Mathematics
Daniel Dugger, Department Head
541-346-4705
205 Fenton Hall
1222 University of Oregon
Eugene, Oregon 97403-1222
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 University 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 long-time 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 precollege-teaching 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, associate 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, K-theory, commutative algebra). BA, 1994, Michigan, Ann Arbor; PhD, 1999, Massachusetts Institute of Technology. (2004)
Ellen E. Eischen, associate 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)
Cassandra Fisher, senior instructor. BS, 2010, George Fox; MS, 2012, Texas Tech. (2012)
Laura Fredrickson (geometric analysis and complex geometry). BS, 2010, California, Irvine; PhD, 2016, Texas, Austin. (2019)
Peter B. Gilkey, professor (global analysis, differential geometry). BS, MA, 1967, Yale; PhD, 1972, Harvard. (1981)
Hayden Harker, senior 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)
Patricia Hersh, professor (combinatorics). BA, 1995, Harvard; PhD, 1999, Massachusetts Institute of Technology. (2019)
James A. Isenberg, professor (mathematical physics, differential geometry, nonlinear partial differential equations). AB, 1973, Princeton; PhD, 1979, Maryland. (1982)
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, 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)
Victor V. Ostrik, professor (representation theory). MS, 1995, PhD, 1999, Moscow State. (2003)
Liliana Pazdan-Siudeja, instructor. MS, 2010, Illinois, Urbana-Champaign. (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 II; 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, associate 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)
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, senior instructor. BSc, 2004, Alberta; MA, 2006, State University of New York, Binghamton; PhD, 2012, British Columbia. (2013)
Jennifer Thorenson, senior 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)
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)
Micah Warren, associate 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, associate professor (combinatorics). BS, 2001, MS, 2002, Carleton; PhD, 2008, British Columbia. (2012)
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 College; 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, Technion-Israel 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)
Brad S. Shelton, professor emeritus. BA, 1976, Arizona; MS, PhD, 1982, Washington (Seattle). (1985)
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)
Hao Wang, associate professor (mathematics of finance, probability, statistics). BS, 1980, MS, 1985, Wuhan (China); PhD, 1995, Carleton (Canada). (2000)
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)
Sergey Yuzvinsky, professor (representation theory, combinatorics, multiplication of forms). MA, 1963, PhD, 1966, Leningrad. (1980)
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 I-III | 12 |
| MATH 211–213 | Fundamentals of Elementary Mathematics I-III | 12 |
| MATH 231–233 | Elements of Discrete Mathematics I-III | 12 |
| MATH 241–242 & MATH 243 | Calculus for Business and Social Science I-II and Introduction to Methods of Probability and Statistics | 12 |
| MATH 246–247 | Calculus for the Biological Sciences I-II | 8 |
| MATH 251–253 | Calculus I-III | 12 |
| MATH 261–263 | Calculus with Theory I-III | 12 |
| MATH 307 | Introduction to Proof | 4 |
The 100-level 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 upper-division 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 400-level course other than Elementary Linear Algebra (MATH 341–342), Statistical Methods I-II (MATH 425–426), or Partial Differential Equations: Fourier Analysis I-II (MATH 421–422).
The bridge requirement is one of the following:
| Code | Title | Credits |
|---|---|---|
| MATH 307 and four of MATH 201, MATH 202, MATH 203, MATH 204, MATH 205, and MATH 206 | 12 | |
| MATH 231, MATH 232, and two of MATH 201, MATH 202, MATH 203, MATH 204, MATH 205, and MATH 206 | 12 | |
| MATH 261, MATH 262, and two of MATH 201, MATH 202, MATH 203, MATH 204, MATH 205, and MATH 206 | 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 251–253 |
|
| MATH 261–263 |
|
| MATH 246–247, MATH 253 |
|
| MATH 241–242 |
|
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 I-III | 12 | |
| Calculus with Theory I-III | 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 | |
| Several-Variable Calculus I-II | 8 | |
| Elementary Linear Algebra | 8 | |
| Select one of the following | 8 | |
| Elements of Discrete Mathematics I-II | 8 | |
| Calculus with Theory I-II | 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 I-II | 8 | |
| Fundamentals of Number Theory I-II | 8 | |
| Fundamentals of Abstract Algebra I-II | 8 | |
| One upper division mathematics course | 4 | |
| Fourth Year | ||
| Three upper-division 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 I-III (MATH 413–415), Introduction to Abstract Algebra I-III (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.
