Mathematics

This course emphasizes reasoning and communicating to clarify and refine thinking in practical areas of life. Students will gain confidence in their ability to apply their mathematical skills to applied problems and decision making. Topics will be chosen from: set theory, probability, financial mathematics, visual representation of information, geometry, and graph theory.

For prospective elementary teachers. Introduction to mathematics concepts, their understanding and communication. Topics include an introduction to problem solving, set operations and their application to arithmetic, numeration systems, arithmetic, and measurement. Emphasis is on developing a deep understanding of the fundamental ideas of elementary school mathematics.

This class is intended for students who are preparing to take calculus. Trigonometry will be defined using the unit circle approach, with emphasis on the geometry of the circle. Classical right triangle trigonometry will be studied, along with trigonometric identities and equations, the laws of sines and cosines, and graphs and properties of the trigonometric functions and their inverses. Additional topics from algebra will include logarithmic and exponential functions. A graphical approach will be utilized throughout, with an emphasis on solving application problems. Students will develop skills in basic trigonometry and its applications, with an emphasis on modeling with functions and other algebraic skills necessary for the study of calculus.

A general introduction to descriptive and inferential statistics, designed for non-mathematics majors. Topics include elementary probability, distributions, estimation of population parameters, confidence intervals, hypothesis testing, correlation, and regression. Students will use statistical analysis technology.

This course is the first of a two-semester sequence that integrates Precalculus and Calculus I topics. The course includes the study of the geometric and analytic properties of algebraic and transcendental functions. The course will examine limits, continuity, and derivatives of algebraic and transcendental functions. Applications of differentiation include motion and related rates.

This course is the second of a two-semester sequence that integrates Precalculus and Calculus I topics. The course continues the study of the geometric and analytic properties of algebraic and transcendental functions. The course will explore applications for differentiation including optimization and graphical analysis of functions, as well as the theory of integration and basic integration techniques. Applications of integration include area.

Special topics course offered in response to student and faculty interest.

A study of functions, limits, continuity, the derivative, and the integral. Applications of differentiation and integration include maxima, minima, marginal cost and revenue, rectilinear motion, and areas. Students will use technology for exploration and problem solving.

A continuation of the calculus of functions of one variable. Topics include volumes of rotation, transcendental functions, integration techniques, polar coordinates, parametric equations, and infinite series. Students will use technology for exploration and problem solving.

A study of vectors in two and three dimensions, vector algebra, vector functions, vector calculus and multivariable calculus. This includes three-dimensional analytic geometry, partial differentiation and multiple integrals, line and surface integrals, Green's Theorem, Divergence Theorem, Stokes' Theorem and applications. Students will use technology for exploration and problem solving.

A study of vector spaces, linear transformations, matrices, determinants, and their applications. Students will use technology for exploration and problem solving.

An introduction to statistics for mathematically inclined students, focusing on the process of statistical investigations. Observational studies, controlled experiments, sampling, randomization, descriptive statistics, probability distributions, significance tests, confidence intervals, one-and two sample inference procedures, linear regression. Statistical software will be used throughout the course.

This course is a study of logic and an introduction to various techniques of mathematical proof, including direct proof, indirect proof, and proof by induction. Students will be involved actively in the construction and exposition of proofs from multiple representations - visually, numerically, symbolically - and will present their reasoning in both oral and written form. Topics covered include sets and basic properties of the integers, rational numbers, and real numbers. Throughout the course, students will explore strategies of problem-solving and active mathematical investigation. After completing this course, a student would have an appropriate background for upper-level theoretical mathematics courses.

The second course intended for prospective elementary teachers continues an in-depth introduction to mathematical concepts focusing on student understanding and communication. Topics include geometric concepts (shape and space, area and volume, transformations and symmetry), algebraic concepts (patterns, equations, and functions), and statistical concepts (designing investigations, gathering & analyzing data, and basic probability). The course will utilize investigative activities and instructional technology. Emphasis is on developing a deep understanding of the fundamental ideas of elementary school mathematics and transitioning from inductive to deductive reasoning.

