Math

Courses

The Mathematics curriculum is traditional, although many of the best practices for mathematics classrooms (technology, group projects, inquiry-based learning, writing mathematics, etc.) are being incorporated where appropriate to enhance the traditional topics.

The following list of courses represents current or recent course offerings. See the course catalog for updated information.

  • 52-104 Explorations in Mathematics
    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)
  • 52-114 Introduction to Statistics
    This course provides students in the social and biological sciences with the skills necessary to perform elementary statistical analysis. Topics include descriptive measures, probability, sampling theory, random variables, binomial and normal distributions, estimation and hypothesis testing, analysis of variance, regression and correlation. This course may not be used for the Mathematics major or minor. Contributes to Data Science and Health Studies (Fall, Spring) (NS)
  • 52-164 Modern Calculus I
    This course focuses on introducing calculus with a modeling first approach. The topics include functions as models of data, dimensional analysis, estimation techniques, differential calculus of functions of one and several variables, optimization, integration, and Taylor polynomials. Applications are drawn from varied areas, including biology, chemistry, economics, and physics. There is a strong emphasis on developing scientific computing. (Fall, Spring) (NS)
  • 52-204 Topics in Mathematics
    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)
  • 52-264 Modern Calculus II
    This course focuses on calculus useful for both theoretical and applied work in the mathematical, natural, and social sciences. Topics include: differential equations, integration techniques, partial derivatives, gradients, contour plots, constrained and unconstrained optimization, 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)
  • 52-291 Putnam Power Hour
    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 P/D/F. Prerequisite: Consent of instructor. (Fall)
  • 52-364 Modern Calculus III
    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; the divergence 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)
  • 52-384 Discrete Mathematics
    See Computer Science 54-384. (Fall) (NS)
  • 52-404 Geometry
    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)
  • 52-414 Operations Research
    See Computer Science 54-414 and Business 30-414. Contributes to Data Science.
  • 52-524 Introduction to Numerical Analysis
    This course investigates the derivations and applications of numerical techniques most frequently used by scientists: 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)
  • 52-574 Probability and Mathematical Statistics
    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. Prerequisite: Mathematics 52-264. Contributes to Data Science. (Spring) (NS)
  • 52-674 Linear Algebra
    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. (Fall, Spring) (NS)
  • 52-684 Algebraic Structures
    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)
  • 52-754 Differential Equations
    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)
  • 52-834 Complex Analysis
    This course investigates the algebra and geometry of complex numbers. Topics include analytic and harmonic functions, series, contour integration, conformal maps and transformations. Prerequisite: Mathematics 52-364, or permission of instructor. (Fall, even years) (NS)
  • 52-844 Seminar in Special Topics
    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)
  • 52-854 Real Analysis
    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)
  • 52-874 Seminar in Advanced Topics
    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)
  • 52-894 Senior Seminar in Mathematical Modeling
    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 include optimization methods with sensitivity analysis, numerical and analytic methods, linear and non-linear differential and difference equations, curve and surface fitting, statistics, and stochastic methods. 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 from each student; an external presentation may also be required. Prerequisites: Six courses in the major at the 300 level or above, Computer Science 54-184, and permission of instructor. Must have completed one of MAT52-574, MAT52-674, or MAT52-754. (Fall) (NS) (WA)