Upper-division 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 upper-division requirement. At least 12 credits in upper-division 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 | Several-Variable Calculus I-II | 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 | |
| Select one of the following Fundamentals sequences: | 8 | |
| Fundamentals of Analysis I-II | ||
| Fundamentals of Number Theory I-II | ||
| Fundamentals of Abstract Algebra I-II | ||
| Select four of the following, including at least one two-term sequence: 2 | 16 | |
| Fundamentals of Analysis I | ||
| Fundamentals of Analysis II | ||
| Theory of Differential Equations | ||
| Statistical Models and Methods 3 | ||
| 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 | ||
| 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 3 | ||
| Mathematical Methods of Regression Analysis and Analysis of Variance | ||
| Stochastic Processes | ||
| Total Credits | 60 | |
| 1 | For students who have completed Calculus with Theory I-III (MATH 261–263) with a grade of mid-C or better, the department will waive the requirement for Fundamentals of Analysis I-II (MATH 316–317). |
| 2 | Sequences include MATH 316-317, 347-348, 351-352, 391-392, 394-395, 411-412, 421M-422, 413-415, 431-432, 444-446, 461-462, 461-467; credit for these courses cannot count for both the two-term Fundamentals sequence and the four upper-division electives. |
| 3 | Students cannot receive credit for both Statistical Models and Methods (MATH 343) and Introduction to Mathematical Methods of Statistics II (MATH 462). |
Bachelor of Science: Standard Track
| Code | Title | Credits |
|---|---|---|
| MATH 253 | Calculus III | 4 |
| MATH 281–282 | Several-Variable Calculus I-II | 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 | |
| Select one of the following Fundamentals sequences: 1 | 8 | |
| Fundamentals of Analysis I-II | ||
| Fundamentals of Number Theory I-II | ||
| Fundamentals of Abstract Algebra I-II | ||
| Select four of the following, including at least one two-term sequence: 2 | 16 | |
| Fundamentals of Analysis I | ||
| Fundamentals of Analysis II | ||
| Theory of Differential Equations | ||
| Statistical Models and Methods 3 | ||
| 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 | ||
| 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 3 | ||
| Mathematical Methods of Regression Analysis and Analysis of Variance | ||
| Stochastic Processes | ||
| Total Credits | 60 | |
| 1 | For students who have completed Calculus with Theory I-III (MATH 261–263) with a grade of mid-C or better, the department will waive the requirement for Fundamentals of Analysis I-II (MATH 316–317). |
| 2 | Sequences include MATH 316-317, 347-348, 351-352, 391-392, 394-395, 411-412, 421M-422, 413-415, 431-432, 444-446, 461-462, 461-467; credit for these courses cannot count for both the two-term Fundamentals sequence and the four upper-division electives. |
| 3 | Students cannot receive credit for both Statistical Models and Methods (MATH 343) and Introduction to Mathematical Methods of Statistics II (MATH 462). |
Bachelor of Arts: Pure Mathematics
| Code | Title | Credits |
|---|---|---|
| MATH 253 | Calculus III | 4 |
| MATH 281–282 | Several-Variable Calculus I-II | 8 |
| MATH 316–317 | Fundamentals of Analysis I-II 1 | 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 | |
| Elements of Discrete Mathematics I-II (and two from MATH 201–206) | ||
| Calculus with Theory I-II (and two from MATH 201–206) | ||
| Introduction to Proof (and four from MATH 201–206) | ||
| Select one of the following Abstract Algebra sequences: | 8 | |
| Fundamentals of Abstract Algebra I-II | ||
| Introduction to Abstract Algebra I-II | ||
| Select two of the following: 2 | 8 | |
| Theory of Differential Equations | ||
| Statistical Models and Methods 3 | ||
| 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 | ||
| 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 3 | ||
| Mathematical Methods of Regression Analysis and Analysis of Variance | ||
| Stochastic Processes | ||
| Total Credits | 60 | |
| 1 | For students who have completed Calculus with Theory I-III (MATH 261–263) with grades of mid-C or better, the department will waive the requirement for Fundamentals of Analysis I-II (MATH 316–317). |
| 2 | The two-term abstract algebra sequence—Introduction to Abstract Algebra I (MATH 444), Introduction to Abstract Algebra II (MATH 445)—cannot also count toward the two upper-division electives. |
| 3 | Students cannot receive credit for both Statistical Models and Methods (MATH 343) and Introduction to Mathematical Methods of Statistics II (MATH 462). |
Bachelor of Science: Pure Mathematics
| Code | Title | Credits |
|---|---|---|
| MATH 253 | Calculus III | 4 |
| MATH 281–282 | Several-Variable Calculus I-II | 8 |
| MATH 316–317 | Fundamentals of Analysis I-II 1 | 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 | |
| Elements of Discrete Mathematics I-II (and two from MATH 201–206) | ||
