Mathematics and Statistics
Intellectually situated in the liberal arts tradition, the Department of Mathematics and Statistics champions a broad spectrum of mathematical and computational inquiry, both abstract and applied. Our faculty practice and teach the corresponding modes of analysis and problem solving, ranging from formal and symbolic reasoning to technology-driven computation. We value the art of communication within our discipline—the careful reading, precise writing, and clear discussion of technical material.
Our department also values interdisciplinary interactions. To other fields of inquiry we bring mathematical and computational methods for the modeling and simulation of phenomena, and the analysis of data. These methods provide important insight into problems arising in other disciplines, as well as give rise to new and challenging mathematical problems, thereby spurring the development of both fields.
At its core, the department is a community of passionate scholars, consisting not only of the faculty and staff, but also the students. We seek to nurture relationships within this community as well as with the larger geographic and intellectual communities to which we belong.
Resources for Nonmajors
Classes of interest to nonmajors:
- MATH 131 Calculus I is modeling- and applications-driven. It features applications to economics, the life sciences, and physics.
- MATH 225 Linear Algebra is a useful elective for numerous programs. It is highly recommended for students who have already completed single-variable calculus.
- MATH 255 Statistical Concepts and Methods introduces the main ideas of modern statistics with applications to problems encountered in various disciplines, especially the natural sciences.
Courses at the level of MATH 131 or above assume some exposure to precalculus. Interested students who have not yet had this kind of math experience should contact the department.
The Major Program
The majority of students who are interested in majoring in mathematics start with single variable calculus (MATH 131 Calculus I or MATH 132 Calculus II). Those who have already completed the equivalent of MATH 132 are advised to start with MATH 225 Linear Algebra or MATH 255 Statistical Concepts and Methods.
If going right into MATH 131 or MATH 132 doesn't seem like a good fit for you, for any reason, we encourage you to contact the department chair to learn more about proper placement.
Students majoring in mathematics may not earn a minor in mathematics.
Major Requirements: Mathematics
A minimum of 36 semester credits in mathematics courses numbered 171 and above, including the following:
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CS 171 Computer Science I
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MATH 215 Discrete Mathematics
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MATH 225 Linear Algebra
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MATH 233 Multivariable and Vector Calculus
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At least 16 additional semester credits at the 300 or 400 level, at least 12 of which must be in mathematics courses.
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At least 4 additional semester credits in mathematics or computer science courses numbered 171 and above.
CS 230 Computational Mathematics does not count toward this major.
Minor Requirements: Mathematics
A minimum of 16 semester credits in mathematics courses numbered 200 and above, including the following:
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MATH 215 Discrete Mathematics
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MATH 225 Linear Algebra
- At least 4 semester credits in mathematics at the 300 or 400 level
Honors
Departmental honors will be awarded by the department to students who produce an outstanding senior thesis. Students who have produced exceptional work in MATH 491 Thesis Preparation, or as part of a summer research project, submit a thesis proposal before the first day of the term in which they wish to complete their thesis. If the department approves the proposal, then the student may enroll in MATH 496 Senior Thesis, as appropriate, and no later than the 12th week of the semester submit the completed thesis to the department for approval. If the honors thesis is approved, the student presents a summary at a departmental forum. A cumulative GPA of 3.500 or higher, both in the major and overall, is required.
Faculty
Paul T. Allen. Associate professor of mathematics. Geometric Analysis, Differential Equations, Mathematical Relativity. PhD 2007, MS 2003 University of Oregon. BS 2001 University of Puget Sound.
Yung-Pin Chen. Professor of statistics. Statistics, Sequential Designs. Probability, Stochastic Processes. PhD 1994 Purdue University. BS 1984 National Chengchi University, Taiwan.
Andrew Fry. Assistant professor of mathematics. Combinatorics, Moduli Spaces, Tropical Geometry. PhD 2021, MS 2019 Colorado State University. BS 2015 Western Oregon University.
Elizabeth A. Stanhope. Professor of mathematics. Differential geometry, spectral geometry. PhD 2002, AM 1999 Dartmouth College. BA 1995 Carleton College.
Iva Stavrov. Professor of mathematics and department chair. Differential geometry, mathematical general relativity. PhD 2003, MS 2001 University of Oregon. BS 1998 University of Belgrade.
Sweta Suryanarayan. Assistant professor with term of mathematics. Algebraic topology, algebraic geometry, combinatorics. PhD 2012 University of Washington. MSc 2004 Indian Institute of Technology, Bombay, India. BSc 2002 SIES College of Arts, Science and Commerce, University of Mumbai.
