Mathematics
Daniel Dugger, Department Head
5413464705
205 Fenton Hall
1222 University of Oregon
Eugene, Oregon 974031222
Courses offered by the Department of Mathematics are designed to satisfy the needs of majors and nonmajors interested in mathematics primarily as part of a broad liberal education. They provide basic mathematical and statistical training for students in the social, biological, and physical sciences and in the professional schools; prepare teachers of mathematics; and provide advanced and graduate work for students specializing in the field.
Facilities
The department office and the Mathematics Library are housed in Fenton Hall. A reading and study area is located in the Moursund Reading Room of the Mathematics Library. The Hilbert Space, an undergraduate mathematics center, is in Deady Hall.
Awards and Prizes
 The William Lowell Putnam examination, a competitive, nationally administered mathematics examination, is given early each December. It contains twelve very challenging problems, and prizes are awarded to the top finishers in the nation. Interested students should consult the chair of the undergraduate affairs committee at the beginning of fall term
 The Anderson Award, endowed by Frank and Dorothy Anderson, is awarded to one or more graduate students with outstanding teaching records
 The Jack and Peggy Borsting Award for Scholastic Achievement in Graduate Mathematics is awarded to a finishing graduate student based on outstanding academic work
 The Charles W. and Elizabeth H. Curtis Scholarship is awarded to a sophomore or junior to continue their studies in mathematics
 The DeCou Prize, which honors a former longtime department head, E. E. DeCou, and his son, E. J. DeCou, is awarded to an outstanding graduating senior
 The Juilfs Scholarship, in honor of Erwin and Gertrude Juilfs, is awarded to one or more students who show exceptional promise for achievement as evidenced by GPA, originality of research, or other applicable criteria
 The Marion Walter Future Teachers Award, which honors Professor Emerita Marion Walter, is awarded to an outstanding senior graduating with a precollegeteaching option
 The Civin Graduate Award, endowed by the family of Paul and Harriet Civin, is awarded for the purpose of attracting and retaining promising graduate students and encouraging underrepresented students in mathematics

The Harrison Memory Award, endowed by Ann Hill Harrison in honor of former mathematics professor David K. Harrison, is awarded to outstanding students in mathematics
Faculty
Nicolas Addington, assistant professor (algebraic geometry). BS, 2004, Washington (Seattle); PhD, 2009, Wisconsin, Madison. (2015)
Shabnam Akhtari, assistant professor (number theory). BA, 2002, Sharif University of Technology; PhD, 2008, British Columbia. (2012)
Arkadiy D. Berenstein, professor (quantum groups, representation theory). MS, 1988, Moscow Transport Institute; PhD, 1996, Northeastern. (2000)
Tricia H. Bevans, senior instructor. BA, 1995, MS, 1998, Oregon. (2013)
Boris Botvinnik, professor (algebraic topology). MS, 1978, Novosibirsk State; PhD, 1984, USSR Academy of Sciences, Novosibirsk. (1993)
Marcin Bownik, professor (harmonic analysis, wavelets). Magister, 1995, Warsaw, Poland; MA, 1997, PhD, 2000, Washington (St. Louis). (2003)
Jonathan Brundan, professor (Lie theory, representation theory). BA, 1992, Queens College, Cambridge; PhD, 1996, University of London. (1997)
Daniel K. Dugger, professor (algebraic topology and geometry, Ktheory, commutative algebra). BA, 1994, Michigan, Ann Arbor; PhD, 1999, Massachusetts Institute of Technology. (2004)
Ellen E. Eischen, assistant professor (number theory). BA, 2003, Princeton; PhD, 2009, Michigan, Ann Arbor. (2015)
Ben Elias, associate professor (representation theory, categorification). BA, 2005, Princeton; PhD, 2011, Columbia. (2014)
Hannah Feng, Paul Olum Postdoctoral Scholar (harmonic analysis). MS, 2013, PhD, 2016, Alberta. (2016)
Cassandra Fisher, instructor. BS, 2010, George Fox; MS, 2012, Texas Tech. (2012)
Peter B. Gilkey, professor (global analysis, differential geometry). BS, MA, 1967, Yale; PhD, 1972, Harvard. (1981)
Hayden Harker, instructor. BA, 1995, Oberlin College; MS, 2000, PhD, 2005, Oregon. (2011)
Weiyong He, associate professor (differential geometry, geometric analysis and partial differential equations). MS, 2004, Science and Technology of China; PhD, 2007, Wisconsin, Madison. (2009)
Kristen Henderson, instructor. BA, 2001, California, Berkeley; MS, 2003, Nevada, Reno. (2015)
Fred Hervert, senior instructor. BA, 1983, MS, 1987, Northeastern Illinois. (1999)
James A. Isenberg, professor (mathematical physics, differential geometry, nonlinear partial differential equations). AB, 1973, Princeton; PhD, 1979, Maryland. (1982)
Drew Johnson, Paul Olum Postdoctoral Scholar (algebraic geometry). MS, 2011, Brigham Young; PhD, 2016, Utah. (2016)
Alexander S. Kleshchev, professor (algebra, representation theory). BS, MS, 1988, Moscow State; PhD, 1993, Institute of Mathematics, Academy of Sciences of Belarus, Minsk. (1995)
Elina Kleshcheva, instructor, BS, 1987, MS, 1988, Moscow State. (1995)
David A. Levin, associate professor (probability theory and stochastic processes). BS, 1993, Chicago; MA, 1995, PhD, 1999, California, Berkeley. (2006)
Huaxin Lin, professor (functional analysis). BA, 1980, East China Normal, Shanghai; MS, 1984, PhD, 1986, Purdue. (1995)
Robert Lipshitz, associate professor (differential topology). AB, 2002, Princeton; PhD, 2006, Stanford. (2015)
Peng Lu, professor (differential geometry, geometric analysis). BSc, 1985, Nanjing; MSc, 1988, Nanki Mathematics Institute; PhD, 1996, State University of New York, Stony Brook. (2002)
Eric Merchant, instructor. BA, 1996, MS, 2000, PhD, 2005, Oregon. (2010)
Maria Nemirovskaya, instructor. MS, 1996, Brigham Young; PhD, 2002, Massachusetts Institute of Technology. (2017)
Tammy Nezol, senior instructor. BA, 2004, BS, 2006, MS, 2008, Oregon. (2008)
Jean B. Nganou, instructor (finite dimensional division algebras). MS, 2001, Yaoundé I; PhD, 2009, New Mexico State. (2009)
Victor V. Ostrik, professor (representation theory). MS, 1995, PhD, 1999, Moscow State. (2003)
Vivek Pal, postdoctoral instructional scholar (number theory). MA, 2013, PhD, 2016, Columbia. (2016)
Liliana PazdanSiudeja, instructor. MS, 2010, Illinois, UrbanaChampaign. (2013)
N. Christopher Phillips, professor (functional analysis). AB, 1978, MA, 1980, PhD, 1984, California, Berkeley. (1990)
Alexander Polishchuk, professor (algebraic geometry). MS, 1993, Moscow State; PhD, 1996, Harvard. (2003)
Michael R. Price, senior instructor; assistant department head. BS, 2003, MS, 2005, Oregon. (2005)
Nicholas J. Proudfoot, professor (algebraic geometry, combinatorics, topological groups). AB, 2000, Harvard; PhD, 2004, California, Berkeley. (2007)
Peter Ralph, assistant professor (populations and evolution with genomic data). AB, 2002, PhD, 2009, California, Berkeley. (2016)
Hal Sadofsky, associate professor (algebraic topology, homotopy theory). BS, 1984, Rochester; PhD, 1990, Massachusetts Institute of Technology. (1995)
Bijan Shahir, instructor. MS, 1979, PhD, 1987, Oregon; MSEE, 1999, Washington (Seattle). (2011)
Brad S. Shelton, professor (Lie groups, harmonic analysis, representations). BA, 1976, Arizona; MS, PhD, 1982, Washington (Seattle). (1985)
Christopher D. Sinclair, associate professor (random matrix theory, number theory). BS, 1997, Arizona; PhD, 2005, Texas, Austin. (2009)
Dev P. Sinha, associate professor (algebraic and differential topology). BS, 1993, Massachusetts Institute of Technology; PhD, 1997, Stanford. (2001)
David C Steinberg, instructor. BSc, 2004, Alberta; MA, 2006, State University of New York, Binghamton; PhD, 2012, British Columbia. (2013)
Jennifer Thorenson, instructor. BS, 2003, North Dakota State; MS, 2005, PhD, 2013, Montana State. (2013)
Craig Tingey, senior instructor. BA, BS, 1989, MS, 1991, Utah. (2001)
Arkady Vaintrob, associate professor (algebraic geometry, Lie theory and representation theory, mathematical physics). BA, 1976, Moscow Institute of Railway Engineering; MS, 1979, PhD, 1987, Moscow State. (2000)
Vadim Vologodski, associate professor (algebraic geometry, number theory). MS, 1996, Independent University of Moscow; PhD, 2001, Harvard. (2009)
Hao Wang, associate professor (mathematics of finance, probability, statistics). BS, 1980, MS, 1985, Wuhan (China); PhD, 1995, Carleton (Canada). (2000)
Kai Shyang Wang, instructor. MA, 1985, California, Berkeley. (2009)
Qingyun Wang, Paul Olum Postdoctoral Scholar (operator algebras, Ktheory, dynamic systems). BS, 2008, Zhejiang; MA, 2010, PhD, 2013, Washington (St. Louis). (2016)
Shida Wang, Paul Olum Postdoctoral Scholar (lowdimensional topology, knot theory). BS, 2006, MSc, 2009, Peking; PhD, 2016, Indiana, Bloomington. (2016)
Micah Warren, assistant professor (geometric analysis). BS, 2000, Pacific Lutheran; MS, 2006, PhD, 2008, Washington (Seattle). (2012)
Yuan Xu, professor (numerical analysis). BS, 1982, Northwestern (China); MS, 1984, Beijing Institute of Aeronautics and Astronautics; PhD, 1988, Temple. (1992)
Benjamin Young, assistant professor (combinatorics). BS, 2001, MS, 2002, Carleton; PhD, 2008, British Columbia. (2012)
Sergey Yuzvinsky, professor (representation theory, combinatorics, multiplication of forms). MA, 1963, PhD, 1966, Leningrad. (1980)
Emeriti
Fred C. Andrews, professor emeritus. BS, 1946, MS, 1948, Washington (Seattle); PhD, 1953, California, Berkeley. (1957)
Bruce A. Barnes, professor emeritus. BA, 1960, Dartmouth; PhD, 1964, Cornell. (1966)
Richard B. Barrar, professor emeritus. BS, 1947, MS, 1948, PhD, 1952, Michigan. (1967)
Glenn T. Beelman, senior instructor emeritus. BS, 1938, South Dakota State; AM, 1962, George Washington. (1966)
Charles W. Curtis, professor emeritus. BA, 1947, Bowdoin; MA, 1948, PhD, 1951, Yale. (1963)
Micheal N. Dyer, professor emeritus. BA, 1960, Rice; PhD, 1965, California, Los Angeles. (1967)
Robert S. Freeman, associate professor emeritus. BAE., 1947, New York University; PhD, 1958, California, Berkeley. (1967)
William M. Kantor, professor emeritus. BS, 1964, Brooklyn; MA, 1965, PhD, 1968, Wisconsin, Madison. (1971)
Richard M. Koch, professor emeritus. BA, 1961, Harvard; PhD, 1964, Princeton. (1966)
Shlomo Libeskind, professor emeritus. BS, 1962, MS, 1965, TechnionIsrael Institute of Technology; PhD, 1971, Wisconsin, Madison. (1986)
Theodore W. Palmer, professor emeritus. BA, 1958, MA, 1958, Johns Hopkins; AM, 1959, PhD, 1966, Harvard. (1970)
Kenneth A. Ross, professor emeritus. BS, 1956, Utah; MS, 1958, PhD, 1960, Washington (Seattle). (1964)
Gary M. Seitz, professor emeritus. AB, 1964, MA, 1965, California, Berkeley; PhD, 1968, Oregon. (1970)
Allan J. Sieradski, professor emeritus. BS, 1962, Dayton; MS, 1964, PhD, 1967, Michigan. (1967)
Stuart Thomas, senior instructor emeritus. AB, 1965, California State, Long Beach; MA, 1967, California, Berkeley. (1990)
Marie A. Vitulli, professor emerita. BA, 1971, Rochester; MA, 1973, PhD, 1976, Pennsylvania. (1976)
Marion I. Walter, professor emerita. BA, 1950, Hunter; MS, 1954, New York University; DEd, 1967, Harvard. (1977)
Lewis E. Ward Jr., professor emeritus. AB, 1949, California, Berkeley; MS, 1951, PhD, 1953, Tulane. (1959)
Jerry M. Wolfe, associate professor emeritus. BS, 1966, Oregon State; MA, 1969, PhD, 1972, Washington (Seattle). (1970)
Charles R. B. Wright, professor emeritus. BA, 1956, MA, 1957, Nebraska; PhD, 1959, Wisconsin, Madison. (1961)
The date in parentheses at the end of each entry is the first year on the University of Oregon faculty.
 Bachelor of Arts: Standard Track
 Bachelor of Arts: Pure Mathematics
 Bachelor of Arts: Secondary Teaching
 Bachelor of Science: Standard Track
 Bachelor of Science: Pure Mathematics
 Bachelor of Science: Secondary Teaching
 Minor
Undergraduate Studies
Students planning to major in mathematics at the university should take four years of high school mathematics including a year of mathematics as a senior. Courses in algebra, geometry, trigonometry, and more advanced topics should be included whdether offered as separate courses or as a unit.
College transfer students who have completed a year of calculus should be able to satisfy the major requirements in mathematics at the University of Oregon in two years.
Science Group Requirement
The department offers courses that satisfy the science group requirement:
Code  Title  Credits 