| Calculus with Theory I-II (and two from MATH 201–206) | ||
| Introduction to Proof (and four from MATH 201–206) | ||
| Select one of the following Abstract Algebra sequences: | 8 | |
| Fundamentals of Abstract Algebra I-II | ||
| Introduction to Abstract Algebra I-II | ||
| Select two of the following: 2 | 8 | |
| Theory of Differential Equations | ||
| Statistical Models and Methods 3 | ||
| 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 | ||
| 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 3 | ||
| Mathematical Methods of Regression Analysis and Analysis of Variance | ||
| Stochastic Processes | ||
| Total Credits | 60 | |
| 1 | For students who have completed Calculus with Theory I-III (MATH 261–263) with grades of mid-C or better, the department will waive the requirement for Fundamentals of Analysis I-II (MATH 316–317). |
| 2 | The two-term abstract algebra sequence—Introduction to Abstract Algebra I (MATH 444), Introduction to Abstract Algebra II (MATH 445)—cannot also count toward the two upper-division electives. |
| 3 | Students cannot receive credit for both Statistical Models and Methods (MATH 343) and Introduction to Mathematical Methods of Statistics II (MATH 462). |
Bachelor of Arts: Secondary Teaching
| Code | Title | Credits |
|---|---|---|
| MATH 253 | Calculus III | 4 |
| MATH 281 | Several-Variable 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 | |
| Elements of Discrete Mathematics I-II (and two from MATH 201–206) | ||
| Calculus with Theory I-II (and two from MATH 201–206) | ||
| Introduction to Proof (and from from MATH 201–206) | ||
| Select two of the following Fundamentals sequences: 1 | 16 | |
| Fundamentals of Analysis I-II | ||
| Fundamentals of Number Theory I-II | ||
| Fundamentals of Abstract Algebra I-II | ||
| MATH 394–395 | Geometries from an Advanced Viewpoint I-II | 8 |
| MATH 397 | History and Applications of Calculus | 4 |
| Total Credits | 60 | |
| 1 | For students who have completed Calculus with Theory I-III (MATH 261–263) with grades of mid-C or better, the department will waive the requirement for Fundamentals of Analysis I-II (MATH 316–317). |
Bachelor of Science: Secondary Teaching
| Code | Title | Credits |
|---|---|---|
| MATH 253 | Calculus III | 4 |
| MATH 281 | Several-Variable 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 | |
| Elements of Discrete Mathematics I-II (and two from MATH 201–206) | ||
| Calculus with Theory I-II (and two from MATH 201–206) | ||
| Introduction to Proof (and four from MATH 201–206) | ||
| Select two of the following Fundamentals sequences: 1 | 16 | |
| Fundamentals of Analysis I-II | ||
| Fundamentals of Number Theory I-II | ||
| Fundamentals of Abstract Algebra I-II | ||
| MATH 394–395 | Geometries from an Advanced Viewpoint I-II | 8 |
| MATH 397 | History and Applications of Calculus | 4 |
| Total Credits | 60 | |
| 1 | For students who have completed Calculus with Theory I-III (MATH 261–263) with grades of mid-C or better, the department will waive the requirement for Fundamentals of Analysis I-II (MATH 316–317). |
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 I-II | 8 |
| MATH 461–462 | Introduction to Mathematical Methods of Statistics I-II | 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 I-II | 8 |
| Computer and Information Science | ||
| MATH 231–233 | Elements of Discrete Mathematics I-III | 12 |
| MATH 351–352 | Elementary Numerical Analysis I-II | 8 |
| or MATH 461–462 | Introduction to Mathematical Methods of Statistics I-II | |
| MATH 456 | Networks and Combinatorics | 4 |
| Economics, Business, and Social Science | ||
| MATH 461–462 | Introduction to Mathematical Methods of Statistics I-II 2 | 8 |
| Physical Sciences and Engineering | ||
| MATH 351–352 | Elementary Numerical Analysis I-II | 8 |
| MATH 411–412 | Functions of a Complex Variable I-II | 8 |
| MATH 420 | 4 | |
| MATH 421–422 | Partial Differential Equations: Fourier Analysis I-II | 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 upper-division mathematics courses should take Calculus I-II (MATH 251–252) in place of Calculus for Business and Social Science I-II (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 upper-division mathematics credits; Statistical Methods I (MATH 425) cannot be used toward the upper-division 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 upper-division requirement. All upper-division 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 fifth-year program for middle-secondary licensure in mathematics and for elementary teaching. For more information, see the College of Education section of this catalog.
Four-Year 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.
To enroll with courses that have prerequisites, students must complete the prerequisite course with grades of C– or better or P. All upper-division mathematics courses must be taken for letter grades to count toward a mathematics major or minor, and only one D grade (D+ or D or D–) may be counted toward the upper-division requirements for the major or minor.