Mathematics and Statistics Courses
MATH 115 Elementary Functions
Content: The basic functions encountered in calculus, discrete mathematics, and computer science: polynomial, rational, exponential, logarithmic, and trigonometric functions and their inverses. Graphs of these functions, their use in problem-solving, their analytical properties. May not be taken for credit if AP Calculus credit has been granted.
Prerequisites: QR 101 or equivalent.
Usually offered: Annually, fall and spring semester.
Semester credits: 4.
MATH 131 Calculus I
Content: Basic analytical and quantitative reasoning and problem-solving skills that depend on the concept of the limit. Continuity, the derivative and its applications, the fundamental theorem of calculus, introduction to the definite integral with applications. May not be taken for credit if AP calculus credit has been granted.
Prerequisites: MATH 115 or equivalent.
Usually offered: Annually, fall and spring semester.
Semester credits: 4.
MATH 132 Calculus II
Content: Further development of the definite integral including techniques of integration, applications of the definite integral, indeterminate forms, and improper integrals. Sequences, series of constants, power series, Taylor polynomials and series, introduction to elementary differential equations. May not be taken for credit if AP Calculus BC credit has been granted.
Prerequisites: MATH 131 or equivalent.
Usually offered: Annually, fall and spring semester.
Semester credits: 4.
MATH 215 Discrete Mathematics
Content: Basic techniques of abstract formal reasoning and representation used in the mathematical sciences. First-order logic, elementary set theory, proof by induction and other techniques, enumeration, relations and functions, graphs, recurrence relations.
Prerequisites: MATH 132 or equivalent.
Usually offered: Annually, fall and spring semester.
Semester credits: 4.
MATH 225 Linear Algebra
Content: Basic skills and concepts that evolve from the study of systems of linear equations. Systems of linear equations, Euclidean vector spaces and function spaces, linear transformations, matrices and determinants, inner product spaces, eigenvalue problems, symmetric transformations.
Prerequisites: MATH 132 or equivalent.
Usually offered: Annually, fall and spring semester.
Semester credits: 4.
MATH 233 Multivariable and Vector Calculus
Content: Curvilinear coordinates; parameterization of curves, surfaces, and regions; geometry of vectors and vector fields; differential calculus of functions of several variables; integration over curves, surfaces, and regions; work and flux integrals, divergence, curl, and gradients; theorems of Green, Gauss, and Stokes.
Prerequisites: MATH 132 or equivalent.
Usually offered: Annually, fall and spring semester.
Semester credits: 4.
MATH 235 Differential Equations
Content: Introduction to theory, methods, and applications of differential equations, emphasizing the analysis of dynamical systems. Elementary modeling, numerical techniques, solutions to linear systems, qualitative analysis of nonlinear systems, nonlinear oscillators, introduction to advanced topics.
Prerequisites: MATH 132 or equivalent.
Usually offered: Annually, fall semester.
Semester credits: 4.
MATH 244 Math Practicum
Content: Tutoring opportunities (two to four hours onsite per week) at community schools to include one-on-one tutoring or classroom aid for site supervisor. Written reports and consultation with instructor required during semester. Specific math courses or grade levels to be determined by student, site supervisor, and instructor. Credit-no credit. May be taken twice for credit with at most 2 credits counted toward math major.
Prerequisites: None.
Restrictions: Sophomore standing and consent required.
Usually offered: Annually, fall and spring semester.
Semester credits: 1-4.
MATH 255 Statistical Concepts and Methods
Content: Introduction to principal statistical concepts and methods with emphasis on data. Statistical thinking, the application of statistical methods to other disciplines, and the communication of statistics, both verbally and in writing. Exploratory data analysis, random variables, regression analysis, data production, and statistical inference. Mathematical tools and skills used to address problems posed by collecting, analyzing, and modeling data.
Prerequisites: MATH 131 or equivalent.
Usually offered: Annually, spring semester.
Semester credits: 4.
MATH 281 Putnam Exam Preparation
Content: Emphasis on problem-solving skills required for success on the Putnam exam. Participation in the exam is required to earn credit. Credit/no credit. May be taken twice for credit. Instructor consent required.
Prerequisites: None.
Usually offered: Annually, fall semester.
Semester credits: 1.
MATH 282 Modeling Competition Preparation
Content: Emphasis on mathematical modeling skills required for success in the COMAP Mathematical Modeling Competition and Interdisciplinary Modeling Competition. Participation in the competition is required to earn credit. Credit/no credit. May be taken twice for credit.