MATH 105–107  University Mathematics IIII  12 
MATH 211–213  Fundamentals of Elementary Mathematics IIII  12 
MATH 231–233  Elements of Discrete Mathematics IIII  12 
MATH 241–242 & MATH 243  Calculus for Business and Social Science III and Introduction to Methods of Probability and Statistics  12 
MATH 246–247  Calculus for the Biological Sciences III  8 
MATH 251–253  Calculus IIII  12 
MATH 261–263  Calculus with Theory IIII  12 
MATH 307  Introduction to Proof  4 
The 100level courses present important mathematical ideas in an elementary setting, stressing concepts more than computation. They do not provide preparation for other mathematics courses but are compatible with further study in mathematics.
Enrollment in Courses
Beginning and transfer students must take a placement examination before enrolling in their first UO mathematics course; the examination is given during each registration period. Students who transfer credit for calculus to the university are excused from the examination.
To enroll in courses that have prerequisites, students must complete the prerequisite courses with grades of C– or better or P.
Students cannot receive credit for a course that is a prerequisite to a course they have already taken. For example, a student with credit in Calculus for Business and Social Science I (MATH 241) cannot later receive credit for College Algebra (MATH 111). For more information about credit restrictions, contact a mathematics advisor.
Bridge Requirement
Most upperdivision courses include mathematical proof as a significant element. To prepare for this, students must satisfy the bridge requirement as a prerequisite to taking any 300 or 400level course other than Elementary Linear Algebra (MATH 341–342), Statistical Methods III (MATH 425–426), or Partial Differential Equations: Fourier Analysis III (MATH 421–422).
The bridge requirement is one of the following:
Code  Title  Credits 

MATH 307 AND four of: MATH 201206206  12  
MATH 231–232232 AND two of: MATH 201206206  12  
MATH 261–262262 AND two of: MATH 201206206  12 
Calculus Sequences
The department offers four calculus sequences. Students need to consult an advisor in mathematics or in their major field about which sequence to take.
Sequence  Description 

MATH 251–253253 

MATH 261–263263 

MATH 246–247247, MATH 253 

MATH 241–242242 

The first three sequences are equivalent as far as department requirements for majors or minors and as far as prerequisites for more advanced courses.
Program Plan Example
First Year  Credits  

Select one of the following:  12  
Calculus IIII  12  
Calculus with Theory IIII  12  
Select two of the following  4  
Algebra Math Lab  2  
Geometry Math Lab  2  
Analysis and Number Theory Math Lab  2  
Second Year  
Select two of the following  4  
Probability and Statistics Math Lab  2  
Foundations Math Lab  2  
Combinatorics Math Lab  2  
Select one of the following  8  
SeveralVariable Calculus III  8  
Elementary Linear Algebra  8  
Select one of the following  8  
Elements of Discrete Mathematics III  8  
Calculus with Theory III  8  
Introduction to Proof  4  
Third Year  
Complete second year sequence as necessary  
CIS 122  Introduction to Programming and Problem Solving  4 
Select one of the following Fundamentals sequences  8  
Fundamentals of Analysis III  8  
Fundamentals of Number Theory III  8  
Fundamentals of Abstract Algebra III  8  
One upper division mathematics course  4  
Fourth Year  
Three upperdivision mathematics courses  12  
Total Credits:  64 
Students who are considering graduate school in mathematics should take at least one or two of the pure math sequences, Introduction to Analysis IIII (MATH 413–415), Introduction to Abstract Algebra IIII (MATH 444–446), or Introduction to Topology (MATH 431–432) and Introduction to Differential Geometry (MATH 433). The choice merits discussion with an advisor.
Bachelor's Degree Requirements
The department offers undergraduate preparation for positions in government, business, and industry and for graduate work in mathematics and statistics. Each student’s major program is individually constructed in consultation with an advisor.
Upperdivision courses used to satisfy major requirements must be taken for letter grades, and only one D grade (D+ or D or D–) may be counted toward the upperdivision requirement. At least 12 credits in upperdivision mathematics courses must be taken in residence at the university.
Statistical Methods I (MATH 425) cannot be used to satisfy requirements for a mathematics major or minor.
To qualify for a bachelor’s degree with a major in mathematics, a student must satisfy the requirements for one of three options: the standard track, pure mathematics, or secondary teaching. In each option, most courses require calculus as a prerequisite, and in each option some of the courses require satisfying the bridge requirement.
Bachelor of Arts: Standard Track
Code  Title  Credits 

MATH 253  Calculus III  4 
MATH 281–282  SeveralVariable Calculus III  8 
MATH 341–342  Elementary Linear Algebra  8 
CIS 122  Introduction to Programming and Problem Solving (or another programming course approved by advisor)  4 
Select one of the following sets of Bridge courses:  12  
MATH 231–232232 and two of MATH 201206206  
MATH 261–262262 and two of MATH 201206206  
MATH 307 and four of MATH 201206206  
Select one of the following Fundamentals sequences:  8  
Fundamentals of Analysis III  
Fundamentals of Number Theory III  
Fundamentals of Abstract Algebra III  
Select four of the following, including at least one twoterm sequence: ^{2}  16  
Fundamentals of Analysis I  
Fundamentals of Analysis II  
Theory of Differential Equations  
Statistical Models and Methods  
Fundamentals of Number Theory I  
Fundamentals of Number Theory II  
Elementary Numerical Analysis I  
Elementary Numerical Analysis II  
Fundamentals of Abstract Algebra I  
Fundamentals of Abstract Algebra II  
Geometries from an Advanced Viewpoint I  
Geometries from an Advanced Viewpoint II  
History and Applications of Calculus  
Functions of a Complex Variable I  
Functions of a Complex Variable II  
Ordinary Differential Equations  
Partial Differential Equations: Fourier Analysis I  
Partial Differential Equations: Fourier Analysis II  
Networks and Combinatorics  
Discrete Dynamical Systems  
Introduction to Mathematical Cryptography  
Introduction to Mathematical Methods of Statistics I  
Introduction to Mathematical Methods of Statistics II  
Mathematical Methods of Regression Analysis and Analysis of Variance  
Stochastic Processes  
Total Credits  60 
^{1}  For students who have completed Calculus with Theory IIII (MATH 261–263) with a grade of midC or better, the department will waive the requirement for Fundamentals of Analysis I (MATH 316). 
^{2}  Sequences include MATH 316317, 347348, 351352, 391392, 411412, 421M422, 413414, 431432, 444446, 461462, 461467; no courses can count for both the twoterm Fundamentals sequence AND toward the four upper division classes. 
Bachelor of Science: Standard Track
Code  Title  Credits 