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 | 4 | |
| WR 121 | College Composition I | 4 | |
| First term of first-year second-language sequence | 5 | ||
| Credits | 15 | ||
| Winter | |||
| MATH 252 | Calculus II | 4 | |
| WR 122 | College Composition II | 4 | |
| MATH 201 | Algebra Math Lab | 2 | |
| Second term of first-year second-language sequence | 5 | ||
| Credits | 15 | ||
| Spring | |||
| MATH 253 | Calculus III | 4 | |
| Third term of first-year second-language sequence | 5 | ||
| Social science group-satisfying course | 4 | ||
| Science group group-satisfying course | 4 | ||
| Credits | 17 | ||
| Second Year | |||
| Fall | |||
| MATH 281 | Several-Variable Calculus I | 4 | |
| MATH 341 | Elementary Linear Algebra | 4 | |
| Arts and letters group-satisfying course | 4 | ||
| First term of second-year second-language sequence | 4 | ||
| Credits | 16 | ||
| Winter | |||
| MATH 282 | Several-Variable Calculus II | 4 | |
| MATH 342 | Elementary Linear Algebra | 4 | |
| Second term of second-year second-language sequence | 4 | ||
| Social science group-satisfying course | 4 | ||
| Credits | 16 | ||
| Spring | |||
| MATH 202 | Geometry Math Lab | 2 | |
| MATH 205 | Foundations Math Lab | 2 | |
| MATH 307 | Introduction to Proof | Mathematics major bridge requirement completed | 4 |
| Third term of second-year second-language sequence | BA language requirement completed | 4 | |
| Science group-satisfying course | 4 | ||
| Credits | 16 | ||
| Third Year | |||
| Fall | |||
| MATH 316 | Fundamentals of Analysis I | 4 | |
| Arts and letters group satisfying course | 4 | ||
| Science group-satisfying course | Science group requirement completed | 4 | |
| Upper-division Elective | 4 | ||
| Credits | 16 | ||
| Winter | |||
| MATH 317 | Fundamentals of Analysis II | Mathematics major fundamentals requirement completed | 4 |
| Social science group satisfying course | 4 | ||
| Arts and letters group satisfying course | 4 | ||
| Upper-division elective | 4 | ||
| Credits | 16 | ||
| Spring | |||
| MATH 458 | Introduction to Mathematical Cryptography | 4 | |
| CIS 122 | Introduction to Programming and Problem Solving | Mathematics 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 | |
| Upper-division elective | 4 | ||
| Upper-division elective | Completed the multicultural requirement | 4 | |
| Credits | 12 | ||
| Winter | |||
| MATH 462 | Introduction to Mathematical Methods of Statistics II | Upper-division mathematics sequence completed | 4 |
| Upper-division elective | 4 | ||
| Upper-division elective | Need 26 upper-division credits beyond the mathematics major | 4 | |
| Credits | 12 | ||
| Spring | |||
| MATH 397 | History and Applications of Calculus | Mathematics major requirements completed | 4 |
| Upper-division 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 | BS mathematics requirement completed; | 4 |
| WR 121 | College Composition I | 4 | |
| Social science group-satisfying course | 4 | ||
| Science group-satisfying course | 4 | ||
| Credits | 16 | ||
| Winter | |||
| WR 122 | College Composition II | 4 | |
| Arts and letters group-satisfying 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 group-satisfying course | 4 | ||
| Social science group-satisfying course | 4 | ||
| Elective | 4 | ||
| Credits | 16 | ||
| Second Year | |||
| Fall | |||
| MATH 202 | Geometry Math Lab | 2 | |
| MATH 205 | Foundations Math Lab | 2 | |
| MATH 281 | Several-Variable Calculus I | 4 | |
| Arts and letters group-satisfying course | 4 | ||
| Science group-satisfying course | 4 | ||
| Credits | 16 | ||
| Winter | |||
| MATH 282 | Several-Variable Calculus II | 4 | |
| MATH 341 | Elementary Linear Algebra | 4 | |
| Elective | 4 | ||
| Social science group-satisfying course | 4 | ||
| Credits | 16 | ||
| Spring | |||
| MATH 307 | Introduction to Proof | Mathematics major bridge requirement completed | 4 |
| MATH 342 | Elementary Linear Algebra | 4 | |
| Arts and letters group-satisfying course | Arts and letters group requirement completed | 4 | |
| Science group-satisfying course | 4 | ||
| Credits | 16 | ||
| Third Year | |||
| Fall | |||
| CIS 210 | Computer Science I | Mathematics major CIS requirement completed | 4 |
| MATH 391 | Fundamentals of Abstract Algebra I | 4 | |
| Social science group-satisfying course | Social science group requirement completed | 4 | |
| Upper-division Elective | 4 | ||
| Credits | 16 | ||
| Winter | |||
| MATH 392 | Fundamentals of Abstract Algebra II | Mathematics major fundamentals requirement completed | 4 |
| Upper-division elective | 4 | ||
| Elective | 4 | ||
| Elective | 4 | ||
| Credits | 16 | ||
| Spring | |||
| MATH 397 | History and Applications of Calculus | 4 | |
| Upper-division elective | 4 | ||
| Upper-division elective | 4 | ||
| Elective | 4 | ||
| Credits | 16 | ||
| Fourth Year | |||
| Fall | |||
| MATH 444 | Introduction to Abstract Algebra I | 4 | |
| Upper-division elective | 4 | ||
| Elective | Completed multicultural requirement | 4 | |
| Credits | 12 | ||
| Winter | |||
| MATH 445 | Introduction to Abstract Algebra II | Mathematics major upper-division sequence requirement completed | 4 |
| Upper-division elective | 4 | ||
| Upper-division elective | 4 | ||
