
MATH 7194
Group Studies in Mathematics
Designed to give groups of advanced PhD students an opportunity to pursue special studies not otherwise offered.
Prereq: Permission of department. Repeatable.
MATH 7211.01
Functional Analysis I
Linear spaces and linear maps; Hahn-Banach theorem and its applications; normed linear spaces and their duals; Hilbert spaces and applications; weak and weak* topologies; Choquet theorems; bounded linear maps.
Prereq: 6212. Not open to students with credit for 7211.02.
MATH 7211.02
Functional Analysis I
Linear spaces and linear maps; Hahn-Banach theorem and its applications; normed linear spaces and their duals; Hilbert spaces and applications; weak and weak* topologies; Choquet theorems; bounded linear maps.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7212.01
Functional Analysis II
Banach algebras, elementary spectral theory; Gelfand's theory of commutative Banach algebras; examples of families of operators; spectral theory of normal, unitary, self-adjoint operators; semigroups of operators; distributions; applications.
Prereq: 7211.01. Not open to students with credit for 7212.02.
MATH 7212.02
Functional Analysis II
Banach algebras, elementary spectral theory; Gelfand's theory of commutative Banach algebras; examples of families of operators; spectral theory of normal, unitary, self-adjoint operators; semigroups of operators; distributions; applications.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7221.01
Ergodic Theory I
Measure preserving transformations; isomorphism, conjugacy, spectral isomorphism; measure preserving systems with discrete spectrum; hierarchy of mixing properties; invariant measures for continuous transformations; topological and symbolic dynamics.
Prereq: 6211. Not open to students with credit for 7221.02.
MATH 7221.02
Ergodic Theory I
Measure preserving transformations; isomorphism, conjugacy, spectral isomorphism; measure preserving systems with discrete spectrum; hierarchy of mixing properties; invariant measures for continuous transformations; topological and symbolic dynamics.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7222.01
Ergodic Theory II
Entropy; topological entropy; flows on homogeneous spaces; structure theory of measure preserving systems; applications to combinatorics and number theory.
Prereq: 7221.01. Not open to students with credit for 7222.02.
MATH 7222.02
Ergodic Theory II
Entropy; topological entropy; flows on homogeneous spaces; structure theory of measure preserving systems; applications to combinatorics and number theory. This course section is open only to mathematics postcandidacy students.
Prereq: Permission of instructor. This course is graded S/U.
MATH 7412.01
Ordinary Differential Equations II
Topological equivalence of nonlinear systems; normal forms of Poincare-Dulac-Birkhoff; classification of vector fields near critical points; local bifurcation theory; topological dynamics; limit sets; flows on the torus.
Prereq: 6451. Not open to students with credit for 7412.02.
MATH 7412.02
Ordinary Differential Equations II
Topological equivalence of nonlinear systems; normal forms of Poincare-Dulac-Birkhoff; classification of vector fields near critical points; local bifurcation theory; topological dynamics; limit sets; flows on the torus.
Prereq: Post-candidacy standing in Math, and permission of instructor. This course is graded S/U.
MATH 7413
Ordinary Differential Equations III
Structural stability; singularity theory of Thom and Arnol'd; versal deformations; global deformations at separatrix cycle; Anosov diffeomorphisms; Axiom A; symbolic dynamics.
Prereq: 7412 (821). Not open to students with credit for 822.
MATH 7452.01
Partial Differential Equations II
Sobolev spaces, Sobolev inequalities and embedding theorems; Lax-Milgram theorem, Fredholm alternatives, weak compactness; linear elliptic equations: existence, regularity, maximum principles; hyperbolic equations; first order hyperbolic systems.
Prereq: 6451 and 6212. Not open to students with credit for 7452.02.
MATH 7452.02
Partial Differential Equations II
Sobolev spaces, Sobolev inequalities and embedding theorems; Lax-Milgram theorem, Fredholm alternatives, weak compactness; linear elliptic equations: existence, regularity, maximum principles; hyperbolic equations; first order hyperbolic systems.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7453.01
Partial Differential Equations III
Harnack inequalities, De Giorgi-Nash-Moser theory; calculus of variations; monotonicity and sub-super solution methods, Pohozaev identity; hyperbolic conservation laws; quasilinear elliptic and parabolic equations; Schauder theory; strong solutions.
Prereq: 7452.01. Not open to students with credit for 7453.02.