MATH 253  Calculus III  4 
MATH 281–282  SeveralVariable Calculus III  8 
MATH 341–342  Elementary Linear Algebra  8 
CIS 122  Introduction to Programming and Problem Solving (or another programming course approved by advisor)  4 
Select one of the following sets of Bridge courses:  12  
MATH 231–232232 and two of MATH 201206206  
MATH 261–262262 and two of MATH 201206206  
MATH 307 and four of MATH 201206206  
Select one of the following Fundamentals sequences:  8  
Fundamentals of Analysis III  
Fundamentals of Number Theory III  
Fundamentals of Abstract Algebra III  
Select four of the following, including at least one twoterm sequence: ^{2}  16  
Fundamentals of Analysis I  
Fundamentals of Analysis II  
Theory of Differential Equations  
Statistical Models and Methods  
Fundamentals of Number Theory I  
Fundamentals of Number Theory II  
Elementary Numerical Analysis I  
Elementary Numerical Analysis II  
Fundamentals of Abstract Algebra I  
Fundamentals of Abstract Algebra II  
Geometries from an Advanced Viewpoint I  
Geometries from an Advanced Viewpoint II  
History and Applications of Calculus  
Functions of a Complex Variable I  
Functions of a Complex Variable II  
Ordinary Differential Equations  
Partial Differential Equations: Fourier Analysis I  
Partial Differential Equations: Fourier Analysis II  
Networks and Combinatorics  
Discrete Dynamical Systems  
Introduction to Mathematical Cryptography  
Introduction to Mathematical Methods of Statistics I  
Introduction to Mathematical Methods of Statistics II  
Mathematical Methods of Regression Analysis and Analysis of Variance  
Stochastic Processes  
Total Credits  60 
^{1}  For students who have completed Calculus with Theory IIII (MATH 261–263) with a grade of midC or better, the department will waive the requirement for Fundamentals of Analysis I (MATH 316). 
^{2}  Sequences include MATH 316317, 347348, 351352, 391392, 411412, 421M422, 413414, 431432, 444446, 461462, 461467; no courses can count for both the twoterm Fundamentals sequence AND toward the four upper division classes. 
Bachelor of Arts: Pure Mathematics
Course List
Code  Title  Credits 

MATH 253  Calculus III  4 
MATH 281–282  SeveralVariable Calculus III  8 
MATH 341–342  Elementary Linear Algebra  8 
CIS 122  Introduction to Programming and Problem Solving (or another programming course approved by advisor)  4 
Select one of the following sets of Bridge courses:  12  
MATH 231–232232 and two of MATH 201206206  
MATH 261–262262 and two of MATH 201206206  
MATH 307 and four of MATH 201206206  
MATH 316–317  Fundamentals of Analysis III  8 
Select one of the following Abstract Algebra sequences:  8  
Fundamentals of Abstract Algebra III  
Introduction to Abstract Algebra III  
Select two of the following: ^{2}  8  
Theory of Differential Equations  
Statistical Models and Methods  
Fundamentals of Number Theory I  
Fundamentals of Number Theory II  
Elementary Numerical Analysis I  
Elementary Numerical Analysis II  
Fundamentals of Abstract Algebra I  
Fundamentals of Abstract Algebra II  
Geometries from an Advanced Viewpoint I  
Geometries from an Advanced Viewpoint II  
History and Applications of Calculus  
Functions of a Complex Variable I  
Functions of a Complex Variable II  
Introduction to Analysis I  
Introduction to Analysis II  
Introduction to Analysis III  
Ordinary Differential Equations  
Partial Differential Equations: Fourier Analysis I  
Partial Differential Equations: Fourier Analysis II  
Introduction to Topology  
Introduction to Topology  
Introduction to Differential Geometry  
Linear Algebra  
Introduction to Abstract Algebra I  
Introduction to Abstract Algebra II  
Introduction to Abstract Algebra III  
Introduction to Mathematical Methods of Statistics I  
Introduction to Mathematical Methods of Statistics II  
Mathematical Methods of Regression Analysis and Analysis of Variance  
Stochastic Processes  
Total Credits  60 
^{1}  For students who have completed Calculus with Theory IIII (MATH 261–263) with grades of midC or better, the department will waive the requirement for MATH 316317. 
^{2}  No courses can count for both the twoterm Abstract Algebra sequence AND toward the two upper division classes. 
Bachelor of Science: Pure Mathematics
Course List
Code  Title  Credits 

MATH 253  Calculus III  4 
MATH 281–282  SeveralVariable Calculus III  8 
MATH 341–342  Elementary Linear Algebra  8 
CIS 122  Introduction to Programming and Problem Solving (or another programming course approved by advisor)  4 
Select one of the following sets of Bridge courses:  12  
MATH 231–232232 and two of MATH 201206206  
MATH 261–262262 and two of MATH 201206206  
MATH 307 and four of MATH 201206206  
MATH 316–317  Fundamentals of Analysis III  8 
Select one of the following Abstract Algebra sequences:  8  
Fundamentals of Abstract Algebra III  
Introduction to Abstract Algebra III  
Select two of the following: ^{2}  8  
Theory of Differential Equations  
Statistical Models and Methods  
Fundamentals of Number Theory I  
Fundamentals of Number Theory II  
Elementary Numerical Analysis I  
Elementary Numerical Analysis II  
Fundamentals of Abstract Algebra I  
Fundamentals of Abstract Algebra II  
Geometries from an Advanced Viewpoint I  
Geometries from an Advanced Viewpoint II  
History and Applications of Calculus  
Functions of a Complex Variable I  
Functions of a Complex Variable II  
Introduction to Analysis I  
Introduction to Analysis II  
Introduction to Analysis III  
Ordinary Differential Equations  
Partial Differential Equations: Fourier Analysis I  
Partial Differential Equations: Fourier Analysis II  
Introduction to Topology  
Introduction to Topology  
Introduction to Differential Geometry  
Linear Algebra  
Introduction to Abstract Algebra I  
Introduction to Abstract Algebra II  
Introduction to Abstract Algebra III  
Introduction to Mathematical Methods of Statistics I  
Introduction to Mathematical Methods of Statistics II  
Mathematical Methods of Regression Analysis and Analysis of Variance  
Stochastic Processes  
Total Credits  60 
^{1}  For students who have completed Calculus with Theory IIII (MATH 261–263) with grades of midC or better, the department will waive the requirement for MATH 316317. 
^{2}  No courses can count for both the twoterm Abstract Algebra sequence AND toward the two upper division classes. 
Bachelor of Arts: Secondary Teaching
Code  Title  Credits 

MATH 253  Calculus III  4 
MATH 281  SeveralVariable Calculus I  4 
MATH 341  Elementary Linear Algebra  4 
MATH 343  Statistical Models and Methods  4 
CIS 122  Introduction to Programming and Problem Solving (or another programming course approved by advisor)  4 
Select one of the following sets of Bridge courses:  12  
MATH 231–232232 and two of MATH 201206206  
MATH 261–262262 and two of MATH 201206206  
MATH 307 and four of MATH 201206206  
Select two of the following Fundamentals sequences: ^{1}  16  
Fundamentals of Analysis III  
Fundamentals of Number Theory III  
Fundamentals of Abstract Algebra III  
MATH 394–395  Geometries from an Advanced Viewpoint III  8 
MATH 397  History and Applications of Calculus  4 
Total Credits  60 
^{1}  For students who have completed Calculus with Theory IIII (MATH 261–263) with grades of midC or better, the department will waive the requirement for MATH 316317. 
Bachelor of Science: Secondary Teaching
Code  Title  Credits 

MATH 253  Calculus III  4 
MATH 281  SeveralVariable Calculus I  4 
MATH 341  Elementary Linear Algebra  4 
MATH 343  Statistical Models and Methods  4 
CIS 122  Introduction to Programming and Problem Solving (or another programming course approved by advisor)  4 
Select one of the following sets of Bridge courses:  12  
MATH 231–232232 and two of MATH 201206206  
MATH 261–262262 and two of MATH 201206206  
MATH 307 and four of MATH 201206206  
Select two of the following Fundamentals sequences: ^{1}  16  
Fundamentals of Analysis III  
Fundamentals of Number Theory III  
Fundamentals of Abstract Algebra III  
MATH 394–395  Geometries from an Advanced Viewpoint III  8 
MATH 397  History and Applications of Calculus  4 
Total Credits  60 
^{1}  For students who have completed Calculus with Theory IIII (MATH 261–263) with grades of midC or better, the department will waive the requirement for MATH 316317. 
Mathematics and Computer Science
The Department of Mathematics and the Department of Computer and Information Science jointly offer an undergraduate major in mathematics and computer science, leading to a bachelor of arts or a bachelor of science degree. This program is described in the Mathematics and Computer Science section of this catalog.
Recommended Mathematics Courses for Other Areas
Students with an undergraduate mathematics degree often change fields when enrolling in graduate school. Common choices for a graduate career include computer science, economics, engineering, law, medicine, and physics. It is not unusual for a mathematics major to complete a second major as well. The following mathematics courses are recommended for students interested in other areas:
Code  Title  Credits 

Actuarial Science  
MATH 351–352  Elementary Numerical Analysis III  8 
MATH 461–462  Introduction to Mathematical Methods of Statistics III  8 
MATH 463  Mathematical Methods of Regression Analysis and Analysis of Variance ^{1}  4 
Biological Sciences  
MATH 461–462  Introduction to Mathematical Methods of Statistics III  8 
Computer and Information Science  
MATH 231–233  Elements of Discrete Mathematics IIII  12 
MATH 351–352  Elementary Numerical Analysis III  8 
or MATH 461–462  Introduction to Mathematical Methods of Statistics III  
MATH 456  Networks and Combinatorics  4 
Economics, Business, and Social Science  
MATH 461–462  Introduction to Mathematical Methods of Statistics III ^{2}  8 
Physical Sciences and Engineering  
MATH 351–352  Elementary Numerical Analysis III  8 
MATH 411–412  Functions of a Complex Variable III  8 
MATH 420  Ordinary Differential Equations  4 
MATH 421–422  Partial Differential Equations: Fourier Analysis III  8 
^{1}  Courses in computer science, accounting, and economics are also recommended. It is possible to take the first few actuarial examinations (on calculus, statistics, and numerical analysis) as an undergraduate student. 
^{2}  Students who want to take upperdivision mathematics courses should take Calculus III (MATH 251–252) in place of Calculus for Business and Social Science III (MATH 241–242). 
Honors Program
Students preparing to graduate with honors in mathematics should notify the department’s honors advisor no later than the first term of their senior year (and ideally during the penultimate year of study). There are two requirements for receiving departmental honors:
 Complete all upper division mathematics courses with a net GPA of 3.7 or greater.
 Write a thesis covering advanced topics as assigned by the honors advisor.
The degree with departmental honors is awarded to students whose work is judged truly exceptional.
Minor Requirements
To earn a minor in mathematics, a student must complete at least 30 credits in mathematics at the 200 level or higher, with at least 15 upperdivision mathematics credits; Statistical Methods I (MATH 425) cannot be used toward the upperdivision requirement. A minimum of 15 credits must be taken at the University of Oregon.
Only one D grade (D+ or D or D–) may be counted toward fulfilling the upperdivision requirement. All upperdivision courses must be taken for letter grades. The flexibility of the mathematics minor program allows each student, in consultation with a mathematics advisor, to tailor the program to his or her needs.
The minor is intended for any student, regardless of major, with a strong interest in mathematics. While students in such closely allied fields as computer and information science or physics often complete double majors, students with more distantly related majors such as psychology or history may find the minor useful.
Preparation for Kindergarten through Secondary School Teaching Careers
The College of Education offers a fifthyear program for middlesecondary licensure in mathematics and for elementary teaching. For more information, see the College of Education section of this catalog.
FourYear Degree Plan
The degree plan shown is only a sample of how students may complete their degrees in four years. There are alternative ways. Students should consult their advisor to determine the best path for them.
Bachelor of Arts in Mathematics: Standard Track
First Year  

