# Courses

### Courses in Mathematics

**MA 032**Mathematical Foundations

This course provides a survey of topics necessary for success in collegiate mathematics courses. Students will examine manipulations of real numbers, algebraic expressions, solving linear equations and inequalities, operation with polynomials, factoring polynomials, graphs of equations and inequalities, solving systems of two linear equations, and some basic statistical concepts. This course is offered for nondegree credit.

Students must complete MA 032 with a C- or higher grade to place into core curriculum mathematics courses.

Prerequisite: Placement

**MA 111**Analyzing Arithmetic for Educators

In this course, students will develop concepts and topics in elementary and middle school math. Students will study numeration systems, working with whole numbers, fractions, decimals, integers, percents, and proportions. Students will also explore number theory, estimation and beginning algebra concepts. Effective mathematical pedagogy for children will be modeled, emphasizing the development of patterns and relationships, various instructional techniques, and the view of mathematics as problem solving, communicating, reasoning, and making connections.

Prerequisites: Elementary, middle grades or mathematics education major and MA 032 or placement

**MA 112**Analyzing Geometry and Statistics for Educators

In this course, students will develop concepts and topics in elementary and middle school math. Students will study characteristics of two and three-dimensional shapes, the development of spatial sense, geometry, standard and metric measurement, transformational and coordinate approaches to geometry, data analysis, and probability. Effective mathematical pedagogy for children will be modeled, emphasizing the development of patterns and relationships, the use of various instructional techniques, and the view of mathematics as problem solving, communicating, reasoning, and making connections.

Prerequisites: Elementary, middle grades or mathematics education major and MA 032 or placement

**MA 115**Mathematics for Society and the Liberal Arts

This course is a survey of mathematics and its applications in contemporary society. Topics will vary and are selected from among the following or from other subjects chosen by the instructor: graph theory, descriptive statistics, voting theory and social choice, information coding, symmetry and patterns, game theory, and financial mathematics.

Prerequisite: MA 032 or placement

**MA 141**College Algebra and Trigonometry

This course is designed to equip students with the algebra and trigonometry skills necessary for success in physics and calculus courses. Students will study topics such as polynomials, rational functions, exponents, equations, inequalities, graphs, and trigonometric functions of real numbers.

Prerequisite: MA 032 or placement

**MA 151**Introduction to Probability and Statistics

This course provides an introduction to elementary probability and statistics. Students will study descriptive statistics, including measures of central tendency and variability, and use graphs to represent data. Students will explore normal distributions and their applications; probability, including laws of probability and an intuitive introduction to random variables; and inferential statistics, including correlation and regression, sampling distributions, confidence intervals, and hypothesis testing (z-tests for means and proportions, t-tests, and the chi-square test). Students will also examine experiment and study design, including sources of bias and techniques for minimizing them. Students will learn to recognize the use and misuse of statistics in society and will investigate ways to guard against common statistical mistakes.

Prerequisite: MA 032 or placement

**MA 161**Mathematics for Managerial and Social Sciences

This course is a survey of mathematical concepts and techniques useful in business and the social sciences. Students will review important concepts from algebra, including functions and linear and quadratic polynomials. Students will explore elementary linear algebra and applications, including systems of linear equations, matrix operations, and linear programming. An intuitive introduction to differential calculus and its applications will also be covered.

Prerequisite: MA 032 or placement

**MA 165**Introduction to Discrete Mathematics

This course is a survey of elementary discrete mathematics and its applications. Students will study topics in the following areas: sets, logic, combinatorics, graph theory, elementary number theory, and recursion. Applications of these topics, especially to computer science, will also be included.

Prerequisite: MA 032 or placement

**MA 171**Calculus I

This course is the first course of a three-semester calculus sequence. The core of the course is an introduction to differential calculus, including limits, continuity, the derivative, and applications of differentiation. Students will also be introduced to antiderivatives and essential concepts integration, including the fundamental theorem of calculus.

Prerequisite: MA 141 or placement

**MA 172**Calculus II

This course is the second course of a three-semester calculus sequence. Students will study applications of integration; techniques of integration, including integration by parts and trigonometric substitution; and improper integrals. Students will examine infinite sequences and series, including Taylor series of common functions. Additional topics include further applications of integration, an introduction to differential equations, parametric equations and polar coordinates, and vectors and vector operations.

Prerequisite: MA 171

**MA 205**Introduction to Mathematical Proofs

This course is an introduction to mathematical proofs and foundational concepts of mathematics. Students will study first-order predicate logic; elementary set theory; types of proofs and proof strategies; methods of formulating and writing proofs; mathematical induction; and applications of proof techniques to problems involving numbers, sets, functions, and relations.

Prerequisite: MA 165 or 171

**MA 210**History of Mathematics

This course is a survey of the history of mathematics around the world from ancient times up to the present. Students will focus on the development of important mathematical ideas and the key figures in that development. Willingness to engage with mathematics will be needed, but no particular mathematical knowledge is required.