Prerequisites: None.
Usually offered: Annually, fall semester.
Semester credits: 1.
MATH 299 Independent Study
Content: Independent study topic to be arranged with instructor.
Prerequisites: None.
Restrictions: Sophomore standing and consent required.
Usually offered: Annually, fall and spring semester.
Semester credits: 1-4.
MATH 305 Partial Differential Equations with Applications
Content: Using techniques of multivariate calculus to derive and study the classical linear partial differential equations. Topics include the calculus of variations, initial and boundary value problems, the method of separation of variables, Hilbert spaces, and Fourier series. Additional topics may include special functions, the Fourier transform, and Green's functions. Sophomore standing required.
Prerequisites: MATH 233. MATH 235.
Restrictions: Sophomore standing required.
Usually offered: Annually, spring semester.
Semester credits: 4.
MATH 315 Number Theory
Content: Divisibility properties of the integers, unique factorization, linear Diophantine equations, congruences, Fermat's and Wilson's theorems, arithmetic functions. Other topics selected from the following: primitive roots and indices, quadratic reciprocity, the theory of prime numbers, continued fractions, sums of squares, analytic number theory. Sophomore standing required.
Prerequisites: MATH 215.
Restrictions: Sophomore standing required.
Usually offered: Alternate Years, fall semester.
Semester credits: 4.
MATH 325 Combinatorics
Content: Introduction to combinatorial theory, including one or more of the following: enumeration, algebraic enumeration, optimization, graph theory, coding theory, design theory, finite geometries, Latin squares, posets, lattices, Polya counting, Ramsey theory. Sophomore standing required.
Prerequisites: MATH 215.
Restrictions: Sophomore standing required.
Usually offered: Alternate Years, spring semester.
Semester credits: 4.
MATH 341 Real Analysis
Content: Development of the ability to understand, construct, and write proofs in analysis. Topics include limits, continuity, differentiation, integration, metric spaces, applications, and generalizations, from an axiomatic perspective. Sophomore standing required.
Prerequisites: MATH 215.
Restrictions: Sophomore standing required.
Usually offered: Annually, fall semester.
Semester credits: 4.
MATH 345 Numerical Analysis
Content: The theoretical basis, error analysis, and practical techniques of numerical computations. Topics chosen from the following: solutions of systems of linear equations, solutions of nonlinear equations, numerical integration and differentiation, solutions of ordinary differential equations, eigenvalue problems, interpolation, approximation. Sophomore standing required.
Prerequisites: CS 171. MATH 132.
Restrictions: Sophomore standing required.
Usually offered: Alternate Years, spring semester.
Semester credits: 4.
MATH 351 Linear Models
Content: Introduction to statistical modeling. General model-building methods; linear regression analysis widely employed for modeling the relationship between a response variable and a set of explanatory variables. Blend of theory and applications to gain an understanding of the concepts and methods for applying statistical modeling techniques in a wide variety of disciplines.
Prerequisites: ECON 103, PSY 200, MATH 105, or MATH 255.
Usually offered: Alternate Years, spring semester.
Semester credits: 4.
MATH 352 Simulation-Based Statistical Methods
Content: Introduction to simulation-based methods used in statistical inference and scientific computation. Problems in the life sciences will be used to motivate various randomization-based methods including sampling techniques from various distributions, permutation test, bootstrap, random walk, nonparametric inference, Bayesian inference, and Markov chain Monte Carlo.
Prerequisites: ECON 103, PSY 200, MATH 105, MATH 255 or equivalent.
Usually offered: Alternate Years, spring semester.
Semester credits: 4.
MATH 355 Geometry
Content: Concepts of geometry encompassing both Euclidean and non-Euclidean geometries. Parallelism, distance, angles, triangles, other geometric notions studied from the viewpoint of logic and foundations, transformations or differential geometry. Sophomore standing required.
Prerequisites: MATH 215.
Restrictions: Sophomore standing required.
Usually offered: Alternate Years, spring semester.
Semester credits: 4.
MATH 365 Complex Variables
Content: Concepts of complex analysis. Complex number system, analytic functions, integration of functions of a complex variable, power series representation, conformal mappings, residue theory. Sophomore standing required.
Prerequisites: MATH 233.
Restrictions: Sophomore standing required.
Usually offered: Alternate Years, spring semester.
Semester credits: 4.