Fall  Milestones  Credits  
MATH 203  Analysis and Number Theory Math Lab  2  
MATH 251  Calculus I (Only one MATH course can be counted toward science group requirement)  4  
WR 121  College Composition I  4  
First term of firstyear secondlanguage sequence  5  
Credits  15  
Winter  
MATH 252  Calculus II  4  
WR 122  College Composition II  4  
Second term of firstyear secondlanguage sequence  5  
MATH 201  Algebra Math Lab  2  
Credits  15  
Spring  
MATH 253  Calculus III  4  
Third term of firstyear secondlanguage sequence  5  
Social science groupsatisfying course  4  
Science group groupsatisfying course  4  
Credits  17  
Second Year  
Fall  
MATH 281  SeveralVariable Calculus I  4  
MATH 341  Elementary Linear Algebra  4  
Arts and letters groupsatisfying course  4  
First term of secondyear secondlanguage sequence  4  
Credits  16  
Winter  
MATH 282  SeveralVariable Calculus II  4  
MATH 342  Elementary Linear Algebra  4  
Second term of secondyear secondlanguage sequence  4  
Social science groupsatisfying course  4  
Credits  16  
Spring  
MATH 202  Geometry Math Lab  2  
MATH 205  Foundations Math Lab  2  
MATH 307  Introduction to Proof  MATH major Bridge requirement completed  4 
Third term of secondyear secondlanguage sequence  BA language requirement completed  4  
Science groupsatisfying course  4  
Credits  16  
Third Year  
Fall  
MATH 316  Fundamentals of Analysis I  4  
Arts and letters group satisfying course  4  
Science groupsatisfying course  Science group requirement completed  4  
Upperdivision Elective  4  
Credits  16  
Winter  
MATH 317  Fundamentals of Analysis II  MATH major Fundamentals requirement completed  4 
Social science group satisfying course  4  
Arts and letters group satisfying course  4  
Upperdivision elective  4  
Credits  16  
Spring  
MATH 458  Introduction to Mathematical Cryptography  4  
CIS 122  Introduction to Programming and Problem Solving  MATH major CIS requirement completed  4 
Social science group satisfying course  Social science group requirement completed  4  
Arts and letters group satisfying course  Arts and letters group requirement completed  4  
Credits  16  
Fourth Year  
Fall  
MATH 461  Introduction to Mathematical Methods of Statistics I  4  
Upperdivision elective  4  
Upperdivision elective  Complete the multicultural requirement by now  4  
Credits  12  
Winter  
MATH 462  Introduction to Mathematical Methods of Statistics II  Upperdivision MATH sequence completed  4 
Upperdivision elective  4  
Upperdivision elective  Need 26 upper division credits beyond the MATH major  4  
Credits  12  
Spring  
MATH 397  History and Applications of Calculus  MATH major requirements completed  4 
Upperdivision elective  4  
Elective  4  
Elective  180 credits completed  4  
Credits  16  
Total Credits  183 
Bachelor of Science in Mathematics: Standard Track
First Year  

Fall  Milestones  Credits  
MATH 251  Calculus I (Only one MATH course can be counted toward science group requirement)  BS MATH requirement completed  4 
WR 121  College Composition I  4  
Social science groupsatisfying course  5  
Science groupsatisfying course  4  
Credits  17  
Winter  
WR 122  College Composition II  4  
Arts and letters groupsatisfying course  4  
MATH 201  Algebra Math Lab  2  
MATH 206  Combinatorics Math Lab  2  
MATH 252  Calculus II  4  
Credits  16  
Spring  
MATH 253  Calculus III  4  
Arts and letters groupsatisfying course  4  
Social science groupsatisfying course  4  
Elective  4  
Credits  16  
Second Year  
Fall  
MATH 202  Geometry Math Lab  2  
MATH 205  Foundations Math Lab  2  
MATH 281  SeveralVariable Calculus I  4  
Arts and letters groupsatisfying course  4  
Science groupsatisfying course  4  
Credits  16  
Winter  
MATH 282  SeveralVariable Calculus II  4  
MATH 341  Elementary Linear Algebra  4  
Elective  4  
Social science groupsatisfying course  4  
Credits  16  
Spring  
MATH 307  Introduction to Proof  MATH major Bridge requirement completed  4 
MATH 342  Elementary Linear Algebra  4  
Arts and letters groupsatisfying course  Arts and letters group requirement completed  4  
Science groupsatisfying course  4  
Credits  16  
Third Year  
Fall  
CIS 210  Computer Science I  MATH major CIS requirement completed  4 
MATH 391  Fundamentals of Abstract Algebra I  4  
Social science groupsatisfying course  Social science group requirement completed  4  
Upperdivision Elective  4  
Credits  16  
Winter  
MATH 392  Fundamentals of Abstract Algebra II  MATH major Fundamentals requirement completed  4 
Upperdivision elective  4  
Elective  4  
Elective  4  
Credits  16  
Spring  
MATH 397  History and Applications of Calculus  4  
Upperdivision elective  4  
Upperdivision elective  4  
Elective  4  
Credits  16  
Fourth Year  
Fall  
MATH 444  Introduction to Abstract Algebra I  4  
Upperdivision elective  4  
Elective  Complete the multicultural requirement by now  4  
Credits  12  
Winter  
MATH 445  Introduction to Abstract Algebra II  MATH major upperdivision sequence requirement completed  4 
Upperdivision elective  4  
Upperdivision elective  Need 26 upper division credits beyond the MATH major  4  
Credits  12  
Spring  
MATH 458  Introduction to Mathematical Cryptography  MATH major completed  4 
Elective  4  
Elective  180 credits completed  4  
Credits  12  
Total Credits  181 
Bachelor of Arts in Mathematics: Pure Mathematics
First Year  

Fall  Milestones  Credits  
MATH 203  Analysis and Number Theory Math Lab  2  
MATH 251  Calculus I (Only one MATH course can be counted toward science group requirement)  4  
WR 121  College Composition I  4  
First term of firstyear secondlanguage sequence  5  
Credits  15  
Winter  
WR 122  College Composition II  4  
MATH 201  Algebra Math Lab  2  
MATH 252  Calculus II  4  
Second term of firstyear secondlanguage sequence  5  
Credits  15  
Spring  
MATH 253  Calculus III  4  
Third term of firstyear secondlanguage sequence  5  
Social science groupsatisfying course  4  
Science group groupsatisfying course  4  
Credits  17  
Second Year  
Fall  
MATH 281  SeveralVariable Calculus I  4  
MATH 341  Elementary Linear Algebra  4  
Arts and letters groupsatisfying course  4  
First term of secondyear secondlanguage sequence  4  
Credits  16  
Winter  
MATH 282  SeveralVariable Calculus II  4  
MATH 342  Elementary Linear Algebra  4  
Second term of secondyear secondlanguage sequence  4  
Social science groupsatisfying course  4  
Credits  16  
Spring  
MATH 202  Geometry Math Lab  2  
MATH 205  Foundations Math Lab  2  
MATH 307  Introduction to Proof  MATH major Bridge requirement completed  4 
Third term of secondyear secondlanguage sequence  BA language requirement completed  4  
Science groupsatisfying course  4  
Credits  16  
Third Year  
Fall  
MATH 316  Fundamentals of Analysis I  4  
Arts and letters group satisfying course  4  
Science groupsatisfying course  Science group requirement completed  4  
Upperdivision Elective  4  
Credits  16  
Winter  
MATH 317  Fundamentals of Analysis II  MATH major Analysis requirement completed  4 
Social science group satisfying course  4  
Arts and letters group satisfying course  4  
Upperdivision elective  4  
Credits  16  
Spring  
CIS 122  Introduction to Programming and Problem Solving  MATH major CIS requirement completed  4 
MATH 433  Introduction to Differential Geometry  4  
Social science group satisfying course  Social science group requirement completed  4  
Arts and letters group satisfying course  Arts and letters group requirement completed  4  
Credits  16  
Fourth Year  
Fall  
MATH 444  Introduction to Abstract Algebra I  4  
Upperdivision elective  4  
Upperdivision elective  Complete the multicultural requirement by now  4  
Credits  12  
Winter  
MATH 445  Introduction to Abstract Algebra II  MATH major Abstract Algebra requirement completed  4 
Upperdivision elective  4  
Upperdivision elective  Need 26 upper division credits beyond the MATH major  4  
Credits  12  
Spring  
MATH 320  Theory of Differential Equations (MATH major requirements completed)  4  
Upperdivision elective  4  
Elective  4  
Elective  180 credits completed  4  
Credits  16  
Total Credits  183 
Bachelor of Science in Mathematics: Pure Mathematics
First Year  

Fall  Milestones  Credits  
WR 121  College Composition I  4  
MATH 251  Calculus I (Only one MATH course can be counted toward science group requirement)  BS MATH requirement completed  4 
Social science groupsatisfying course  5  
Science groupsatisfying course  4  
Credits  17  
Winter  
WR 122  College Composition II  4  
MATH 201  Algebra Math Lab  2  
MATH 206  Combinatorics Math Lab  2  
MATH 252  Calculus II  4  
Arts and letters groupsatisfying course  4  
Credits  16  
Spring  
MATH 253  Calculus III  4  
Arts and letters groupsatisfying course  4  
Social science groupsatisfying course  4  
Elective  4  
Credits  16  
Second Year  
Fall  
MATH 202  Geometry Math Lab  2  
MATH 205  Foundations Math Lab  2  
MATH 281  SeveralVariable Calculus I  4  
Arts and letters groupsatisfying course  4  
Science groupsatisfying course  4  
Credits  16  
Winter  
MATH 282  SeveralVariable Calculus II  4  
MATH 341  Elementary Linear Algebra  4  
Elective  4  
Social science groupsatisfying course  4  
Credits  16  
Spring  
MATH 307  Introduction to Proof  MATH major Bridge requirement completed  4 
MATH 342  Elementary Linear Algebra  4  
Arts and letters groupsatisfying course  Arts and letters group requirement completed  4  
Science groupsatisfying course  4  
Credits  16  
Third Year  
Fall  
CIS 210  Computer Science I  MATH major CIS requirement completed  4 
MATH 391  Fundamentals of Abstract Algebra I  4  
Social science groupsatisfying course  Social science group requirement completed  4  
Upperdivision Elective  4  
Credits  16  
Winter  
MATH 392  Fundamentals of Abstract Algebra II  MATH major Abstract Algebra requirement completed  4 
Upperdivision elective  4  
Elective  4  
Elective  4  
Credits  16  
Spring  
MATH 320  Theory of Differential Equations  4  
Upperdivision elective  4  
Upperdivision elective  4  
Elective  4  
Credits  16  
Fourth Year  
Fall  
MATH 316  Fundamentals of Analysis I  4  
Upperdivision elective  4  
Elective  Complete the multicultural requirement by now  4  
Credits  12  
Winter  
MATH 317  Fundamentals of Analysis II  MATH major Analysis requirement complete  4 
Upperdivision elective  4  
Upperdivision elective  Need 26 upper division credits beyond the MATH major  4  
Credits  12  
Spring  
MATH 458  Introduction to Mathematical Cryptography  MATH major completed  4 
Elective  4  
Elective  180 credits completed  4  
Credits  12  
Total Credits  181 
Bachelor of Arts in Mathematics: Secondary Teaching
First Year  

