Mathematics (MTH)

This course is a seven week course designed to prepare the student needing additional background before taking MTH 108. Topics will include: order of operations, basic algebraic rearrangement of equations, and graphing linear equations.

This course is a seven week course designed to prepare the student needing additional background before taking MTH 110. Topics will include: exponent rules, factoring, and solving the quadratic equation.

The course emphasizes basic strategies of thought and analysis by introducing the student to some of the most commonly encountered mathematical ideas. Topics include but are not limited to, problem solving, linear models, mathematics of finance, probability and statistics, as well as practical applications of these topics to situations the student may encounter outside the classroom.

Introduction to statistical reasoning as required by an informed citizen. Emphasis on concepts rather than in-depth coverage of traditional statistical methods. Topics include sampling and experimentation, descriptive statistics, concepts of basic probability, the normal distribution, estimation of a population mean and proportion, single sample and two sample hypothesis tests, regression and correlation, and ethical considerations.

Designed to prepare students in mathematics or science for entry into the calculus sequence. An analytical approach to algebraic and trigonometric functions as models of real world phenomena. Real and complex numbers, theory of polynomial and rational equations and inequalities, exponential, logarithmic, and trigonometric functions.

A continuation of Math 110. Analytic trigonometry, laws of sines and cosines, systems of equations and inequalities, matrices and determinants, sequences, series, conics, polar coordinates, and parametric equations.

A collection of topics essential to further study of mathematics, or computer science. Topics include the Boolean algebra in the form of propositional logic and elementary set theory, partitions, foundations of number theory and modular arithmetic with applications to cryptography, relations and functions on discrete sets, permutations, algorithms and recursive sequences, and combinatorics.

Fundamental concepts of function, limit of a function, continuity, derivatives, applications of derivatives, antiderivatives, and the definite integral. Emphasis on analytical, numerical, and graphical approaches.

A continuation of MTH 241. Transcendental functions, applications of integration, integration techniques, and infinite series.

A continuation of Math 242. Vectors and vector-valued functions, functions of several variables, multiple integration, and vector analysis.

Intensive survey course with applications for the sciences. Topics include descriptive statistics, probability theory, random variables, binomial, Poisson, normal, t, F, and Chi-Square distributions, estimation and hypothesis testing of common parameters, analysis of variance, correlation, linear regression, and ethical considerations. Familiarity with a Windows based computer environment is strongly suggested.

Linear systems of equations, row-reduction, vector algebra, linear transformations, matrix algebra, concrete and abstract vector spaces and subspaces, structure theorems, determinants, change of basis theory, real eigenvalues and eigenvectors, diagonalization, with applications to nutrition, engineering, chemistry, computer graphics, business, economics, discrete time population models, and more.

Events and sets, the algebra of probability, Bayes' theorem, single and multivariate discrete and continuous random variables, expectation, transformation of random variables, moments and moment generating functions, sums of random variables and introductory concepts in estimation. This course includes some preparation for Society of Actuaries Exam P.

A rigorous treatment of the most common estimators and hypothesis testing procedures at the undergraduate level. Including modes of convergence and limit theorems, theory and implementation for unbiased, consistent, and maximum likelihood estimators, as well as introductions to Fisher information and efficiency, Shannon entropy and sufficiency, and Bayesian estimation.

Ordinary differential equations of first and second order, linear differential equations, Laplace transform approach to initial value problems, exact and approximate power series solutions, and linear systems of differential equations, with applications including population growth models, accumulation of interest in annuities and loans, economic models, epidemiology, chemical kinetics, projectile motion with air resistance, spring-mass and (RLC) electrical oscillators, pendulums, buoyancy, and more. Introduction to separation of variables and Fourier series solutions to the heat and wave PDEs as time permits.

A thorough treatment of interest theory with introduction to derivatives markets as time permits. Topics will include present, current, and accumulated value of money, annuity and loan payments, bonds, yield curves and analysis of portfolios, immunization, and determinants of interest rates. Additional topics may include forward contracts, insurance, hedging, call and put options. This course includes some preparation for Society of Actuaries Exam FM.

Expected to be offered: Sufficient demand

Theory of complex eigenvalues with application to discrete and continuous linear dynamical systems; theory of inner products and orthonormal bases with application to the general least squares regression problem, polynomial trend analysis, and Fourier series; spectral theory of symmetric matrices and singular value decomposition with applications to principal component analysis for data dimension reduction and the use of a covariance matrix in multivariate Gaussian data modeling.

Properties of the real numbers, convergence of sequences, functions, continuity, differentiability and integration.

Analysis in Rn and introduction to abstract metric spaces. Implicit and inverse function theorems. Sequences and series of functions, modes of convergence.

Topics and techniques of abstract algebra. Prepares students for graduate work in mathematics or applications in cryptography while furnishing the theoretical foundations of the familiar: groups, rings, fields, vector spaces.

After the groundbreaking work of Morgenstern and vonNeumann in 1944, game theory quickly progressed to reshape and dominate modern economics, business analytics, and even military strategy. This course for mathematically and economically prepared undergraduates lays a rigorous foundation for further study, while also providing abundant examples for the terminal student of how game-theoretic setups and analyses are applied in concrete situations arising in business, economics, finance, sports, and everyday life.

Numerical approaches to single-variable equations, polynomial approximation, integration and differentiation, initial value problems, and selected topics in numerical linear algebra. Emphasis on supporting topics from real analysis and practical software implementations. Software usage will include Geogebra and Octave/Matlab.

Credit for research, workshops, special problems, and independent study.

Expected to be offered: Sufficient demand

This upper division course for mathematics majors requires submission of a written report (thesis) and oral seminar presentation based on critical evaluation of scientific literature and/or an independent research project.