This course presents the spirit and beauty of mathematics through topics chosen by the instructor, emphasizing the role that mathematics plays in society. Topics may include mathematics in art and literature, Euclid's Elements, game theory and voting theory. The mathematical content may include geometry, algebra, and number systems. The course is suitable for a general audience with a broad spectrum of backgrounds and abilities and also satisfies requirements for EC-6 or 4-8 teacher certification. This course may not be used for the Mathematics major or minor. (NS)

This course provides students in the social and natural sciences with the skills necessary to perform elementary statistical analysis. Topics include descriptive measures, sampling theory, Student-T and normal distributions, estimation and hypothesis testing with p-values, regression and correlation. This course may not be used for the Mathematics major or minor. Contributes to Data Analytics, Data Science, and Health Studies. (Fall, Spring) (NS)

This course focuses on introducing calculus with a modeling first approach. The topics include functions as models of data, estimation techniques, vectors, differential calculus of functions of one and several variables, optimization, and integration. Applications are drawn from varied areas, including biology, chemistry, economics, and physics. There is a strong emphasis on developing scientific computing. (Fall, Spring) (NS)

This course investigates a topic in Mathematics that varies according to the interests of professor. This course may be repeated with a change in the topic. (NS)

This course focuses on calculus useful for both theoretical and applied work in the mathematical, natural, and social sciences. Topics include: differential equations, Taylor polynomials, techniques and applications of integration, partial derivatives, gradients, contour plots, constrained and unconstrained optimization of multivariable functions, multiple integration, polar coordinates, and limits. Attention is given to both symbolic and numerical computing. Prerequisite: Mathematics 52-164. (Fall, Spring) (NS)

This course is designed to sharpen problem solving abilities. Students will tackle challenging problems from the William Lowell Putnam Competitions of previous years and study some of the published solutions. Students enrolled in this course will be encouraged to compete in the Putnam Competition in early December. This course may be repeated for credit, but may not be counted toward the major or minor, and must be taken Pass/D/F. Prerequisite: Consent of instructor. (Fall)

May be repeated with change in topic. Prerequisite: Permission of instructor.

This course focuses on calculus useful for the mathematical and physical sciences. Topics include: scalar and vector-valued functions and derivatives; parameterization and integration over regions, curves, and surfaces; divergence; curl; Green's theorem; infinite series; power series; Taylor series; and mathematical definitions of the integral, derivative, and limit. Attention is given to both symbolic and numerical computing. Applications drawn from the natural sciences, probability, and other areas of mathematics. Prerequisite: Mathematics 52-264. (Fall, Spring) (NS)

See Computer Science 54-384. (Fall) (NS)

This course investigates various approaches to geometry. Topics may include synthetic geometry, analytic geometry, projective geometry, differential geometry, Euclidean geometry and non-Euclidean geometry. Prerequisite: Permission of instructor. (Fall, odd years) (NS)

See Computer Science 54-414 and Business 30-414. Contributes to Data Analytics and Data Science.

This course investigates the derivations and applications of numerical techniques. Topics include: interpolation, approximation, numerical differentiation and integration, zeroes of functions and solution of linear systems. Also Computer Science 54-524. Prerequisites: Mathematics 52-264, 52-674, and Computer Science 54-184, or permission of instructor. (NS)

This course is a calculus-based, mathematical introduction to the fundamental principles of probability theory and applications. Topics include combinatorial analysis used in computing probabilities, the axioms and properties of probability, conditional probability, independence of events, discrete and continuous random variables, the standard distributions, expected value and variance, joint distributions, distributions of a function of a random variable, and sampling distributions. Also included are theoretical results such as Bayes' Theorem, Central Limit Theorem, Law of Large Numbers, the Empirical Rule, Hypothesis Testing and Confidence intervals at least for a single mean and a single proportion. Contributes to Data Analytics and Data Science. Prerequisite: Mathematics 52-264. (Spring) (NS)

This course is an introduction to the basic structure of proofs, linear equations and matrices, vector spaces, linear mappings, determinants, quadratic forms, vector products and groups of symmetries. Prerequisite: Mathematics 52-164, and one approved Mathematics or Computer Science course at the 200-level or above, or permission of instructor. (Annually) (NS)

This course investigates the theory of sets, relations, functions, groups and rings. A rigorous approach to learning and writing proofs is emphasized. Prerequisite: Mathematics 52-674 or permission of instructor. (Fall) (NS)

This course investigates the theory and application of differential equations. Topics include both linear and nonlinear first order ordinary differential equations, numerical solutions, and higher order linear ordinary differential equations. Solution techniques may include undetermined coefficients, variation of parameters, power series solutions, and Laplace transforms. Additional topics may be chosen from linear systems, nonlinear systems and Fourier series analysis of partial differential equations with boundary conditions. Prerequisite: Mathematics 52-364, or permission of instructor. (Spring) (NS)

This course investigates functions of a complex variable. Topics include algebra and geometry of complex numbers, analytic and harmonic functions, mappings, Taylor and Laurent series, and contour integration. Prerequisite: Mathematics 52-364, or permission of instructor. (Fall, even years) (NS)

This course is a limited enrollment seminar in a major area of mathematics not generally covered in other courses. Topics may include but are not limited to advanced analysis, combinatorics, logic and history of mathematics. The course may be repeated for credit as topics vary. (NS)

This course investigates the algebra and topology of the real numbers. Topics include completeness, sequences, limits and continuity, differentiation, the Mean-Value Theorem, Taylors Theorem and infinite series. May also include sequences and series of functions. A rigorous approach to learning and writing proofs is emphasized. Prerequisite: Mathematics 52-674, or permission of instructor. (Spring) (NS)

This course is intended to provide additional depth in one of the core subject areas offered in the department. It primarily serves as a second-semester course in algebraic structures, differential equations, or real analysis. The course may be repeated for credit as topics vary. Prerequisite: Permission of instructor. (NS)

This course will fulfill the capstone requirement in Mathematics. Since it serves as a culmination of the student's undergraduate mathematical experience, a balance is sought between application and theory. Topics may vary with the instructor. Applications will be taken from the social and natural sciences. Collaboration and significant class participation are expected. Each student will take the Major Field Test. A major semester project resulting in a written paper and an oral presentation is required; an external presentation may also be required. Prerequisites: Five courses in the major at the 300 level or above, Computer Science 54-184, and permission of instructor. (Fall) (NS) (WA)