Fall  Milestones  Credits  
WR 121  College Composition I  4  
MATH 203  Analysis and Number Theory Math Lab  2  
MATH 251  Calculus I (Only one MATH course can be counted toward science group requirement)  4  
First term of firstyear secondlanguage sequence  5  
Credits  15  
Winter  
WR 122  College Composition II  4  
MATH 201  Algebra Math Lab  2  
MATH 252  Calculus II  4  
Second term of firstyear secondlanguage sequence  5  
Credits  15  
Spring  
MATH 253  Calculus III  4  
Third term of firstyear secondlanguage sequence  5  
Social science groupsatisfying course  4  
Science groupsatisfying course  4  
Credits  17  
Second Year  
Fall  
MATH 281  SeveralVariable Calculus I  4  
MATH 341  Elementary Linear Algebra  4  
Arts and letters groupsatisfying course  4  
First term of secondyear secondlanguage sequence  4  
Credits  16  
Winter  
CIS 122  Introduction to Programming and Problem Solving  MATH major CIS requirement completed  4 
MATH 307  Introduction to Proof  4  
Second term of secondyear secondlanguage sequence  4  
Social science groupsatisfying course  4  
Credits  16  
Spring  
MATH 202  Geometry Math Lab  2  
MATH 205  Foundations Math Lab  MATH major Bridge requirement completed  2 
MATH 343  Statistical Models and Methods  4  
Third term of secondyear secondlanguage sequence  BA language requirement completed  4  
Science groupsatisfying course  Science group requirement completed  4  
Credits  16  
Third Year  
Fall  
MATH 391  Fundamentals of Abstract Algebra I  4  
Science groupsatisfying course  Science group requirement completed  4  
Arts and letters group satisfying course  4  
Upperdivision Elective  4  
Credits  16  
Winter  
MATH 392  Fundamentals of Abstract Algebra II  4  
Upperdivision elective  4  
Social science group satisfying course  4  
Arts and letters group satisfying course  4  
Credits  16  
Spring  
MATH 397  History and Applications of Calculus  4  
Social science group satisfying course  Social science group requirement completed  4  
Arts and letters group satisfying course  Arts and letters group requirement completed  4  
Elective  4  
Credits  16  
Fourth Year  
Fall  
MATH 394  Geometries from an Advanced Viewpoint I  4  
Upperdivision elective  4  
Upperdivision elective  Complete the multicultural requirement by now  4  
Credits  12  
Winter  
MATH 347  Fundamentals of Number Theory I  4  
MATH 395  Geometries from an Advanced Viewpoint II  4  
Upperdivision elective  4  
Upperdivision elective  Need 26 upper division credits beyond the MATH major  4  
Credits  16  
Spring  
MATH 348  Fundamentals of Number Theory II  MATH major completed  4 
Upperdivision elective  4  
Elective  180 credits completed  4  
Credits  12  
Total Credits  183 
Bachelor of Science in Mathematics: Secondary Teaching
First Year  

Fall  Milestones  Credits  
WR 121  College Composition I  4  
MATH 251  Calculus I (Only one MATH course can be counted toward science group requirement)  BS MATH requirement completed  4 
Social science groupsatisfying course  5  
Science groupsatisfying course  4  
Credits  17  
Winter  
WR 122  College Composition II  4  
MATH 201  Algebra Math Lab  2  
MATH 206  Combinatorics Math Lab  2  
MATH 252  Calculus II  4  
Arts and letters groupsatisfying course  4  
Credits  16  
Spring  
MATH 253  Calculus III  4  
Arts and letters groupsatisfying course  4  
Social science groupsatisfying course  4  
Elective  4  
Credits  16  
Second Year  
Fall  
MATH 202  Geometry Math Lab  2  
MATH 205  Foundations Math Lab  2  
MATH 281  SeveralVariable Calculus I  4  
Arts and letters groupsatisfying course  4  
Science groupsatisfying course  4  
Credits  16  
Winter  
MATH 307  Introduction to Proof  MATH major Bridge requirement completed  4 
MATH 341  Elementary Linear Algebra  4  
Elective  4  
Social science groupsatisfying course  4  
Credits  16  
Spring  
CIS 122  Introduction to Programming and Problem Solving  MATH major CIS requirement completed  4 
MATH 343  Statistical Models and Methods  4  
Arts and letters groupsatisfying course  Arts and letters group requirement completed  4  
Science groupsatisfying course  4  
Credits  16  
Third Year  
Fall  
MATH 391  Fundamentals of Abstract Algebra I  4  
Social science groupsatisfying course  Social science group requirement completed  4  
Elective  4  
Upperdivision elective  4  
Credits  16  
Winter  
MATH 347  Fundamentals of Number Theory I  4  
MATH 392  Fundamentals of Abstract Algebra II  MATH major Abstract Algebra requirement completed  4 
Upperdivision elective  4  
Elective  4  
Credits  16  
Spring  
MATH 348  Fundamentals of Number Theory II  4  
Upperdivision elective  4  
Upperdivision elective  4  
Elective  4  
Credits  16  
Fourth Year  
Fall  
MATH 394  Geometries from an Advanced Viewpoint I  4  
Upperdivision elective  4  
Elective  Complete the multicultural requirement by now  4  
Credits  12  
Winter  
MATH 395  Geometries from an Advanced Viewpoint II  4  
Upperdivision elective  4  
Upperdivision elective  Need 26 upper division credits beyond the MATH major  4  
Credits  12  
Spring  
MATH 397  History and Applications of Calculus (MATH major requirements completed)  4  
Elective  4  
Elective  180 credits completed  4  
Credits  12  
Total Credits  181 
 Master of Arts
 Master of Science
 Master of Arts: PrePhD
 Master of Science: PrePhD
 Doctor of Philosophy
Graduate Studies
The university offers graduate study in mathematics leading to the master of arts (MA), master of science (MS), and doctor of philosophy (PhD) degrees.
Master’s degree programs are available to suit the needs of students with various objectives. There are programs for students who intend to enter a doctoral program and for those who plan to conclude their formal study of pure or applied mathematics at the master’s level.
Admission depends on the student’s academic record—both overall academic quality and adequate mathematical background for the applicant’s proposed degree program. The application for admission is available online. Prospective applicants should note the general university requirements for graduate admission that appear in the Graduate School section of this catalog as well as requirements specific to the department at math.uoregon.edu/graduate/admissions.
Transcripts from all undergraduate and graduate institutions attended and copies of Graduate Record Examinations (GRE) scores in the verbal, quantitative, and mathematics tests (general and subject GREs) should be submitted to the department.
In addition to general Graduate School requirements, the specific graduate program courses and conditions listed below must be fulfilled. More details can be found in the Department of Mathematics Graduate Student Handbook, available in the department office and online. All mathematics courses applied to degree requirements, including associated reading courses, must be taken for letter grades. A final written or oral examination or both is required for master’s degrees except under the prePhD option outlined below. This examination is waived under circumstances outlined in the departmental Graduate Student Handbook.
Master’s Degree Programs
Master of Arts: PrePhD Requirements
Code  Title  Credits 

Two 600level mathematics sequences ^{1}  2445  
Other 600level courses ^{1, 2}  1215  
Total Credits  45 
^{1}  Students must complete two 600level sequences acceptable for the qualifying examinations in the PhD program. In addition, they must complete one other 600level sequence or a combination of three terms of 600level courses approved by the master’s degree subcommittee of the graduate affairs committee. 
^{2}  As many as 15 credits from graduatelevel courses outside mathematics may be used toward the degree. 
Master of Science: PrePhD Requirements
Code  Title  Credits 

Two 600level mathematics sequences ^{1}  2445  
Other 600level courses ^{1, 2}  1215  
Total Credits  45 
^{1}  Students must complete two 600level sequences acceptable for the qualifying examinations in the PhD program. In addition, they must complete one other 600level sequence or a combination of three terms of 600level courses approved by the master’s degree subcommittee of the graduate affairs committee. 
^{2}  As many as 15 credits from graduatelevel courses outside mathematics may be used toward the degree. 
Master of Arts Degree Requirements
Code  Title  Credits 

Option 1  
One 600level sequence ^{1}  1215  
Select two of the following:  24  
Introduction to Analysis IIII  
Introduction to Topology and Introduction to Differential Geometry  
Introduction to Abstract Algebra IIII  
Option 2  
Two 600level sequences ^{1}  2430  
Select one of the following:  12  
Introduction to Analysis IIII  
Introduction to Topology and Introduction to Differential Geometry  
Introduction to Abstract Algebra IIII 
^{1}  Excluding Reading and Conference: [Topic] (MATH 605) 
Of the required 45 credits, 15 may be in graduatelevel courses other than mathematics. Students should also have taken a threeterm upperdivision or graduate sequence in statistics, numerical analysis, computing, or other applied mathematics.
Master of Science Degree Requirements
Code  Title  Credits 