MATH 7453.02
Partial Differential Equations III
Harnack inequalities, De Giorgi-Nash-Moser theory; calculus of variations; monotonicity and sub-super solution methods, Pohozaev identity; hyperbolic conservation laws; quasilinear elliptic and parabolic equations; Schauder theory; strong solutions.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7611
Computational Partial Differential Equations I
Numerical methods for boundary value problems (BVP); extension to separable elliptic PDEs, fast solvers; irregular domains, variable coefficients; iterative methods; diffusion equations; error analysis; variable coefficients in nonlinear problems.
Prereq: 6602 (709). Not open to students with credit for 807.
MATH 7612
Computational Partial Differential Equations II
Linear hyperbolic equations, finite difference methods; quasi-linear and non-linear equations with shock formation, Lax-Wendroff theorem; flux-limiters, WENO methods; multi-dimensional problems; transport equations; adaptive grids, grid generation.
Prereq: 7611 (808). Not open to students with credit for 809.
MATH 7651.01
Applied Complex Variables and Asymptotics I
Contour integration, conformal mapping; asymptotics of integrals; asymptotic properties of Laplace and Fourier transforms; Riemann-Hilbert problems, applications to singular integral equations; introduction to the theory of elliptic functions.
Prereq: 5251 and 5201 and 6451. Not open to students with credit for 7651.02.
MATH 7651.02
Applied Complex Variables and Asymptotics I
Contour integration, conformal mapping; asymptotics of integrals; asymptotic properties of Laplace and Fourier transforms; Riemann-Hilbert problems, applications to singular integral equations; introduction to the theory of elliptic functions.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7652.01
Applied Complex Variables and Asymptotics II
Asymptotic expansions; Watson's and Borel-Ritt lemma, stationary phase, steepest descent methods; contractive mapping methods; WKB and boundary layer methods; analyzable functions, transseries; Borel transform; Borel summability of solutions.
Prereq: 7651.01. Not open to students with credit for 7652.02.
MATH 7652.02
Applied Complex Variables and Asymptotics II
Asymptotic expansions; Watson's and Borel-Ritt lemma, stationary phase, steepest descent methods; contractive mapping methods; WKB and boundary layer methods; analyzable functions, transseries; Borel transform; Borel summability of solutions.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7711.01
Riemannian Geometry
Basic concepts of (pseudo) Riemannian geometry, such as curvature and Ricci tensors, Riemannian distance, geodesics, the Laplacian, and proofs of some fundamental results, including the Frobenius and Lie-subgroup theorems, the local structure of constant-curvature metrics, characterization of conformal flatness, the Hopf-Rinow, Myers, Lichnerowicz and Singer-Thorpe theorems.
Prereq: 6702. Not open to students with credit for 7711.02.
MATH 7711.02
Riemannian Geometry
Basic concepts of (pseudo) Riemannian geometry, such as curvature and Ricci tensors, Riemannian distance, geodesics, the Laplacian, and proofs of some fundamental results, including the Frobenius and Lie-subgroup theorems, the local structure of constant-curvature metrics, characterization of conformal flatness, the Hopf-Rinow, Myers, Lichnerowicz and Singer-Thorpe theorems.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7721.01
Kahler Geometry
Basic concepts of Kahler geometry, such as the Kahler and Ricci forms, positivity/negativity in cohomology, Kahler-Einstein metrics, and proofs of some fundamental results, including the d-d-bar lemma, Calabi's uniqueness theorems, Matsushima's reductivity theorem for Kahler-Einstein manifolds, and Futaki's isomorphism theorem.
Prereq: 6701 and 6221. Not open to students with credit for 7721.02.
MATH 7721.02
Kahler Geometry
Basic concepts of Kahler geometry, such as the Kahler and Ricci forms, positivity/negativity in cohomology, Kahler-Einstein metrics, and proofs of some fundamental results, including the d-d-bar lemma, Calabi's uniqueness theorems, Matsushima's reductivity theorem for Kahler-Einstein manifolds, and Futaki's isomorphism theorem.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7811.01
Homotopy Theory
Homotopy groups, Whitehead's theorem, CW approximation; homotopy excision, Hurewicz theorem; fibrations, mapping path and loop spaces; fibre bundles, sphere bundles over spheres; obstruction theory, relation to cohomology; Postnikov towers.
Prereq: 6802. Not open to students with credit for 7811.02.