| Credits | 12 | ||
| Spring | |||
| MATH 458 | Introduction to Mathematical Cryptography | Mathematics major completed | 4 |
| Elective | 4 | ||
| Elective | 180 credits completed | 4 | |
| Credits | 12 | ||
| Total Credits | 180 | ||
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 | 4 | |
| WR 121 | College Composition I | 4 | |
| First term of first-year second-language 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 first-year second-language sequence | 5 | ||
| Credits | 15 | ||
| Spring | |||
| MATH 253 | Calculus III | 4 | |
| Third term of first-year second-language sequence | 5 | ||
| Social science group-satisfying course | 4 | ||
| Science group group-satisfying course | 4 | ||
| Credits | 17 | ||
| Second Year | |||
| Fall | |||
| MATH 281 | Several-Variable Calculus I | 4 | |
| MATH 341 | Elementary Linear Algebra | 4 | |
| Arts and letters group-satisfying course | 4 | ||
| First term of second-year second-language sequence | 4 | ||
| Credits | 16 | ||
| Winter | |||
| MATH 282 | Several-Variable Calculus II | 4 | |
| MATH 342 | Elementary Linear Algebra | 4 | |
| Second term of second-year second-language sequence | 4 | ||
| Social science group-satisfying 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 second-year second-language sequence | BA language requirement completed | 4 | |
| Science group-satisfying course | 4 | ||
| Credits | 16 | ||
| Third Year | |||
| Fall | |||
| MATH 316 | Fundamentals of Analysis I | 4 | |
| Arts and letters group satisfying course | 4 | ||
| Science group-satisfying course | Science group requirement completed | 4 | |
| Upper-division 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 | ||
| Upper-division 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 | |
| Upper-division elective | 4 | ||
| Upper-division elective | Complete the multi-cultural requirement by now | 4 | |
| Credits | 12 | ||
| Winter | |||
| MATH 445 | Introduction to Abstract Algebra II | MATH major Abstract Algebra requirement completed | 4 |
| Upper-division elective | 4 | ||
| Upper-division elective | 4 | ||
| Credits | 12 | ||
| Spring | |||
| MATH 320 | Theory of Differential Equations (MATH major requirements completed) | 4 | |
| Upper-division 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 group-satisfying course | 4 | ||
| Science group-satisfying course | 4 | ||
| Credits | 16 | ||
| 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 group-satisfying course | 4 | ||
| Credits | 16 | ||
| Spring | |||
| MATH 253 | Calculus III | 4 | |
| Arts and letters group-satisfying course | 4 | ||
| Social science group-satisfying course | 4 | ||
| Elective | 4 | ||
| Credits | 16 | ||
| Second Year | |||
| Fall | |||
| MATH 202 | Geometry Math Lab | 2 | |
| MATH 205 | Foundations Math Lab | 2 | |
| MATH 281 | Several-Variable Calculus I | 4 | |
| Arts and letters group-satisfying course | 4 | ||
| Science group-satisfying course | 4 | ||
| Credits | 16 | ||
| Winter | |||
| MATH 282 | Several-Variable Calculus II | 4 | |
| MATH 341 | Elementary Linear Algebra | 4 | |
| Elective | 4 | ||
| Social science group-satisfying 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 group-satisfying course | Arts and letters group requirement completed | 4 | |
| Science group-satisfying 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 group-satisfying course | Social science group requirement completed | 4 | |
| Upper-division Elective | 4 | ||
| Credits | 16 | ||
| Winter | |||
| MATH 392 | Fundamentals of Abstract Algebra II | MATH major Abstract Algebra requirement completed | 4 |
| Upper-division elective | 4 | ||
| Elective | 4 | ||
| Elective | 4 | ||
| Credits | 16 | ||
| Spring | |||
| MATH 320 | Theory of Differential Equations | 4 | |
| Upper-division elective | 4 | ||
| Upper-division elective | 4 | ||
| Elective | 4 | ||
| Credits | 16 | ||
| Fourth Year | |||
| Fall | |||
| MATH 316 | Fundamentals of Analysis I | 4 | |
| Upper-division elective | 4 | ||
| Elective | Complete the multi-cultural requirement by now | 4 | |
| Credits | 12 | ||
| Winter | |||
| MATH 317 | Fundamentals of Analysis II | MATH major Analysis requirement complete | 4 |
| Upper-division elective | 4 | ||
| Upper-division elective | 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 | 180 | ||
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 first-year second-language 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 first-year second-language sequence | 5 | ||
| Credits | 15 | ||
| Spring | |||
| MATH 253 | Calculus III | 4 | |
| Third term of first-year second-language sequence | 5 | ||
| Social science group-satisfying course | 4 | ||
| Science group-satisfying course | 4 | ||
| Credits | 17 | ||
| Second Year | |||
| Fall | |||
| MATH 281 | Several-Variable Calculus I | 4 | |
| MATH 341 | Elementary Linear Algebra | 4 | |
| Arts and letters group-satisfying course | 4 | ||
| First term of second-year second-language 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 second-year second-language sequence | 4 | ||
| Social science group-satisfying 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 second-year second-language sequence | BA language requirement completed | 4 | |