Option 1  
One 600level sequence ^{1}  1215  
Select two of the following:  24  
Introduction to Analysis IIII  
Introduction to Topology and Introduction to Differential Geometry  
Introduction to Abstract Algebra IIII  
Option 2  
Two 600level sequences ^{1}  2430  
Select one of the following:  12  
Introduction to Analysis IIII  
Introduction to Topology and Introduction to Differential Geometry  
Introduction to Abstract Algebra IIII 
^{1}  Excluding Reading and Conference: [Topic] (MATH 605) 
Of the required 45 credits, 15 may be in graduatelevel courses other than mathematics. Students should also have taken a threeterm upperdivision or graduate sequence in statistics, numerical analysis, computing, or other applied mathematics.
Doctor of Philosophy
The PhD is a degree of distinction not to be conferred in routine fashion after completion of a specific number of courses or after attendance in Graduate School for a given number of years.
The department offers programs leading to the PhD degree in the areas of algebra, analysis, applied mathematics, combinatorics, geometry, mathematical physics, numerical analysis, probability, statistics, and topology. Advanced graduate courses in these areas are typically offered in Seminar: [Topic] (MATH 607). Each student, upon entering the graduate degree program in mathematics, reviews previous studies and objectives with the graduate advising committee. Based on this consultation, conditional admission to the master’s degree program or the prePhD program is granted. A student in the prePhD program may also be a candidate for the master’s degree.
PrePhD Program
To be admitted to the prePhD program, an entering graduate student must have completed a course of study equivalent to the graduate preparatory bachelor’s degree program described above. Other students are placed in the master’s degree program and may apply for admission to the prePhD program following a year of graduate study. Students in the prePhD program must take the qualifying examination by the beginning of their third year, during the week before classes begin fall term. It consists of examinations on two basic 600level graduate course sequences, one each from two of the following three categories:
 algebra
 analysis and probability
 topology and geometry
PhD Program
Admission to the PhD program is based on the following criteria:
 satisfactory performance on the qualifying examination
 completion of three courses at a level commensurate with study toward a PhD
 satisfactory performance in seminars or other courses taken as a part of the prePhD or PhD program.
Students who are not admitted to the PhD program because of unsatisfactory performance on the fallterm qualifying examination may retake the examination at the beginning of winter term.
A student in the PhD program is advanced to candidacy after passing a language examination and the comprehensive examination. To complete the requirements for the PhD, candidates must submit a dissertation, have it read and approved by a dissertation committee, and defend it orally in a formal public meeting.
Language Requirement
The department expects PhD candidates to be able to read mathematical material in a second language selected from French, German, and Russian. Other languages are acceptable in certain fields. To fulfill the language requirement, the student must meet with a faculty member—a doctoral advisor or a member of the PhD committee—to obtain advice for a suitable paper or book. The paper or book should be written in French, German, or Russian and have mathematical material beneficial to the student’s area of study. After reading, translating, and understanding the material, the student meets with the faculty member again. The faculty member determines whether the student understands the material. If satisfied, the faculty member deems the requirement met and the decision is added in writing to the student’s record.
Comprehensive Examination
This oral examination emphasizes the basic material in the student’s general area of interest. A student is expected to take this examination by the end of the second academic year in the PhD program. To be eligible to take this examination, a student must have completed the language examination and nearly all the course work needed for the PhD.
Dissertation
PhD candidates in mathematics must submit a dissertation containing substantial original work in mathematics. Requirements for final defense of the dissertation are those of the Graduate School.
Courses
MATH 070. Elementary Algebra. 4 Credits.
Basics of algebra, including arithmetic of signed numbers, order of operations, arithmetic of polynomials, linear equations, word problems, factoring, graphing lines, exponents, radicals. Credit for enrollment (eligibility) but not for graduation; satisfies no university or college requirement. Additional fee.
MATH 095. Intermediate Algebra. 4 Credits.
Topics include problem solving, linear equations, systems of equations, polynomials and factoring techniques, rational expressions, radicals and exponents, quadratic equations. Credit for enrollment (eligibility) but not for graduation; satisfies no university or college requirement. Additional fee.
Prereq: MATH 70 or satisfactory placement test score.
MATH 105. University Mathematics I. 4 Credits.
Topics include logic, sets and counting, probability, and statistics. Instructors may include historical context of selected topics and applications to finance and biology.
Prereq: MATH 95 or satisfactory placement test score.
MATH 106. University Mathematics II. 4 Credits.
Topics include mathematics of finance, applied geometry, exponential growth and decay, and a nontechnical introduction to the concepts of calculus.
Prereq: MATH 95 or satisfactory placement test score.
MATH 107. University Mathematics III. 4 Credits.
Topics chosen from modular arithmetic and coding, tilings and symmetry, voting methods, apportionment, fair division, introductory graph theory, or scheduling.
Prereq: MATH 95 or satisfactory placement test score.
MATH 111. College Algebra. 4 Credits.
Algebra needed for calculus including graph sketching, algebra of functions, polynomial functions, rational functions, exponential and logarithmic functions, linear and nonlinear functions.
Prereq: MATH 95 or satisfactory placement test score.
MATH 112. Elementary Functions. 4 Credits.
Exponential, logarithmic, and trigonometric functions. Intended as preparation for MATH 251.
Prereq: MATH 111 or satisfactory placement test score.
MATH 199. Special Studies: [Topic]. 15 Credits.
Repeatable.
MATH 201. Algebra Math Lab. 2 Credits.
Exploratory course in mathematics. Course focuses on techniques of mathematical exploration and discovery, the language of mathematics, and foundational issues. Topics from algebra.
MATH 202. Geometry Math Lab. 2 Credits.
Exploratory course in mathematics. Course focuses on techniques of mathematical exploration and discovery, the language of mathematics, and foundational issues. Topics from geometry.
MATH 203. Analysis and Number Theory Math Lab. 2 Credits.
Exploratory course in mathematics. Course focuses on techniques of mathematical exploration and discovery, the language of mathematics, and foundational issues. Topics from analysis and the theory of numbers.
MATH 204. Probability and Statistics Math Lab. 2 Credits.
Exploratory course in mathematics. Course focuses on techniques of mathematical exploration and discovery, the language of mathematics, and foundational issues. Topics from probability and statistics.
MATH 205. Foundations Math Lab. 2 Credits.
Exploratory course in mathematics. Course focuses on techniques of mathematical exploration and discovery, the language of mathematics, and foundational issues. Topics from the foundations of mathematics.
MATH 206. Combinatorics Math Lab. 2 Credits.
Exploratory course in mathematics. Course focuses on techniques of mathematical exploration and discovery, the language of mathematics, and foundational issues. Topics from combinatorics.
MATH 211. Fundamentals of Elementary Mathematics I. 4 Credits.
Structure of the number system, logical thinking, topics in geometry, simple functions, and basic statistics and probability. Calculators, concrete materials, and problem solving are used when appropriate. Covers the mathematics needed to teach grades K–8. Sequence.
Prereq: MATH 111 or satisfactory placement test score.
MATH 212. Fundamentals of Elementary Mathematics II. 4 Credits.
Structure of the number system, logical thinking, topics in geometry, simple functions, and basic statistics and probability. Calculators, concrete materials, and problem solving are used when appropriate. Covers the mathematics needed to teach grades K–8. Sequence.
Prereq: MATH 211, C or better.
MATH 213. Fundamentals of Elementary Mathematics III. 4 Credits.
Structure of the number system, logical thinking, topics in geometry, simple functions, and basic statistics and probability. Calculators, concrete materials, and problem solving are used when appropriate. Covers the mathematics needed to teach grades K–8. Sequence.
Prereq: MATH 212, C or better.
MATH 231. Elements of Discrete Mathematics I. 4 Credits.
Sets, mathematical logic, induction, sequences, and functions. Sequence.
Prereq: MATH 112 or satisfactory placement test score.
MATH 232. Elements of Discrete Mathematics II. 4 Credits.
Relations, theory of graphs and trees with applications, permutations and combinations.
Prereq: MATH 231.
MATH 241. Calculus for Business and Social Science I. 4 Credits.
Introduction to topics in differential and integral calculus including some aspects of the calculus of several variables. Sequence. Students cannot receive credit for both MATH 241 and 251.
Prereq: MATH 111 or satisfactory placement test score; a programmable calculator capable of displaying function graphs.
MATH 242. Calculus for Business and Social Science II. 4 Credits.
Introduction to topics in differential and integral calculus including some aspects of the calculus of several variables. Students cannot receive credit for both MATH 242 and 252.
Prereq: MATH 241.
MATH 243. Introduction to Methods of Probability and Statistics. 4 Credits.
Discrete and continuous probability, data description and analysis, sampling distributions, emphasizes confidence intervals and hypothesis testing. Students cannot receive credit for both MATH 243 and 425.
Prereq: MATH 95 or satisfactory placement test score; MATH 111 recommended; a programmable calculator capable of displaying function graphs.
MATH 246. Calculus for the Biological Sciences I. 4 Credits.
For students in biological science and related fields. Emphasizes modeling and applications to biology. Differential calculus and applications. Sequence. Students cannot receive credit for more than one of MATH 241, 246, 251.
Prereq: MATH 112 or satisfactory placement test score.
MATH 247. Calculus for the Biological Sciences II. 4 Credits.
For students in biological science and related fields. Emphasizes modeling and applications to biology. Integral calculus and applications. Students cannot receive credit for more than one of MATH 242, 247, 252.
Prereq: MATH 246.
MATH 251. Calculus I. 4 Credits.
Standard sequence for students of physical and social sciences and of mathematics. Differential calculus and applications. Sequence. Students cannot receive credit for more than one of MATH 241, 246, 251.
Prereq: MATH 112 or satisfactory placement test score.
MATH 252. Calculus II. 4 Credits.
Standard sequence for students of physical and social sciences and of mathematics. Integral calculus. Sequence. Students cannot receive credit for more than one of MATH 242, 247, 252.
