The course will offer students the opportunity to solve challenging mathematical problems unlike standard homework problems in any course. Class time will be spent studying problems, discovering solutions, writing up solutions formally, and discussing the important ideas of each solution. Most problems will be of the kind appearing on the Putnam Exam, an annual international mathematics competition. This course may be repeated for credit.
A survey of contemporary topics in mathematics such as: voting systems and power, apportionment, fair division of divisible and indivisible assets, efficient distribution, scheduling and routing, growth and decay in nature and economics, symmetry and fractal geometry, probability and statistics.
This course is an introduction to descriptive and inferential statistical analysis. The following topics will be examined: scales of measurement; frequency distributions; graphing data; measures of central tendency, dispersion and skewness; sampling distributions; probability distributions; the binomial, Poisson and normal distributions; hypothesis testing; confidence intervals and interval estimation; t-tests; analysis of variance; correlational analysis; regression analysis; and analysis of nominal-level data.
Modeling with Calculus introduces and applies the concept of calculus to solve open-ended, real-word problems, especially those in the natural and social sciences. The emphasis is on developing and interpreting mathematical models. Topics include differential calculus, linear algebra, and differential equations. This course takes advantage of computational tools so that the focus can be on calculus concepts useful in applied work. This course is appropriate for students with no prior calculus experience.
MATH 150 is an introduction to differential calculus that includes some review of algebra and trigonometry. Topics covered include limits, the definition of the derivative, rules of differentiation, applications of the derivative, the definition of the definite integral, and the Fundamental Theorem of Calculus. Review of algebra and trigonometry will be included.
A first course in calculus for students with some previous exposure to the subject. Topics covered include limits; continuity; derivatives of algebraic, trigonometric, and exponential functions; implicit differentiation; the Mean Value Theorem; and optimization.
A second course in Calculus. Topics covered include definite and indefinite integrals, the Fundamental Theorem of Calculus, volume, arc length and surface areas, integration techniques, improper integrals, polar coordinates and parametric equations, sequences and series, Taylor Polynomials, Taylor Series, convergence, and Fourier Series.
A half-semester course on sequences and series. Topics covered include sequences and series, Taylor Polynomials, Taylor Series, convergence, and Fourier Series.
Introduction to basic techniques and modes of reasoning in combinatorial problem-solving. Topics will be chosen from combinatorial mathematics, logic and Boolean algebra, difference equations, graph theory and applied algebra.
A semester-long study of topics in Mathematics. Topics and emphases will vary according to the instructor. This course may be repeated for credit with different topics. See the New and Topics Courses page on the Registrar’s webpage for descriptions and applicability to majors/minors in other departments.
The general linear model is a fundamental tool frequently implemented by statisticians to describe the relationship between a quantitative response variable and one or more qualitative and/or quantitative explanatory variables. In this course, we will explore the implementation of the general linear model which will ultimately lead us to common model fitting techniques, including one-sample t-tests, two-sample t-tests, simple and multiple linear regressing, ANOVA, and ANCOVA. While theoretical results will occasionally be covered to provide necessary justification, the primary focus of the class will be on applying the aforementioned model fitting techniques to real data sets. The statistical software R will be used throughout the course to perform data analysis. Students enrolled in this course are presumed to have strong quantitative backgrounds and/or previous statistics experience.
Three-dimensional analytic geometry; partial differentiation; maxima-minima problems; multiple integrals; vector fields, curl and divergence; line and surface integrals; applications.
This course provides an introduction to logic and the methods of proof commonly used in mathematics. Applications covered in the course are the foundations of set theory, equivalence relations, elementary number theory and other areas of mathematics.
Systems of linear equations, matrices, vector spaces and linear transformations.
Elementary differential equations; linear differential equations of second order; Laplace transformations; infinite series solutions; systems of linear differential equations.
A calculus-based introduction to probability and statistics. Topics include summary statistics, probability theory, discrete and continuous random variables, distribution, limit theorems, estimation, hypothesis testing, and linear regression.