| Science group-satisfying course | Science group requirement completed | 4 | |
| Credits | 16 | ||
| Third Year | |||
| Fall | |||
| MATH 391 | Fundamentals of Abstract Algebra I | 4 | |
| Science group-satisfying course | Science group requirement completed | 4 | |
| Arts and letters group satisfying course | 4 | ||
| Upper-division Elective | 4 | ||
| Credits | 16 | ||
| Winter | |||
| MATH 392 | Fundamentals of Abstract Algebra II | 4 | |
| Upper-division 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 | |
| Upper-division elective | 4 | ||
| Upper-division elective | Complete the multi-cultural requirement by now | 4 | |
| Credits | 12 | ||
| Winter | |||
| MATH 347 | Fundamentals of Number Theory I | 4 | |
| MATH 395 | Geometries from an Advanced Viewpoint II | 4 | |
| Upper-division elective | 4 | ||
| Upper-division elective | 4 | ||
| Credits | 16 | ||
| Spring | |||
| MATH 348 | Fundamentals of Number Theory II | MATH major completed | 4 |
| Upper-division 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 group-satisfying course | 4 | ||
| Science group-satisfying course | 4 | ||
| Credits | 16 | ||
| 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 group-satisfying course | 4 | ||
| Credits | 16 | ||
| Spring | |||
| MATH 253 | Calculus III | 4 | |
| Arts and letters group-satisfying course | 4 | ||
| Social science group-satisfying course | 4 | ||
| Elective | 4 | ||
| Credits | 16 | ||
| Second Year | |||
| Fall | |||
| MATH 202 | Geometry Math Lab | 2 | |
| MATH 205 | Foundations Math Lab | 2 | |
| MATH 281 | Several-Variable Calculus I | 4 | |
| Arts and letters group-satisfying course | 4 | ||
| Science group-satisfying 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 group-satisfying 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 group-satisfying course | Arts and letters group requirement completed | 4 | |
| Science group-satisfying course | 4 | ||
| Credits | 16 | ||
| Third Year | |||
| Fall | |||
| MATH 391 | Fundamentals of Abstract Algebra I | 4 | |
| Social science group-satisfying course | Social science group requirement completed | 4 | |
| Elective | 4 | ||
| Upper-division 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 |
| Upper-division elective | 4 | ||
| Elective | 4 | ||
| Credits | 16 | ||
| Spring | |||
| MATH 348 | Fundamentals of Number Theory II | 4 | |
| Upper-division elective | 4 | ||
| Upper-division elective | 4 | ||
| Elective | 4 | ||
| Credits | 16 | ||
| Fourth Year | |||
| Fall | |||
| MATH 394 | Geometries from an Advanced Viewpoint I | 4 | |
| Upper-division elective | 4 | ||
| Elective | Complete the multi-cultural requirement by now | 4 | |
| Credits | 12 | ||
| Winter | |||
| MATH 395 | Geometries from an Advanced Viewpoint II | 4 | |
| Upper-division elective | 4 | ||
| Upper-division elective | 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 | 180 | ||
- 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 pre-PhD option outlined below. This examination is waived under circumstances outlined in the departmental Graduate Student Handbook.
Master’s Degree Programs
Master of Arts: Pre-PhD Requirements
| Code | Title | Credits |
|---|---|---|
| Two 600-level mathematics sequences 1 | 24-45 | |
| Other 600-level courses 1, 2 | 12-15 | |
| Total Credits | 45 | |
| 1 | Students must complete two 600-level sequences acceptable for the qualifying examinations in the PhD program. In addition, they must complete one other 600-level sequence or a combination of three terms of 600-level courses approved by the master’s degree subcommittee of the graduate affairs committee. |
| 2 | As many as 15 credits from graduate-level courses outside mathematics may be used toward the degree. |
Master of Science: Pre-PhD Requirements
| Code | Title | Credits |
|---|---|---|
| Two 600-level mathematics sequences 1 | 24-45 | |
| Other 600-level courses 1, 2 | 12-15 | |
| Total Credits | 45 | |
| 1 | Students must complete two 600-level sequences acceptable for the qualifying examinations in the PhD program. In addition, they must complete one other 600-level sequence or a combination of three terms of 600-level courses approved by the master’s degree subcommittee of the graduate affairs committee. |
| 2 | As many as 15 credits from graduate-level courses outside mathematics may be used toward the degree. |
Master of Arts Degree Requirements
| Code | Title | Credits |
|---|---|---|
| Option 1 | ||
| One 600-level sequence 1 | 12-15 | |
| Select two of the following: | 24 | |
| Introduction to Analysis I-III | ||
| Introduction to Topology and Introduction to Differential Geometry | ||
| Introduction to Abstract Algebra I-III | ||
| Option 2 | ||
| Two 600-level sequences 1 | 24-30 | |
| Select one of the following: | 12 | |
| Introduction to Analysis I-III | ||
| Introduction to Topology and Introduction to Differential Geometry | ||
| Introduction to Abstract Algebra I-III | ||
| 1 | Excluding Reading and Conference: [Topic] (MATH 605) |
Of the required 45 credits, 15 may be in graduate-level courses other than mathematics. Students should also have taken a three-term upper-division or graduate sequence in statistics, numerical analysis, computing, or other applied mathematics.