Prereq: MATH 251.
MATH 253. Calculus III. 4 Credits.
Standard sequence for students of physical and social sciences and of mathematics. Introduction to improper integrals, infinite sequences and series, Taylor series, and differential equations. Sequence.
Prereq: MATH 252.
MATH 256. Introduction to Differential Equations. 4 Credits.
Introduction to differential equations and applications. Linear algebra is introduced as needed.
Prereq: MATH 253.
MATH 261. Calculus with Theory I. 4 Credits.
Covers both applications of calculus and its theoretical background. Axiomatic treatment of the real numbers, limits, and the least upper bound property.
MATH 262. Calculus with Theory II. 4 Credits.
Covers both applications of calculus and its theoretical background. Differential and integral calculus.
Prereq: MATH 261.
MATH 263. Calculus with Theory III. 4 Credits.
Covers both applications of calculus and its theoretical background. Sequences and series, Taylor's theorem.
Prereq: MATH 262.
MATH 281. SeveralVariable Calculus I. 4 Credits.
Introduction to calculus of functions of several variables including partial differentiation; gradient, divergence, and curl; line and surface integrals; Green's and Stokes's theorems. Linear algebra introduced as needed. Sequence.
Prereq: MATH 253.
MATH 282. SeveralVariable Calculus II. 4 Credits.
Introduction to calculus of functions of several variables including partial differentiation; gradient, divergence, and curl; line and surface integrals; Green's and Stokes's theorems. Linear algebra introduced as needed.
Prereq: MATH 281.
MATH 307. Introduction to Proof. 4 Credits.
Proof is how mathematics establishes truth and communicates ideas. Introduces students to proof in the context of interesting mathematical problems.
Prereq: MATH 247 or 252 or 262.
MATH 316. Fundamentals of Analysis I. 4 Credits.
Rigorous treatment of topics introduced in calculus such as limits, sequences, series, the Cauchy condition, and continuity. Development of mathematical proof in these contexts. Sequence with MATH 317.
Prereq: MATH 253 or equivalent; one from MATH 232, MATH 262, MATH 307.
MATH 317. Fundamentals of Analysis II. 4 Credits.
Rigorous treatment of topics introduced in calculus such as continuity, uniform convergence, power series, differentiation, and integration. Development of mathematical proof in these contexts. Sequence with MATH 316.
Prereq: MATH 316.
MATH 320. Theory of Differential Equations. 4 Credits.
An introduction to differential equations for students with background in linear algebra, with a mixture of applications and theory. Topics include linear and nonlinear equations, systems of equations, and questions of existence and uniqueness.
Prereq: MATH 281, MATH 342; one from MATH 232, MATH 262, MATH 307.
MATH 341. Elementary Linear Algebra. 4 Credits.
Vector and matrix algebra; ndimensional vector spaces; systems of linear equations; linear independence and dimension; linear transformations; rank and nullity; determinants; eigenvalues; inner product spaces; theory of a single linear transformation. Sequence.
Prereq: MATH 252. MATH 253 is recommended.
MATH 342. Elementary Linear Algebra. 4 Credits.
Vector and matrix algebra; ndimensional vector spaces; systems of linear equations; linear independence and dimension; linear transformations; rank and nullity; determinants; eigenvalues; inner product spaces; theory of a single linear transformation.
Prereq: MATH 341.
MATH 343. Statistical Models and Methods. 4 Credits.
Review of theory and applications of mathematical statistics including estimation and hypothesis testing.
Prereq: MATH 252.
MATH 347. Fundamentals of Number Theory I. 4 Credits.
A study of congruences, the Chinese remainder theorem, the theory of prime numbers and divisors, Diophantine equations, and quadratic reciprocity. Development of mathematical proof in these contexts. Sequence with MATH 348.
Prereq: MATH 253 or equivalent; one from MATH 232, MATH 262, MATH 307.
MATH 348. Fundamentals of Number Theory II. 4 Credits.
Study of nonlinear Diophantine equations, sums of squares, the theory of partitions, geometric number theory, and the distribution of prime numbers. Development of mathematical proof in these contexts. Sequence with MATH 347.
Prereq: MATH 347.
MATH 351. Elementary Numerical Analysis I. 4 Credits.
Basic techniques of numerical analysis and their use on computers. Topics include root approximation, linear systems, interpolation, integration, and differential equations. Sequence.
Prereq: MATH 253 or equivalent; one from MATH 232, 262, 307.
MATH 352. Elementary Numerical Analysis II. 4 Credits.
Basic techniques of numerical analysis and their use on computers. Topics include root approximation, linear systems, interpolation, integration, and differential equations.
Prereq: MATH 351.
MATH 391. Fundamentals of Abstract Algebra I. 4 Credits.
Introduction to algebraic structures including groups, rings, fields, and polynomial rings. Sequence.
Prereq: MATH 341; one from MATH 232, 262, 307.
MATH 392. Fundamentals of Abstract Algebra II. 4 Credits.
Introduction to algebraic structures including groups, rings, fields, and polynomial rings.
Prereq: MATH 391.
MATH 394. Geometries from an Advanced Viewpoint I. 4 Credits.
Topics in Euclidean geometry in two and three dimensions including constructions. Emphasizes investigations, proofs, and challenging problems. For prospective secondary and middle school teachers.
Prereq: MATH 253 or equivalent; one from MATH 232, 262, 307.
MATH 395. Geometries from an Advanced Viewpoint II. 4 Credits.
Analysis of problems in Euclidean geometry using coordinates, vectors, and the synthetic approach. Transformations in the plane and space and their groups. Introduction to nonEuclidean geometries. For prospective secondary teachers.
Prereq: grade of C or better in MATH 394.
MATH 397. History and Applications of Calculus. 4 Credits.
Historical applications of calculus. Topics may include volumes by the method of exhaustion, Archimedean spiral, Kepler problem, calculus of variations, brachistochrone problem, spread of infectious disease, analysis of savings.
Prereq: MATH 253; one from MATH 232, MATH 262, MATH 307.
MATH 399. Special Studies: [Topic]. 15 Credits.
Repeatable.
MATH 401. Research: [Topic]. 121 Credits.
Repeatable.
MATH 403. Thesis. 14 Credits.
Repeatable.
MATH 405. Reading and Conference: [Topic]. 14 Credits.
Repeatable.
MATH 407. Seminar: [Topic]. 14 Credits.
Repeatable.
MATH 410. Experimental Course: [Topic]. 14 Credits.
Repeatable.
MATH 411. Functions of a Complex Variable I. 4 Credits.
Complex numbers, linear fractional transformations, CauchyRiemann equations, Cauchy's theorem and applications, power series, residue theorem, harmonic functions, contour integration, conformal mapping, infinite products. Sequence.
Prereq: MATH 281; one from MATH 232, 262, 307.
MATH 412. Functions of a Complex Variable II. 4 Credits.
Complex numbers, linear fractional transformations, CauchyRiemann equations, Cauchy's theorem and applications, power series, residue theorem, harmonic functions, contour integration, conformal mapping, infinite products.
Prereq: MATH 411.
MATH 413. Introduction to Analysis I. 4 Credits.
Differentiation and integration on the real line and in a dimensional Euclidean space; normed linear spaces and metric spaces; vector field theory and differential forms. Sequence.
Prereq: MATH 282, MATH 317.
MATH 414. Introduction to Analysis II. 4 Credits.
Differentiation and integration on the real line and in a dimensional Euclidean space; normed linear spaces and metric spaces; vector field theory and differential forms.
Prereq: MATH 413.
MATH 415. Introduction to Analysis III. 4 Credits.
Differentiation and integration on the real line and in a dimensional Euclidean space; normed linear spaces and metric spaces; vector field theory and differential forms. Sequence.
Prereq: MATH 414.
MATH 420. Ordinary Differential Equations. 4 Credits.
Ordinary differential equations. General and initial value problems. Explicit, numerical, graphical solutions; phase portraits. Existence, uniqueness, stability. Power series methods. Gradient flow; periodic solutions.
Prereq: MATH 263 or MATH 316.
MATH 421M. Partial Differential Equations: Fourier Analysis I. 4 Credits.
Introduction to PDEs with a view towards applications in physics. Wave and heat equations, classical Fourier series on the circle, Bessel and Legendre series. Multilisted with PHYS 421M.
Prereq: MATH 253; one from MATH 256, MATH 281.
MATH 422. Partial Differential Equations: Fourier Analysis II. 4 Credits.
General theory of PDEs; the Fourier transform. Laplace and Poisson equations; Green's functions and application. Mean value theorem and maxmin principle.
Prereq: MATH 421M or PHYS 421M.
MATH 425. Statistical Methods I. 4 Credits.
Statistical methods for upperdivision and graduate students anticipating research in nonmathematical disciplines. Presentation of data, sampling distributions, tests of significance, confidence intervals, linear regression, analysis of variance, correlation, statistical software. Sequence. Only nonmajors may receive upperdivision credit. Students cannot receive credit for both MATH 243 and 425.
Prereq: MATH 111 or satisfactory placement test score.
MATH 431. Introduction to Topology. 4 Credits.
Elementary pointset topology with an introduction to combinatorial topology and homotopy. Sequence.
Prereq: MATH 317.
MATH 432. Introduction to Topology. 4 Credits.
Introduction to smooth manifolds and differential topology. Sequence.
Prereq: MATH 281, MATH 341, MATH 431.
MATH 433. Introduction to Differential Geometry. 4 Credits.
Plane and space curves, FrenetSerret formula surfaces. Local differential geometry, GaussBonnet formula, introduction to manifolds.
Prereq: MATH 282, 342; one from MATH 232, 262, 307.
MATH 441. Linear Algebra. 4 Credits.
Theory of vector spaces over arbitrary fields, theory of a single linear transformation, minimal polynomials, Jordan and rational canonical forms, quadratic forms, quotient spaces.
Prereq: MATH 342; one from MATH 232, 262, 307.
MATH 444. Introduction to Abstract Algebra I. 4 Credits.
Theory of groups, rings, and fields. Polynomial rings, unique factorization, and Galois theory. Sequence.
Prereq: MATH 342; one from MATH 232, 262, 307.
MATH 445. Introduction to Abstract Algebra II. 4 Credits.
Theory of groups, rings, and fields. Polynomial rings, unique factorization, and Galois theory.
Prereq: MATH 444.
MATH 446. Introduction to Abstract Algebra III. 4 Credits.
Theory of groups, rings, and fields. Polynomial rings, unique factorization, and Galois theory.
Prereq: MATH 445.
MATH 456. Networks and Combinatorics. 4 Credits.
Fundamentals of modern combinatorics; graph theory; networks; trees; enumeration, generating functions, recursion, inclusion and exclusion; ordered sets, lattices, Boolean algebras.
Prereq: one from MATH 232, 262, 307.
MATH 457. Discrete Dynamical Systems. 4 Credits.
Linear and nonlinear firstorder dynamical systems; equilibrium, cobwebs, Newton's method. Bifurcation and chaos. Introduction to higherorder systems. Applications to economics, genetics, ecology.
Prereq: MATH 256; one from MATH 232, 262, 307.
MATH 458. Introduction to Mathematical Cryptography. 4 Credits.
Mathematical theory of public key cryptography. Finite field arithmetic, RSA and DiffieHellman algorithms, elliptic curves, generation of primes, factorization techniques. Offered alternate years.
Prereq: MATH 341.
MATH 461. Introduction to Mathematical Methods of Statistics I. 4 Credits.