MATH 421 Abstract Algebra I
Content: A two-semester sequence in abstract algebraic systems. Structure of groups, subgroups, quotient groups, homomorphisms, Fundamental Isomorphism Theorems, rings, ideals, integral domains, polynomial rings, matrix rings, fields, Galois theory, advanced topics in linear algebra. Sophomore standing required.
Prerequisites: MATH 215. MATH 225.
Restrictions: Sophomore standing required.
Usually offered: Alternate Years, fall semester.
Semester credits: 4.
MATH 422 Abstract Algebra II
Content: A two-semester sequence in abstract algebraic systems. Structure of groups, subgroups, quotient groups, homomorphisms, fundamental isomorphism theorems, rings, ideals, integral domains, polynomial rings, matrix rings, fields, Galois theory, advanced topics in linear algebra. Sophomore standing required.
Prerequisites: MATH 215. MATH 225. MATH 421.
Restrictions: Sophomore standing required.
Usually offered: Alternate Years, spring semester.
Semester credits: 4.
MATH 442 Advanced Topics in Analysis and Topology
Content: Multivariable real analysis with applications to differential topology. Topics selected from fixed-point theorems, implicit and inverse function theorems, integration, manifolds, homotopy, and homology. Sophomore standing required.
Prerequisites: MATH 225. MATH 233. MATH 341.
Restrictions: Sophomore standing required.
Usually offered: Alternate Years, spring semester.
Semester credits: 4.
MATH 444 Practicum
Content: Internship or practicum to be arranged with instructor.
Prerequisites: None.
Restrictions: Sophomore standing and consent required.
Usually offered: Annually, fall and spring semester.
Semester credits: 1-4.
MATH 451 Probability and Statistics I
Content: A two-semester sequence in the theory of probability and mathematical statistics. Elementary probability, discrete and continuous random variables, distributions, limit theorems, point estimation, hypothesis testing, linear models, analysis of variance, nonparametric statistics. Sophomore standing required.
Prerequisites: MATH 215. MATH 233.
Restrictions: Sophomore standing required.
Usually offered: Alternate Years, fall semester.
Semester credits: 4.
MATH 452 Probability and Statistics II
Content: A two-semester sequence in the theory of probability and mathematical statistics. Elementary probability, discrete and continuous random variables, distributions, limit theorems, point estimation, hypothesis testing, linear models, analysis of variance, nonparametric statistics. Sophomore standing required.
Prerequisites: MATH 215. MATH 233. MATH 451.
Restrictions: Sophomore standing required.
Usually offered: Alternate Years, spring semester.
Semester credits: 4.
MATH 490 Topics in Mathematics
Content: Determined by student and/or faculty interest. May continue topics from an existing course or explore new areas. May be taken three times for credit under different topics. Instructor consent and sophomore standing required.
Prerequisites: None.
Restrictions: Sophomore standing and consent required.
Usually offered: Alternate Years, fall and spring semester.
Semester credits: 4.
MATH 491 Thesis Preparation
Content: Independent research project culminating in a written thesis proposal. Details determined by student in consultation with supervising faculty member. Instructor consent required.
Prerequisites: None.
Restrictions: Instructor consent required.
Usually offered: Annually, fall and spring semester.
Semester credits: 1-4.
MATH 496 Senior Thesis
Content: Independent research project, based upon revision of thesis preparation project or summer research experience, suitable for granting departmental honors. Details determined by student in consultation with supervising faculty member. Permission of department to pursue honors required. Instructor consent required.
Prerequisites: None.
Restrictions: Permission of department to pursue honors. Instructor consent required.
Usually offered: Annually, fall and spring semester.
Semester credits: 4.
MATH 499 Independent Study
Content: Independent study topic to be arranged with instructor.
Prerequisites: None.
Restrictions: Sophomore standing and consent required.
Usually offered: Annually, fall and spring semester.
Semester credits: 1-4.
Quantitative Reasoning Courses
QR 101 Foundations of Quantitative Reasoning
Content: Students will apply mathematics, statistics, and algebra to quantitatively analyze, model, and solve problems in authentic contexts with a focus on effectively reporting the results and conclusions. Topics include units, dimensional analysis, estimation, percent change, proportional reasoning, linear and exponential modeling, systems of equations, charts and graphs, descriptive statistics, logarithmic scale, linear regression, correlation, and what-if analysis. Emphasis on using computational tools.
Prerequisites: ALEKS score of 30 or above.
Usually offered: Annually, fall and spring semester.
Semester credits: 4.