MTH - Mathematics

Rational numbers and subsystems. Probability and statistics. Real numbers and geometry. Algebraic structures. Emphasis on problem solving. (Does not fulfill the core requirement.)

Rational numbers and subsystems. Probability and statistics. Real numbers and geometry. Algebraic structures. Emphasis on problem solving. (Does not fulfill the core requirement.)

Review of basic algebra, functions, graphing, logarithm, and exponential functions, systems of linear equations. (Does not fulfill the core requirement.)

Review of exponential and logarithmic functions, their graphs, trigonometric and inverse trigonometric functions. Analytic geometry, sequences, and series.(Does not fulfill the core requirement.)

Two mathematical areas provide the content of the course: (1) Geometry and (2) Algebra and Modeling. Mathematical content and pedagogy are fully integrated using contemporary classroom technologies. (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 study of the differential and integral calculus with emphasis on applications in the natural and physical sciences.

Techniques of integration, numerical integration, applications of integration, sequences and series, including Taylor series.

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.

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 - emphasis of first and second order equations, systems of linear differential 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.

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.

Numerical techniques for computer-aided solution of non-linear equations, systems of equations, interpolation, numerical integration and differentiation, and solution of ordinary differential equations. Fee: $25.

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.

This seminar supports students working in local schools as part of the Outreach Excel Program. Students discuss questioning and group work strategies, classroom management, current school mathematics curriculum, and interaction techniques with middle and high school students. This is a Pass/No Pass course and may be repeated for credit. Does not count towards math major.

Credit arranged.

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.

Topics may include sequences and series of functions, uniform convergence, Fourier series, the Riemann-Stieltjes integral, and functions in several variables.

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.

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.

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

Topics from simple linear and multiple regression, analysis of variance and design of experiments, methods for categorical data, distribution-free methods.

Credit arranged.

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

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.

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.

Topics may include sequences and series of functions, uniform convergence, Fourier series, the Riemann-Stieltjes integral, and functions in several variables.

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.

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.

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

Topics from simple linear and multiple regression, analysis of variance and design of experiments, methods for categorical data, distribution-free methods.