Discrete and continuous probability models; useful distributions; applications of momentgenerating functions; sample theory with applications to tests of hypotheses, point and confidence interval estimates. Sequence.
Prereq: MATH 253 or 263; one from MATH 232, 262, 307.
MATH 462. Introduction to Mathematical Methods of Statistics II. 4 Credits.
Discrete and continuous probability models; useful distributions; applications of momentgenerating functions; sample theory with applications to tests of hypotheses, point and confidence interval estimates.
Prereq: MATH 461.
MATH 463. Mathematical Methods of Regression Analysis and Analysis of Variance. 4 Credits.
Multinomial distribution and chisquare tests of fit, simple and multiple linear regression, analysis of variance and covariance, methods of model selection and evaluation, use of statistical software.
Prereq: MATH 342, MATH 462.
MATH 467. Stochastic Processes. 4 Credits.
Basics of stochastic processes including Markov chains, martingales, Poisson processes, Brownian motion and their applications.
Prereq: MATH 341, MATH 461.
MATH 503. Thesis. 112 Credits.
Repeatable.
MATH 507. Seminar: [Topic]. 14 Credits.
Repeatable.
MATH 510. Experimental Course: [Topic]. 14 Credits.
Repeatable.
MATH 511. Functions of a Complex Variable I. 4 Credits.
Complex numbers, linear fractional transformations, CauchyRiemann equations, Cauchy's theorem and applications, power series, residue theorem, harmonic functions, contour integration, conformal mapping, infinite products. Sequence.
MATH 512. Functions of a Complex Variable II. 4 Credits.
Complex numbers, linear fractional transformations, CauchyRiemann equations, Cauchy's theorem and applications, power series, residue theorem, harmonic functions, contour integration, conformal mapping, infinite products.
Prereq: MATH 411/511.
MATH 513. Introduction to Analysis I. 4 Credits.
Differentiation and integration on the real line and in a dimensional Euclidean space; normed linear spaces and metric spaces; vector field theory and differential forms. Sequence.
MATH 514. Introduction to Analysis II. 4 Credits.
Differentiation and integration on the real line and in a dimensional Euclidean space; normed linear spaces and metric spaces; vector field theory and differential forms. Sequence.
Prereq: MATH 413/513.
MATH 515. Introduction to Analysis III. 4 Credits.
Differentiation and integration on the real line and in a dimensional Euclidean space; normed linear spaces and metric spaces; vector field theory and differential forms. Sequence.
Prereq: MATH 414/514.
MATH 520. Ordinary Differential Equations. 4 Credits.
Ordinary differential equations. General and initial value problems. Explicit, numerical, graphical solutions; phase portraits. Existence, uniqueness, stability. Power series methods. Gradient flow; periodic solutions.
MATH 521M. Partial Differential Equations: Fourier Analysis I. 4 Credits.
Introduction to PDEs with a view towards applications in physics. Wave and heat equations, classical Fourier series on the circle, Bessel and Legendre series. Multilisted with PHYS 521M.
MATH 522. Partial Differential Equations: Fourier Analysis II. 4 Credits.
General theory of PDEs; the Fourier transform. Laplace and Poisson equations; Green's functions and application. Mean value theorem and maxmin principle.
Prereq: MATH 421/521.
MATH 525. Statistical Methods I. 4 Credits.
Statistical methods for upperdivision and graduate students anticipating research in nonmathematical disciplines. Presentation of data, sampling distributions, tests of significance, confidence intervals, linear regression, analysis of variance, correlation, statistical software. Sequence. Only nonmajors may receive graduate credit.
MATH 531. Introduction to Topology. 4 Credits.
Elementary pointset topology with an introduction to combinatorial topology and homotopy. Sequence.
MATH 532. Introduction to Topology. 4 Credits.
Elementary pointset topology with an introduction to combinatorial topology and homotopy. Sequence.
Prereq: MATH 431/531.
MATH 533. Introduction to Differential Geometry. 4 Credits.
Plane and space curves, FrenetSerret formula surfaces. Local differential geometry, GaussBonnet formula, introduction to manifolds.
MATH 541. Linear Algebra. 4 Credits.
Theory of vector spaces over arbitrary fields, theory of a single linear transformation, minimal polynomials, Jordan and rational canonical forms, quadratic forms, quotient spaces.
MATH 544. Introduction to Abstract Algebra I. 4 Credits.
Theory of groups, rings, and fields. Polynomial rings, unique factorization, and Galois theory. Sequence.
MATH 545. Introduction to Abstract Algebra II. 4 Credits.
Theory of groups, rings, and fields. Polynomial rings, unique factorization, and Galois theory.
Prereq: MATH 444/544.
MATH 546. Introduction to Abstract Algebra III. 4 Credits.
Theory of groups, rings, and fields. Polynomial rings, unique factorization, and Galois theory.
Prereq: MATH 445/545.
MATH 556. Networks and Combinatorics. 4 Credits.
Fundamentals of modern combinatorics; graph theory; networks; trees; enumeration, generating functions, recursion, inclusion and exclusion; ordered sets, lattices, Boolean algebras.
MATH 557. Discrete Dynamical Systems. 4 Credits.
Linear and nonlinear firstorder dynamical systems; equilibrium, cobwebs, Newton's method. Bifurcation and chaos. Introduction to higherorder systems. Applications to economics, genetics, ecology.
MATH 561. Introduction to Mathematical Methods of Statistics I. 4 Credits.
Discrete and continuous probability models; useful distributions; applications of momentgenerating functions; sample theory with applications to tests of hypotheses, point and confidence interval estimates. Sequence.
MATH 562. Introduction to Mathematical Methods of Statistics II. 4 Credits.
Discrete and continuous probability models; useful distributions; applications of momentgenerating functions; sample theory with applications to tests of hypotheses, point and confidence interval estimates.
Prereq: MATH 461/561.
MATH 563. Mathematical Methods of Regression Analysis and Analysis of Variance. 4 Credits.
Multinomial distribution and chisquare tests of fit, simple and multiple linear regression, analysis of variance and covariance, methods of model selection and evaluation, use of statistical software.
Prereq: MATH 462/562.
MATH 567. Stochastic Processes. 4 Credits.
Basics of stochastic processes including Markov chains, martingales, Poisson processes, Brownian motion and their applications.
Prereq: MATH 561.
MATH 601. Research: [Topic]. 19 Credits.
Repeatable.
MATH 602. Supervised College Teaching. 116 Credits.
Repeatable.
MATH 603. Dissertation. 116 Credits.
Repeatable.
MATH 605. Reading and Conference: [Topic]. 15 Credits.
Repeatable.
MATH 607. Seminar: [Topic]. 15 Credits.
Repeatable. Topics include Advanced Topics in Geometry, Ring Theory, Teaching Mathematics.
MATH 616. Real Analysis. 45 Credits.
Measure and integration theory, differentiation, and functional analysis with pointset topology as needed. Sequence.
MATH 617. Real Analysis. 45 Credits.
Measure and integration theory, differentiation, and functional analysis with pointset topology as needed. Sequence.
Prereq: MATH 616.
MATH 618. Real Analysis. 45 Credits.
Measure and integration theory, differentiation, and functional analysis with pointset topology as needed. Sequence.
Prereq: MATH 617.
MATH 619. Complex Analysis. 45 Credits.
The theory of Cauchy, power series, contour integration, entire functions, and related topics.
MATH 634. Algebraic Topology. 45 Credits.
Development of homotopy, homology, and cohomology with pointset topology as needed. Sequence.
MATH 635. Algebraic Topology. 45 Credits.
Development of homotopy, homology, and cohomology with pointset topology as needed. Sequence.
Prereq: MATH 634.
MATH 636. Algebraic Topology. 45 Credits.
Development of homotopy, homology, and cohomology with pointset topology as needed. Sequence.
Prereq: MATH 635.
MATH 637. Differential Geometry. 45 Credits.
Topics include curvature and torsion, SerretFrenet formulas, theory of surfaces, differentiable manifolds, tensors, forms and integration. Sequence.
MATH 638. Differential Geometry. 45 Credits.
Topics include curvature and torsion, SerretFrenet formulas, theory of surfaces, differentiable manifolds, tensors, forms and integration. Sequence.
Prereq: MATH 637.
MATH 639. Differential Geometry. 45 Credits.
Topics include curvature and torsion, SerretFrenet formulas, theory of surfaces, differentiable manifolds, tensors, forms and integration. Sequence.
MATH 647. Abstract Algebra. 45 Credits.
Group theory, fields, Galois theory, algebraic numbers, matrices, rings, algebras. Sequence.
MATH 648. Abstract Algebra. 45 Credits.
Group theory, fields, Galois theory, algebraic numbers, matrices, rings, algebras. Sequence.
Prereq: MATH 647.
MATH 649. Abstract Algebra. 45 Credits.
Group theory, fields, Galois theory, algebraic numbers, matrices, rings, algebras. Sequence.
Prereq: MATH 648.
MATH 672. Theory of Probability. 45 Credits.
Measure and integration, probability spaces, laws of large numbers, centrallimit theory, conditioning, martingales, random walks.
Prereq: MATH 671.
MATH 673. Theory of Probability. 45 Credits.
Measure and integration, probability spaces, laws of large numbers, centrallimit theory, conditioning, martingales, random walks.
Prereq: MATH 672.
MATH 681. Advanced Algebra: [Topic]. 45 Credits.
Repeatable. Topics selected from theory of finite groups, representations of finite groups, Lie groups, Lie algebras, algebraic groups, ring theory, algebraic number theory.
MATH 682. Advanced Algebra: [Topic]. 45 Credits.
Repeatable. Topics selected from theory of finite groups, representations of finite groups, Lie groups, Lie algebras, algebraic groups, ring theory, algebraic number theory.
MATH 683. Advanced Algebra: [Topic]. 45 Credits.
Repeatable. Topics selected from theory of finite groups, representations of finite groups, Lie groups, Lie algebras, algebraic groups, ring theory, algebraic number theory.
MATH 684. Advanced Analysis: [Topic]. 45 Credits.
Repeatable. Topics selected from Banach algebras, operator theory, functional analysis, harmonic analysis on topological groups, theory of distributions.
MATH 685. Advanced Analysis: [Topic]. 45 Credits.
Repeatable. Topics selected from Banach algebras, operator theory, functional analysis, harmonic analysis on topological groups, theory of distributions.
MATH 686. Advanced Analysis: [Topic]. 45 Credits.
Repeatable. Topics selected from Banach algebras, operator theory, functional analysis, harmonic analysis on topological groups, theory of distributions.
MATH 690. Advanced Geometry and Topology: [Topic]. 45 Credits.
Repeatable. Topics selected from classical and local differential geometry; symmetric spaces; lowdimensional topology; differential topology; global analysis; homology, cohomology, and homotopy; differential analysis and singularity theory; knot theory.
MATH 691. Advanced Geometry and Topology: [Topic]. 45 Credits.
Repeatable. Topics selected from classical and local differential geometry; symmetric spaces; lowdimensional topology; differential topology; global analysis; homology, cohomology, and homotopy; differential analysis and singularity theory; knot theory.
MATH 692. Advanced Geometry and Topology: [Topic]. 45 Credits.
Repeatable. Topics selected from classical and local differential geometry; symmetric spaces; lowdimensional topology; differential topology; global analysis; homology, cohomology, and homotopy; differential analysis and singularity theory; knot theory.