MATH 7811.02
Homotopy Theory
Homotopy groups, Whitehead's theorem, CW approximation; homotopy excision, Hurewicz theorem; fibrations, mapping path and loop spaces; fibre bundles, sphere bundles over spheres; obstruction theory, relation to cohomology; Postnikov towers.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7821.01
Geometric Group Theory
Caley graphs, Quasi-isometries, Fundamental Lemma of GGT, Bass-Serre theory, Free groups, amalgams, surface groups, Universal covers, Hyperbolic space, Nonpositive curvature and CAT(0) geometry, Hyperbolic groups, Simple complexes of groups, Coxeter groups, Artin groups, Graph products of groups, Actions on CAT(0) cube complexes. Examples of group actions on contractible polyhedra.
Prereq: 6801. Not open to students with credit for 7821.02.
MATH 7821.02
Geometric Group Theory
Caley graphs, Quasi-isometries, Fundamental Lemma of GGT, Bass-Serre theory, Free groups, amalgams, surface groups, Universal covers, Hyperbolic space, Nonpositive curvature and CAT(0) geometry, Hyperbolic groups, Simple complexes of groups, Coxeter groups, Artin groups, Graph products of groups, Actions on CAT(0) cube complexes. Examples of group actions on contractible polyhedra.
Prereq: Post-candidacy status in Mathematics Graduate Program, and permission of instructor. Not open to students with credit for 7821.01. This course is graded S/U.
MATH 7851.01
Differential Topology I
Whitney Immersion and Embedding Theorems, transverse functions, jet-bundles, Thom transversality; classification of vector bundles, collars, tubular neighborhoods, intersection theory; Morse functions and lemma; surgery, Smale cancellation.
Prereq: 6701 and 6801. Not open to students with credit for 7851.02.
MATH 7851.02
Differential Topology I
Whitney Immersion and Embedding Theorems, transverse functions, jet-bundles, Thom transversality; classification of vector bundles, collars, tubular neighborhoods, intersection theory; Morse functions and lemma; surgery, Smale cancellation.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7852.01
Differential Topology II
DeRahm and Cech cohomology; deRahm Theorem; Grassmannians; Stiefel-Whitney, Euler, Chern, and Pontryagin classes; Gysin sequence, Thom isomorphism; characteristic numbers, multiplicative sequences, Hirzebruch signature theorem; Chern-Weil Theory.
Prereq: 6702 and 6802 and 7851.01. Not open to students with credit for 7852.02.
MATH 7852.02
Differential Topology II
DeRahm and Cech cohomology; deRahm Theorem; Grassmannians; Stiefel-Whitney, Euler, Chern, and Pontryagin classes; Gysin sequence, Thom isomorphism; characteristic numbers, multiplicative sequences, Hirzebruch signature theorem; Chern-Weil Theory.
Prereq: Post-candidacy in Math, and permission of instructor. This course is graded S/U.
MATH 7998
Graduate Research
Graduate Research, primarily for intermediate PhD students participating in research projects other than their thesis work.
Prereq: Permission of the department. Repeatable. This course is graded S/U.
MATH 8000
Topics in Foundations of Mathematics
Special topics in foundations of mathematics chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8110
Topics in Algebra
Special topics in algebra chosen by the instructor.
prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8120
Topics in Number Theory
Special topics in number theory chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8140
Topics in Algebraic Geometry
Special topics in algebraic geometry chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8160
Topics in Representation Theory
Special topics in representation theory chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8210
Topics in Real Analysis
Special topics in real analysis chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8220
Topics in Complex Analysis
Special topics in complex analysis chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8250
Topics in Probability Theory
Special topics in probability theory chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8300
Topics in Financial Mathematics
Special topics in financial mathematics chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8410
Topics in Ordinary Differential Equations
Special topics in ordinary differential equations chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8420
Topics in Partial Differential Equations
Special topics in partial differential equations chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8500
Topics in Combinatorics
Special topics in combinatorics chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8610
Topics in Applied Mathematics
Special topics in applied mathematics chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8650
Topics in Mathematical Biology
Special topics in mathematical biology chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8710
Topics in Differential Geometry
Special topics in differential geometry chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8750
Topics in Lie Theory
Special topics in Lie theory chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8800
Topics in Topology
Special topics in topology chosen by the instructor.
Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions.
MATH 8998
Graduate Research
Graduate research, primarily for advanced PhD students participating in research projects other than their thesis work.
Prereq: Permission of department. Repeatable to a maximum of 20 completions. This course is graded S/U.
MATH 8999
Dissertation Research
Graduate research for students working on their PhD dissertation.
Prereq: Permission of department. Repeatable. This course is graded S/U.