Master of Science Degree Requirements
| Code | Title | Credits |
|---|---|---|
| Option 1 | ||
| One 600-level sequence 1 | 12-15 | |
| Select two of the following: | 24 | |
| Introduction to Analysis I-III | ||
| Introduction to Topology and Introduction to Differential Geometry | ||
| Introduction to Abstract Algebra I-III | ||
| Option 2 | ||
| Two 600-level sequences 1 | 24-30 | |
| Select one of the following: | 12 | |
| Introduction to Analysis I-III | ||
| Introduction to Topology and Introduction to Differential Geometry | ||
| Introduction to Abstract Algebra I-III | ||
| 1 | Excluding Reading and Conference: [Topic] (MATH 605) |
Of the required 45 credits, 15 may be in graduate-level courses other than mathematics. Students should also have taken a three-term upper-division 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 pre-PhD program is granted. A student in the pre-PhD program may also be a candidate for the master’s degree.
Pre-PhD Program
To be admitted to the pre-PhD 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 pre-PhD program following a year of graduate study. Students in the pre-PhD 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 600-level 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 pre-PhD or PhD program.
Students who are not admitted to the PhD program because of unsatisfactory performance on the fall-term 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 099. Special Studies: [Topic]. 1-2 Credits.
Credit for enrollment (eligibility) but not for graduation; satisfies no university or college requirement. Repeatable.
MATH 101. Foundations of Algebra and Mathematical Modeling. 4 Credits.
Critical elements of pre-college algebra, topics including equation solving; rational, radical, and polynomial expression evaluation and simplification; lines, linear equations, and quadratic equations. Focus on mathematical modeling and preparation for additional college level mathematics.
Prereq: UO Math Placement Exam with a score of 35-48.
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 101 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 101 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 101 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 101 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]. 1-5 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 101 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. Several-Variable 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. Several-Variable 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; n-dimensional 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; n-dimensional 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 345M. Probability and Statistics for Data Science. 4 Credits.
Introduction to probability and statistics, with an emphasis upon topics relevant for data science. Multilisted with DSCI 345M.
Prereq: MATH 342, CIS 211
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 non-Euclidean 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]. 1-5 Credits.
Repeatable.
MATH 401. Research: [Topic]. 1-21 Credits.
Repeatable.
MATH 403. Thesis. 1-4 Credits.
Repeatable.
MATH 405. Reading and Conference: [Topic]. 1-4 Credits.
Repeatable.
MATH 407. Seminar: [Topic]. 1-4 Credits.
Repeatable.
MATH 410. Experimental Course: [Topic]. 1-5 Credits.
Repeatable.
MATH 411. Functions of a Complex Variable I. 4 Credits.
Complex numbers, linear fractional transformations, Cauchy-Riemann 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, Cauchy-Riemann 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 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 max-min principle.
Prereq: MATH 421M or PHYS 421M.
MATH 425. Statistical Methods I. 4 Credits.
Statistical methods for upper-division 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 upper-division 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 point-set 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, Frenet-Serret formula surfaces. Local differential geometry, Gauss-Bonnet 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 first-order dynamical systems; equilibrium, cobwebs, Newton's method. Bifurcation and chaos. Introduction to higher-order 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 Diffie-Hellman 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 moment-generating 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 moment-generating 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 chi-square 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. 1-12 Credits.
Repeatable.
MATH 507. Seminar: [Topic]. 1-4 Credits.
Repeatable.
MATH 510. Experimental Course: [Topic]. 1-5 Credits.
Repeatable.
MATH 511. Functions of a Complex Variable I. 4 Credits.
Complex numbers, linear fractional transformations, Cauchy-Riemann 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, Cauchy-Riemann 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 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 max-min principle.
Prereq: MATH 421/521.
MATH 525. Statistical Methods I. 4 Credits.
Statistical methods for upper-division 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 point-set topology with an introduction to combinatorial topology and homotopy. Sequence.
MATH 532. Introduction to Topology. 4 Credits.