**MA 273**Calculus III

This course is the third course of a three-semester calculus sequence. Students will begin the course by reviewing vectors and vector operations. Students will study plane and space curves and the calculus of vector-valued functions as well as differential calculus of functions of several variables, including limits, continuity, partial derivatives, applications of partial derivatives, and techniques such as Lagrange multipliers. Students will study multiple integration, including integration in rectangular, polar, cylindrical, and spherical coordinates and applications of multiple integrals. Students will also be introduced to vector calculus, including line integrals and Green's theorem. If time permits, students will investigate surface integrals and Gauss's divergence theorem.

Prerequisite: MA 172

**MA 295**Practicum in Mathematics

Students will complete a practicum in some aspect of mathematics designed to give practical, directed experience.

Prerequisite: Consent

**MA 311**Linear Algebra

This course is an introduction to linear algebra. Students will examine linear transformations, matrix algebra, systems of linear equations, eigenvalues and eigenvectors, abstract vector spaces and applications of linear algebra.

Prerequisite: MA 172 or 205

**MA 321**Number Theory

This course is a survey of elementary number theory and its applications. Students will study primality and divisors, modular arithmetic and the Chinese remainder theorem, continued fractions and Diophantine equations, Fermat's Little Theorem, Euler's phi function, Hensel's lemma, quadratic reciprocity and other essential concepts of number theory. Students will also discuss applications to computer science, including primality testing algorithms and encryption.

Prerequisite: MA 205

**MA 351**Geometry

This course is a survey of important concepts and topics in geometry. Students will examine geometry as an axiomatic system, advanced theorems in Euclidean geometry, and the essentials of non-Euclidean geometry and other geometries such as projective geometry. Emphasis is placed on proofs and careful reasoning from axioms.

Prerequisite: MA 165 or 171

**MA 371**Differential Equations

This course is an introduction to ordinary differential equations, their solution methods, and their applications. Students will learn solution methods for first-order differential equations, second order linear differential equations, and systems of first-order differential equations. In addition, students will study numerical and power-series solutions as well as continuous models and applications.

Prerequisite: MA 172

**MA 411**Abstract Algebra

This course is an introduction to the theory of groups, rings, and fields. Students will study group theory, including permutations, subgroups and Lagrange's theorem, and group homomorphisms and the isomorphism theorems. Students will continue by studying ring theory, including ideals and the ring isomorphism theorems, integral domains, and fields. Students will also explore polynomial rings and the factorization of polynomials as well as applications of abstract algebra to number theory. Time permitting, more advanced topics such as the Sylow theorems or unique factorizations may also be covered.

Prerequisite: MA 205

**MA 431**Real Analysis

This course is an introduction to real analysis. Students will learn about real topology, including completeness, compactness, and connectedness. Students will also study convergence of sequences and series, limits of functions, continuity, derivatives and differentiability of functions, and sequences and series of functions.

Prerequisites: MA 172 and 205 (MA 273 recommended)

**MA 450**Topics in Mathematics

Students will examine a selected topic in the area of mathematics. Potential topics include topology, graph theory, combinatorics, partial differential equations, theory of computation, mathematical logic, and others.

Prerequisite: MA 205

**MA 461**Mathematical Modeling

This course provides an introduction to the modeling of real-world phenomena using mathematics. Students will explore both discrete and continuous models, with subject matter drawn from the natural sciences, social sciences, and finance, depending on the interest of the instructor and students. Some experience with computer programming is recommended.

Prerequisites: MA 371; MA 311 or concurrent

**MA 471**Probability and Mathematical Statistics

This course is an introduction to probability theory and mathematical statistics. Students will study the following topics in probability: basic concepts, including counting arguments, conditional probability, and Bayes' theorem; random variables; distributions of discrete and continuous random variables, including density functions, probability generating functions, and moment generating functions; joint, marginal, and conditional distributions and densities; expected value, variance, and covariance; various important distributions (such as binomial, geometric, negative binomial, uniform, exponential, Poisson, Gaussian, and gamma and beta distributions). Students will study topics in mathematical statistics, including descriptive statistics, distributions of sample statistics, hypothesis testing and parameter estimation, and correlation and regression.

Prerequisites: MA 165 and 273

**MA 481**Seminar in Mathematics

This course is a capstone seminar course for mathematics and mathematics education majors. Students will discuss various aspects of mathematics and its place in the world, including mathematical history, philosophy of mathematics, the teaching of mathematics, and the intersection of mathematics and the Christian faith. Additionally, students will do independent reading on a mathematical topic of their choice. They will write an expository paper and give a presentation on their chosen topic.

Prerequisite: MA 411 or 431

**MA 490**Independent Study

This course is a supervised study of selected topics in the mathematical sciences at an advanced level.

Prerequisite: Consent

**MA 495**Internship in Mathematics

A field experience in mathematics which provides an opportunity for the student to apply theoretical knowledge in a practical setting. Student maintains close cooperation with the supervisory personnel in the field.

Prerequisite: Consent