Mathematics (MATH)

This course will introduce some key concepts of mathematics: sets, logic, and numbers. We will use these to understand the Hindu-Arabic numeration system, arithmetic, and measurement. We look at how numbers and operations correspond to reality and why our computational algorithms work. This course is designed to cover ideas of interest to the elementary education major. Elementary Education majors are given preference in enrolling in this course. Prerequisite: Two years of high school algebra.

Survey topics in applied mathematics stressing the connections between contemporary mathematics and modern society, and deductive versus inductive reasoning in mathematics. Topics include a review of basic algebra, linear functions, exponential/logarithmic functions, financial mathematics, probability, and statistical reasoning.

Study of algebraic, exponential, logarithmic and trigonometric functions; their graphs, properties and applications.

Introduction to single-variable calculus. Topics include limits and L'Hospital's rule, continuity, differentiability, and integrability. The Fundamental Theorem of Calculus, integration with substitution, and the applications of derivatives and integrals to physical and social problems are explored. Prerequisite: MATH-171 with a grade of C or higher, or ACT Math score of at least 28. *An additional course fee will be charged.

A continuation of single-variable calculus that explores advanced techniques of integration including integration by parts, partial fractions, trig substitution, and improper integrals. Applications of the definite integral such as the volume of a solid of revolution, work, and center of mass will be explored. Includes differential equations, infinite sequences and series, polar coordinates, and parametric equations. Prerequisites: MATH-191 with a grade of C or higher, or score of 3 or higher on the AP Calculus AB Exam. *An additional course fee will be charged.

Designed to help students develop skills in reading and understanding elementary mathematical proofs, and in expressing their own mathematical ideas through formal writing. Emphasis will be on precision and style. Math topics include: Logical connectives and quantifiers; types of proof; elementary set theory; functions; integers and induction; equivalence relations; modular arithmetic; matrices.

Introduction to discrete mathematics as used in computer science. Topics include propositional and the predicate logic, simple circuit logic, elementary number theory, sequences and summations, methods of proof (direct, by contradiction, by contraposition, by induction), set theory, graph theory, combinatorics, and discrete probability.

Matrices and systems of linear equations. Determinants. Lines and planes in three-space. Vector spaces and linear transformations. Characteristic equations, eigenvalues, eigenvectors, and diagonalization of matrices.

Limits and continuity of functions of several variables, partial derivatives, directional derivatives, multiple integration, vector fields, and Green's / Stokes' Theorem.

A Calculus-based introduction to probability and the application of mathematical principles to the collection, analysis, and presentation of data. Modern probability concepts, discrete/continuous models, and applications; estimation and statistical inference through modern parametric, and simulation/randomization methods; maximum likelihood; Bayesian methods. This course prepares students for the preliminary P/1 exam of the Society of Actuaries and Casualty Actuarial Society. Pre-/Co-requisites: MATH-192 or equivalent math placement.

Chi-square and F-distributions; analysis of variance; factorial, blocked, and Latin-square experimental design; correlation; linear, nonlinear, robust, and multiple regression; logistic regression and the general linear model; tests for goodness-of-fit and independence; randomization-based methods; multivariate techniques, including multidimensional scaling, cluster analysis, MANOVA.

Case study approach to topics in data science: importing, wrangling, visualizing, modeling, and communicating data, with an emphasis on big data. Statistical learning techniques for classification, tree-based methods, regression, and unsupervised learning

Examine the ethical issues related to method validity and reproducibility, and social impact and responsibility. Topics include privacy and anonymity, data accuracy and validity, transparency, model misuse and misinterpretation, and social responsibility and harm. Topics also include survival analysis, experimental design, and time series.

This course is an introduction to financial mathematics. Topics will include the measurement of interest, annuities using sequences and series, amortization schedules and other relevant topics. An applied math course, this course will prepare students to study for the Society of Actuaries' exam (FM).

First-order ordinary differential equations, linear second order and higher differential equations, series solutions, systems of differential equations and their applications, matrix methods for linear systems, existence and uniqueness theorems.

This course aims to show the student the need for a rigorous, abstract, deductive treatment of geometrics. It includes a study of geometry developed without using a parallel postulate and goes on to show how separate geometrics evolve when different parallel postulates are added, in turn, to common body definitions, axioms, and theorems.

Basic elements of real analysis for students of mathematics. Topics include limits of functions, continuity, and metric spaces including differentiation.

Definitions and basic properties of groups. Homomorphisms, normal subgroups, quotient groups and direct products. Rings, integral domains and fields. Ideals, quotient rings and polynomials.

Use of mathematical applications and markup languages with an emphasis on R, R-studio, and LaTeX. Topics include Poisson processes, properties of discrete Markov chains, introduction to continuous-time Markov chains, functional programming with data analysis, simulation techniques, sampling techniques such as bootstrapping, and Markov chain Monte Carlo methods.

Project based application of previous mathematical statistics and computer science courses related to the Data Science and Analytics program. Use of statistical software and programming languages to complete a report, or project relating to data analytics or data science.

Topics in mathematics chosen by the instructor depending on their area of expertise.