An introduction to various topics chosen from combinatorics, propositional logic and graph theory. Topics include counting techniques, permutations and combinations, induction and recursion, Boolean algebra, planarity, minimal paths and minimum spanning trees.

Special topics course offered in response to student and faculty interest.

This course is a seminar intended for students interested in a major in mathematics. Students will be exposed to various areas of mathematics as well as a brief history of mathematics; students will give short presentations about these topics. Co-curricular opportunities as well as career and graduate school opportunities will be discussed. Students will create materials such as cover letters and resumes.

This course will provide opportunities for freshmen and sophomores to participate in original research in mathematics. Students will submit findings in a formal written report and will give an oral presentation. Students will be expected to work approximately three hours per week on the research project for each semester hour of credit.

A course emphasizing Euclidean geometry and introducing hyperbolic, elliptic, and transformational geometries. Students will use methods of discovery, construction, and proof to study geometric systems. 

The study of probability and statistical inference. Emphasis is placed on the theoretical development of probability distributions, discrete, continuous, and multivariate, and the sampling distributions used in statistical inference. 

A continuation of MAT-245 which includes one- and two-sample inference, two-way tables, simple and multiple regression, and analysis of variance. Application of these topics will be drawn from business, the social and natural sciences, and other areas. Students will use statistical analysis technology.

A study of distribution-free statistical methods. Estimation and hypothesis testing that make relatively mild assumptions about the form of population distribution. Analysis of qualitative (nominal level) and rank (ordinal level) data. Inference for proportions, one- and two-sample location, dispersion, trend, one- and two-way layouts, rank correlation, and regression. Students will use statistical analysis technology. 

A study of first order differential equations, linear differential equations of higher order, Laplace transforms, series solutions, and applications. Students will use a computer package.

A computer-oriented study of analytical methods in mathematics. Topics include solving non-linear equations, least squares approximation, interpolating polynomials, numerical differentiation, and numerical quadrature.

A study of mathematical models used in the social and natural sciences and their role in explaining and predicting real world phenomena. The course will emphasize the development of the skills of model building and will address the use of various types of models, such as continuous, discrete, deterministic and statistical models.

Special topics course offered in response to student and faculty interest.

A rigorous treatment of the foundations of calculus. A study of the algebraic and topological properties of the real numbers; one-variable calculus, including limits, continuity, differentiation, Riemann integration, and series of functions. 

A study of general algebraic systems. Topics covered will include relations, mappings, groups, rings, and fields. Group theory is emphasized. 

Topics chosen from mathematics, applied mathematics, and statistics. Prerequisites vary with the topics studied. May be repeated for credit.

Special topics course offered in response to student and faculty interest.

In conjunction with a faculty mentor, the student will formulate and execute an original research project that will culminate in a paper and a presentation. The research project must meet Honors Program thesis requirements as well as the expectations of the mathematics faculty.

In conjunction with a faculty mentor, the student will formulate and execute an original research project that will culminate in a paper and/or a presentation.

Introduces licensure students to the philosophy and objectives of mathematics education. The course will focus on the content of school mathematics and examine closely both state and national recommended standards of school mathematics curricula. The emphasis of the course will be on developing a deep understanding of school mathematics and pedagogical content knowledge- the mathematical knowledge for teaching. Technologies appropriate for conceptual understanding of mathematics will be introduced. A related field component will be required at a local school site.

A continuation of the study of the philosophy and objectives of mathematics education, emphasizing the methods and materials needed for teaching mathematics in the middle and secondary schools. The course will focus on the selection of worthwhile mathematical tasks, planning for instruction, and assessment of student learning. An emphasis will be placed on technology. Students must demonstrate their skills in planning, teaching, assessing, and making instructional decisions based on formative evidence. Field component will be required at the internship site.