MATHEMATICS (MAT)

An introductory course in basic algebra which covers the following topics: properties of real numbers, linear equations and inequalities, functions and graphs, polynomials, fractional algebra, radicals, and rational exponents. Not open to those who have completed any other mathematics course.

A survey of those topics in algebra, trigonometry, and analytic geometry which provide the background for the study of calculus. Topics to be covered include exponential and logarithmic functions, complex numbers and polynomial functions, trigonometry, plane analytic geometry, and systems of linear equations and inequalities. Not open to those who have completed MAT 117 or 131.

An introductory course in differential calculus. Topics to be covered include limits and continuity, the derivative and applications, and an introduction to integration. Not open to those who complete MAT 131.

The continuation of MAT 117. Topics to be covered include the definite integral and applications, elementary techniques of integration. Not open to those who complete MAT 131 or MAT 132.

A more rigorous introduction to calculus for entering students with good backgrounds in mathematics. Recommended for students considering a major in mathematics. Topics include the real numbers, functions, limits, the derivative and applications. Not open to those who complete MAT 117 or MAT 118.

A more rigorous introduction to calculus for entering students with good backgrounds in mathematics. Recommended for students considering a major in mathematics. Topics include the integral and applications, and techniques of integration. Not open to those who complete MAT 117 or MAT 118.

In this course, students will investigate fundamental mathematics concepts associated with numbers, operations, and patterns. One of the major goals of the course is for students to develop deeper conceptual understandings of the mathematics concepts they will teach in the elementary and middle grades. Not only will students gain computational proficiency but also the ability to explain to students, in multiple ways, why mathematics concepts make sense. The course heavily emphasizes the use of open-ended problem-solving methods of teaching and learning to help students develop their own functional understanding of the major concepts. A significant focus of this course will be on problem solving, reasoning and proof, multiple representations, recognizing connections (across mathematics and other disciplines), and mathematical communication. The course is intended for students planning on pursuing a career in elementary or middle school education. As such, particular attention is given to understanding common misconceptions that children have when learning about specific mathematics concepts and considering the ramifications of these misconceptions for the development of effective classroom instruction. This course is a prerequisite for EDU 324: Mathematics Teaching in the Elementary Classroom.

In this course, students will investigate fundamental mathematics concepts associated with algebra, geometry, and data analysis. One of the major goals of the course is for students to develop deeper conceptual understandings of the mathematics concepts they will teach in the elementary and middle grades. Not only will students gain computational proficiency but also the ability to explain to students, in multiple ways, why mathematics concepts make sense. The course heavily emphasizes the use of open-ended problem-solving methods of teaching and learning to help students develop their own functional understanding of the major concepts. A significant focus of this course will be on problem solving, reasoning and proof, multiple representations, recognizing connections (across content areas and disciplines), and mathematical communication. The course is intended for students planning on pursuing a career in elementary or middle school education. As such, particular attention is given to understanding common misconceptions that children have when learning about specific mathematics concepts and considering the ramifications of these misconceptions for the development of effective classroom instruction. Recommended for elementary education majors and middle/secondary mathematics education majors.

This course is part of a 2-course sequence intended to prepare students to be facilitators/leaders of the Assumption Institute of Mathematics (Camp AIM) in Summer 2025. Students will learn about basic teaching best practices to engage and motivate high school students, receive an introduction to examples of mathematics activities that could be used with high school students during Camp AIM, and develop ideas about the content of the Camp AIM program. This course will meet for one hour per week. The companion spring course is EDU 190 Facilitating a Math Academy II.

This course is an introduction to mathematical logic and discrete systems. Topics include Boolean algebra, mathematical proof, sets, relations, functions, induction, combinatorics, graph theory, and applications.

Linear systems of equations, matrix algebra, determinants, vector spaces, linear transformations, matrix representations of linear transformations, and applications.

Divisibility theory, prime factorization, congruences, Fermat’s theorems, the phi-function, Euler’s Theorem, and applications.

Mathematical theory and practical application of compound interest, including the measurement of interest, annuity calculations, loan repayment, and security valuation. Stress laid on theoretical foundations, derivations, and proofs. Introduction to financial simulation.

Combinatorial problems, conditional probability, dependence and independence, probability measures, distributions, and stochastic processes.

A second-year course in calculus, designed to follow either MAT 118 or MAT 132. Topics to be covered include improper integrals, sequences and series, parametric curves, polar coordinates, and vector geometry.

A course in the calculus of functions of several variables. Topics to be covered include multivariable functions, partial derivatives, multiple integrals and the theorems of Green, Gauss, and Stokes.

This course will explore a mathematics topic based on the interest of the professor and needs of the students. It will use literature, and a cross-disciplinary approach, as appropriate, that is consistent with all other mathematics courses. The course will avail students and faculty an opportunity to investigate mathematical topics that are not part of the regular mathematics curriculum. It fulfills an elective requirement for the Mathematics Major and Minor.

A course in classical real analysis. Topics to be covered include the real number system; convergence of sequences; limits and continuity of functions; differentiation; and integration.

An introductory course in abstract algebra. This course will cover the theory of groups and the definitions of rings and fields.

The continuation of MAT 351. Topics include advanced group theory, and the theory of rings and fields.

An axiomatic approach to geometry built on Euclid’s work with an emphasis on theorems and proofs. Topics include congruence, constructions, area, angle measure, similar figures, circle measure, and perspective geometry.

First and second order differential equations. Linear differential equations and linear systems. Existence and uniqueness theorems. Applications.

Roots of equations. Analysis of errors. Convergence. Interpolation and polynomial approximation. Numerical differentiation and integration. Solving linear systems, unstable matrices. The computer is used throughout the course.

An introductory treatment of both point-set and combinatorial topology. Topics to be covered include topological spaces and metric spaces, classification of surfaces, homology (mod 2), and map-coloring theorems.

The topic is determined by the instructor. Emphasis is placed on student oral presentations. Required course for senior mathematics majors.

Available only to highly qualified students. Under the direction of an individual instructor, each student will complete a thesis (either expository or research) on some advanced topic in mathematics.