Elementary point-set 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, Frenet-Serret formula surfaces. Local differential geometry, Gauss-Bonnet 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 first-order dynamical systems; equilibrium, cobwebs, Newton's method. Bifurcation and chaos. Introduction to higher-order 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 moment-generating 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 moment-generating 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 chi-square 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 600M. Temporary Mulitlisted Course. 1-5 Credits.
Repeatable.
MATH 601. Research: [Topic]. 1-9 Credits.
Repeatable.
MATH 602. Supervised College Teaching. 1-16 Credits.
Repeatable.
MATH 603. Dissertation. 1-16 Credits.
Repeatable.
MATH 605. Reading and Conference: [Topic]. 1-5 Credits.
Repeatable.
MATH 607. Seminar: [Topic]. 1-5 Credits.
Repeatable. Topics include Advanced Topics in Geometry, Ring Theory, Teaching Mathematics.
MATH 610. Experimental Course: [Topic]. 1-5 Credits.
Repeatable.
MATH 616. Real Analysis. 4-5 Credits.
Measure and integration theory, differentiation, and functional analysis with point-set topology as needed. Sequence.
MATH 617. Real Analysis. 4-5 Credits.
Measure and integration theory, differentiation, and functional analysis with point-set topology as needed. Sequence.
Prereq: MATH 616.
MATH 618. Real Analysis. 4-5 Credits.
Measure and integration theory, differentiation, and functional analysis with point-set topology as needed. Sequence.
Prereq: MATH 617.
MATH 619. Complex Analysis. 4-5 Credits.
The theory of Cauchy, power series, contour integration, entire functions, and related topics.
MATH 634. Algebraic Topology. 4-5 Credits.
Development of homotopy, homology, and cohomology with point-set topology as needed. Sequence.
MATH 635. Algebraic Topology. 4-5 Credits.
Development of homotopy, homology, and cohomology with point-set topology as needed. Sequence.
Prereq: MATH 634.
MATH 636. Algebraic Topology. 4-5 Credits.
Development of homotopy, homology, and cohomology with point-set topology as needed. Sequence.
Prereq: MATH 635.
MATH 637. Differential Geometry. 4-5 Credits.
Topics include curvature and torsion, Serret-Frenet formulas, theory of surfaces, differentiable manifolds, tensors, forms and integration. Sequence.
MATH 638. Differential Geometry. 4-5 Credits.
Topics include curvature and torsion, Serret-Frenet formulas, theory of surfaces, differentiable manifolds, tensors, forms and integration. Sequence.
Prereq: MATH 637.
MATH 639. Differential Geometry. 4-5 Credits.
Topics include curvature and torsion, Serret-Frenet formulas, theory of surfaces, differentiable manifolds, tensors, forms and integration. Sequence.
MATH 647. Abstract Algebra. 4-5 Credits.
Group theory, fields, Galois theory, algebraic numbers, matrices, rings, algebras. Sequence.
MATH 648. Abstract Algebra. 4-5 Credits.
Group theory, fields, Galois theory, algebraic numbers, matrices, rings, algebras. Sequence.
Prereq: MATH 647.
MATH 649. Abstract Algebra. 4-5 Credits.
Group theory, fields, Galois theory, algebraic numbers, matrices, rings, algebras. Sequence.
Prereq: MATH 648.
MATH 672. Theory of Probability. 4-5 Credits.
Measure and integration, probability spaces, laws of large numbers, central-limit theory, conditioning, martingales, random walks.
Prereq: MATH 671.
MATH 673. Theory of Probability. 4-5 Credits.
Measure and integration, probability spaces, laws of large numbers, central-limit theory, conditioning, martingales, random walks.
Prereq: MATH 672.
MATH 681. Advanced Algebra: [Topic]. 4-5 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]. 4-5 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]. 4-5 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]. 4-5 Credits.
Repeatable. Topics selected from Banach algebras, operator theory, functional analysis, harmonic analysis on topological groups, theory of distributions.
MATH 685. Advanced Analysis: [Topic]. 4-5 Credits.
Repeatable. Topics selected from Banach algebras, operator theory, functional analysis, harmonic analysis on topological groups, theory of distributions.
MATH 686. Advanced Analysis: [Topic]. 4-5 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]. 4-5 Credits.
Repeatable. Topics selected from classical and local differential geometry; symmetric spaces; low-dimensional topology; differential topology; global analysis; homology, cohomology, and homotopy; differential analysis and singularity theory; knot theory.
MATH 691. Advanced Geometry and Topology: [Topic]. 4-5 Credits.
Repeatable. Topics selected from classical and local differential geometry; symmetric spaces; low-dimensional topology; differential topology; global analysis; homology, cohomology, and homotopy; differential analysis and singularity theory; knot theory.
MATH 692. Advanced Geometry and Topology: [Topic]. 4-5 Credits.
Repeatable. Topics selected from classical and local differential geometry; symmetric spaces; low-dimensional topology; differential topology; global analysis; homology, cohomology, and homotopy; differential analysis and singularity theory; knot theory.