An Introduction to the basic mathematical theory that underlie current data science methods. Students will gain an appreciation for the value of the mathematical theory as well as their limitations. Topics covered in the course will include: 1) Linear modeling and matrix computation (e.g., matrix algebra and factorization, eigenvalues/eigenvectors, and projection/least squares), 2) Optimization (e.g., calculus concepts related to differentiation), 3) Multivariate thinking (e.g., concepts and numerical computation of multivariate derivatives and integrals), and 4) Probabilistic thinking and modeling (e.g., counting principles, univariate and multivariate distributions, and independence). The connection between the mathematical theory and data science applications will be emphasized and the presentation of the theory will be driven by specific data science models and algorithms.
A semester-long study of topics in Mathematics. Topics and emphases will vary according to the instructor. This course may be repeated for credit with different topics. See the New and Topics Courses page on the Registrar’s webpage for descriptions and applicability to majors/minors in other departments.
Complex numbers, limits, differentiation, analytic functions, integration, conformal mapping, Riemann surfaces and applications.
Systems of linear equations, matrices, vector spaces and linear transformations.
This course offers timely exposure to topics in mathematics which are not part of the regular curriculum. Examples of topics which might be offered: Graph Theory, Advanced Linear Algebra, Operations Research.
In this course, students begin developing their Mathematics senior thesis projects under the mentorship of a departmental faculty member. Students will learn foundational techniques and concepts or review the relevant literature. Course meetings include discussion of research articles, peer teaching, learning about open problems, and practice with mathematical communication skills. The course culminates in a progress report that is given as a formal oral presentation.
A semester-long study of topics in Mathematics. Topics and emphases will vary according to the instructor. This course may be repeated for credit with different topics. See the New and Topics Courses page on the Registrar’s webpage for descriptions and applicability to majors/minors in other departments.
A semester-long study of topics in Mathematics. Topics and emphases will vary according to the instructor. This course may be repeated for credit with different topics. See the New and Topics Courses page on the Registrar’s webpage for descriptions and applicability to majors/minors in other departments.
Rigorous study of the real numbers and real-valued functions. Topics include: limits and continuity on the real line, elementary topology of the real numbers, pathological examples. Other topics may include metric spaces, differentiation, vector-valued functions.
A continuation of MATH 446. Topics include: Differentiation and Riemann integration, sequences of functions. Other topics may include point-set topology of the reals, vector-valued functions, topological vector spaces, Lebesgue intetration, introductory measure theory.
Number systems, elementary number theory, groups, rings, fields, polynomials and applications. Additional topics may be chosen from linear algebra, multilinear algebra, Sylow theory and Galois theory.
Course will build on the topics studies in MATH 456, Abstract Algebra I. In addition to Groups, Rings, and Fields, topics may include Galois Theory, Sylow Theory, Cayley Graphs, etc..
An introduction to the theory of numbers to include such topics as divisibility, congruence, diophantine equations, quadratic reciprocity, the theory of prime numbers and analytic number theory.
Elementary point-set topology with an introduction to combinatorial topology and homotopy.
A modern approach to geometry. Topics will be chosen from Euclidean, non-Euclidean, affine, projective and differential geometry.
Directed research to investigate topics of special interest under the guidance of a faculty member. Topics chosen on the basis of the background and interests of the individual student.
A course of directed research designed to enable the exceptional student to continue the investigation of topics of special interest under the guidance of a faculty member.
Students begin their Mathematics senior thesis project under the mentorship of a departmental faculty member. Students will build on foundational techniques and concepts from the Junior Research Seminar. Weekly meetings include peer teaching, study of new problems, presentation of progress on the research plans, and practice with mathematical communication skills. The course culminates in a progress report that is given as a formal oral presentation.
Students complete their Mathematics senior thesis project under the mentorship of a departmental faculty member. Weekly meetings include peer teaching, study of new problems, presentation of progress on the research plans, and practice with mathematical communication skills. The course culminates in a written paper and a formal oral presentation
Willamette University
Ford Hall
900 State Street
Salem
Oregon
97301
U.S.A.