MTH - Mathematics

This course is intended for future elementary teachers and explores mathematical knowledge, communication, and student thinking. Content includes number theory, number systems, operations with numbers, integers, and algebra. There will be an underlying theme of mathematical communication, problem solving, and justification.  (Does not fulfill the core requirement.)

The second half of the sequence of mathematics courses for future elementary teachers includes data analysis and visualization, statistics, measures of center, fraction representations, fraction operations and geometry, with underlying themes of problem solving, math modeling, justification, and mathematics as a representational tool for social justice.  (Does not fulfill the core requirement.)

The ideas necessary for the study of calculus, including modeling and representing exponential, logarithmic, rational, and trigonometric functional relationships.  Precalculus seeks develop a productive mathematical disposition, including persistence in problem-solving, evaluating the reasoning of others, and formulating mathematical justifications. Targeted toward students continuing to MTH 201. (Does not fulfill the core requirement.)

Introduction to differential and integral calculus with emphasis on applications to business and economics.

Matrices, systems of linear equations, linear programming. Sets and counting, probability.

Students will be able to understand, process, and interpret statistical information arising in everyday life using real world examples and case studies from a variety of disciplines. Critical thinking and quantitative decision-making skills will be taught. This course focuses on being a consumer of statistics, interpreting research studies, and learning how statistics are used in the real world.

Elementary statistical calculations and statistical thinking. Examples will be chosen from various disciplines. Topics include sampling, normal distribution, central limit theorem, hypothesis testing, and simple regressions.

The ideas of continuity, limits, differentiation, and integration are explored at both a theoretical level and in applied contexts by studying the relationships between changing quantities. Students will further develop problem-solving skills and improve mathematical communication. Sections labelled BI are designated for Biology majors and focus on applications in the life sciences.

This course deepens the understanding of the foundational topics in calculus, including techniques of integration, applications of integration, and infinite sequences and series, including Taylor series with an emphasis on problem-solving strategies and the development of mathematical communication.

Credit arranged.

The study of functions in several variables: vectors, matrices, partial derivatives, gradients, optimization, and integration. Differentiation and integration of vector-valued functions, line integrals, surface integrals, curl, divergence, Green's Theorem, and Stokes' Theorem.

Computational techniques for solving physics and chemistry problems as well as for simulating, analyzing, and graphically visualizing physical systems and processes. Offered fall of odd years.

Complex numbers and functions of a complex variable; limits, differentiability; Cauchy's theorem; power series, Laurent series, residue theorem with applications, maximum modulus theorem, Liouville's theorem; conformal mapping and applications.

Topics may include: set theory, logic, methods of proof, combinatorics, recurrence relations, graphs, and Boolean algebra.

Introduction to elementary ordinary differential equations with applications to physical processes with emphasis on first and second order equations, systems of linear equations, and Laplace transforms.

Fourier series. Inner product spaces. Solutions to heat, wave, and Laplace's equations. Green's functions.

This course introduces the basic concepts and techniques in the study of dynamical systems, including nonlinear ordinary differential equations, difference equations, and systems of equations. Using a wide variety of applications from the physical sciences, we will cover analytical methods such as linear stability, bifurcations, phase plane analysis, limit cycles, Lorenz equations, chaos, iterated maps, period doubling, and fractals.

This course surveys many of the ideas, methods and applications of graph theory. Topics may include: connectivity, matchings, graph algorithms, network flows, graph colorings, planarity, circuits, cycles, and tournaments.

Systems of linear equations and matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors.

This course covers systems of linear equations and matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors.

An introduction to the study of the integers and related objects. Topics are taken from among the following: divisibility, primes and the Euclidean algorithm, the Euler phi function, special primes and perfect numbers, congruences mod n, quadratic residues, continued fractions, quadratic forms, Diophantine equations.

Ordinary differential equations, complex variables and matrices are developed and illustrated through applications in physics with emphasis on examples from the fields of vibrations and waves.

An introduction to statistical methods utilized across disciplines. Topics include experimental design, randomization and sampling distributions, tests of statistical significance, normal model, confidence intervals, t-procedures, two-sample comparisons, one-way analysis of variance, simple linear regression, and bootstrapping. The course makes substantial use of programming in a statistical software package.

Survey of applied mathematics with an emphasis on modeling problems from science and engineering. Process of formulating the model, solving/simulating, and analyzing/interpreting results. Applications may include: continuous- and discrete-time population models, models of physical and biological phenomena, and statistical models.

Credit arranged.

Credit arranged.

Faculty-directed student research. Before enrolling, a student must consult with a faculty member to define project. May be repeated for credit. Credit arranged.

Practical field experience in selected industries or agencies. Department permission and supervision is required. Students may receive an IP (In Progress) grade until the completion of their internship. 

Credit arranged.

A rigorous treatment of properties of the real numbers and functions of a single real variable. Topics include completeness, limits, continuity, differentiation, integration, and sequences. Additional topics may include series, an introduction to Euclidean or metric spaces.

A rigorous treatment of properties of the real numbers and functions of a single real variable. Topics include completeness, limits, continuity, differentiation, integration, and sequences. Additional topics may include series, an introduction to Euclidean or metric spaces.

A foundations course in elementary geometry discussing the following: incidence geometries; finite, metric, and synthetic geometries; Euclidean, hyperbolic, and elliptical geometries; and some axiomatic theory.

An introduction to fundamental concepts in point-set topology. Topics are taken from the following: open and closed sets, continuity, connectedness, compactness, separability, metric spaces.

The study of algebraic structures that are like the integers, polynomials, and the rational numbers. The integers and their properties. Groups: examples, properties, and counting theorems. Rings: examples and properties. Fields: roots of polynomials and field extensions.

Unique factorization in special rings. Field theory and the use of groups to understand field extensions: finite fields, Galois theory. Classical construction problems, solution of n-th degree polynomials.

Cryptography is the science of encoding and decoding information for the purpose of secure communication. With an emphasis on utilization of both modern and classical cryptosystems, this course introduces students to the mathematical underpinnings of cryptography.

Numerical techniques for computer-aided solution and analysis of systems using MATLAB. Emphasis on applications from engineering and the physical sciences. Topics covered may include non-linear equations, systems of equations, interpolation, integration and differentiation, and ordinary and partial differential equations.

Probability, discrete and continuous random variables, expectation, important probability distributions, introduction to sampling, estimation, and hypothesis testing.

Credit arranged.

Carries a title reflecting the subject or subjects studied and/or the nature of the class structure. May be repeated for credit.

Faculty-directed student research. Before enrolling, a student must consult with a faculty member to define project. May be repeated for credit. Credit arranged.

Practical field experience in selected industries or agencies. Department permission and supervision is required. Students may receive an IP (In Progress) grade until the completion of their internship. 

Credit arranged.

Math 497 is a course for students with strong mathematical preparation.  Students will work in teams on a project from an industrial or governmental firm.  Student success will depend on realistic industry evaluations such as teamwork, communication, individual initiative, and final products.

Research, study, or original work under the direction of a faculty mentor, leading to a scholarly thesis document with a public presentation of results. Requires approval of thesis director, department chair, dean, and the director of the honors program, when appropriate.