Mathematics at Aquinas College

Mathematics Courses

MS107 Elementary Algebra (3)

Real numbers, algebraic expressions, linear, rational and quadratic equations, graphing, factoring. Prerequisite: Designed for students having no more than two years of college-preparatory mathematics. This course is not accepted for the General Education Mathematics requirement.

MS110 Mathematics for Liberal Arts (3) MS

Mathematical ideas for understanding life in our culture; topics include probability, logical thinking, and problem solving with minimal use of algebra. Prerequisite: Two years of college-preparatory mathematics or MS107.

MS111 Intermediate Algebra and Trigonometry (4) MS

Linear and quadratic equations, inequalities and functions; exponential and logarithmic functions; exponents, radicals; polynomial and rational functions. Introduction to trigonometric functions and relationships. Prerequisite: Two years of college-preparatory mathematics or MS107.

MS114 Precalculus (4) MS

Linear and quadratic functions; equations and inequalities; transformations; systems of linear equations and inequalities; polynomial, rational, exponential, logarithmic and trigonometric functions, and graphing; conic sections. Prerequisite: Three (3) years of college-preparatory math or MS111.

MS118 Business Analysis (3) MS

Short course of differential and integral calculus for applications in business, sustainable business and economics and an emphasis on optimization. Prerequisite: Three and one-half (3 1/2) years of college- preparatory math or MS114.

MS121 Calculus I (4) MS

Functions, limits, continuity, derivatives, antiderivatives, Fundamental Theorem of Calculus, solids of revolution. This course has five contact hours per week. Prerequisites: Three and one-half years of college-preparatory math, including trigonometry or MS114.

MS122 Calculus II (4) MS

Inverse functions, integration techniques, integrals with applications, conic sections, polar coordinates, parametric equations, sequences and series. This course has five contact hours per week. Prerequisites: MS121

MS151 Elementary Statistics (3) QR

Designed primarily for students who have had no more than two years of high-school mathematics or its equivalent. Includes the fundamental concepts of descriptive and inferential statistics. Prerequisite: MS107. This course is not accepted for the General Education Mathematics requirement.

MS170 Technology and Mathematics Seminar (1) MS

Introduces programming and applications of computer algebra systems, modeling programs, calculators, and other mathematical software and hardware. This course prepares prospective teachers, minors and majors for higher courses and their own work as educators. Prerequisite: MS121, can be taken concurrently.

MS231 Multivariate Calculus (4) MS

Vector and solid geometry, vector-valued functions, calculus of curves in space, functions of several variables, partial differentiation, multiple integration, and vector analysis. Prerequisite: MS122.

MS232 Linear Algebra (3) MS

Systems of equations, matrices, determinants, vector spaces, linear transformation, eigenvalues, eigenvectors, and canonical forms. Prerequisite: MS122.

MS240 Discrete Mathematics (3) MS

Develop basic techniques and modes of reasoning of combinatorial problem solving; describe and analyze the algebraic structures of certain set-relation systems; illustrate and analyze the wide variety of applications of discrete mathematics. The topics to be covered include mathematical induction, set theory, relations and functions, combinatorics, probability, graph theory, and mathematical logic. Prerequisite: MS121 or department approval.

MS241 Differential Equations (3) MS

Study of the classification and solutions of ordinary differential equations with applications. Prerequisite: MS231.

MS252 Statistics (3)

Designed for students who have had at least three (3) years of high-school mathematics or its equivalent. Topics to be covered include frequency distributions, variability, probability, sampling, estimation, testing, hypotheses, analysis of variance, regression and correlation analysis, and nonparametric tests. (Course counts as three (3) semester hours toward a minor, but only one (1) semester hour toward a major.) Prerequisite: MS114.This course is not accepted for the General Education Mathematics requirement.

MS261 Mathematics for Elementary and Middle School Teachers II (3) MS

Required for elementary certification. Topics appropriate for grades K-8 include: elementary algebraic preparation including linear, quadratic and exponential, probability and statistics. Emphasis is on constructing understanding through experience: exploring, extrapolating, and explaining concepts and relationships. Problem solving, both in groups and individually, is a major theme. Tutoring and field experiences required. Prerequisites: EN201; cumulative grade point average of 2.5 and a minimum grade of C in MS260.

MS271 Mathematics Methods for Elementary and Middle School Teachers (3)

Required for elementary certification. Course expands on the content from MS260, 261, examines ways children learn and fail to learn mathematics, and emphasizes strategies for teaching and designing lessons. New content focuses on concepts and operations of whole numbers, number theory, number patterns, and measurement. Tutoring and field experiences required. Prerequisite: EN201, MS260 , MS261; cumulative grade point average of 2.5 and a grade of C MS111 or equivalent. This course is not accepted for the General Education Mathematics requirement.

MS282 Applied Statistics with R (3) MS

The course is designed to provide participants with a basic understanding of common statistical computing approaches and how to apply those approaches to common industry and research scenarios. Following completion of the course, students will possess the requisite programming skills to function as a programmer analyst in an analytical work environment. Topics include: importing/exporting data in various formats; character and numeric manipulation; merging; subsetting, and combining data sets; effective programing with common data structures; and producing high quality graphics and reports for end users. The free and open source R programming language will be used extensively throughout the course to teach fundamental programming concepts and applied statistical approaches. Introductory Statistics with R {Daalgard 2008} will serve as a supplemental text to aid in retention and understanding of the topics covered.

MS309 Theory of Numbers (3) MS

Divisibility, congruences, quadratic reciprocity, arithmetic functions, multiplicative number theory, Riemann’s zeta function. Prerequisite: MS122

MS310 Modern Cryptography (3) MS

Encoding (RSA, ElGamal and elliptic curves) and decoding methods (Miller- Rabin, Dixon and Pollard) from 1974 to the present. Electronic signatures and hash functions. We will study the math behind these ideas and write programs which perform the encoding and decoding. Prerequisite: MS309.

MS260 Mathematics for Elementary and Middle School Teachers I (3) MS

Required for elementary certification. Topics appropriate for grades K-8 include: rational numbers, patterns and variables, measurement, geometry, logic, and graphing. Emphasis is on constructing understanding through experience: exploring, extrapolating, and explaining concepts and relationships. Problem solving, both in groups and individually, is a major theme. Tutoring and field experiences required. Prerequisites: EN201; cumulative grade point average of 2.5 and a grade of C in MS111 or equivalent.

MS316/PC316 Applied Mathematics for the Physical Sciences (4) MS

An introduction to topics in applied mathematics not covered in a traditional mathematics curriculum. Topics include Complex Numbers, Fourier Series, Fourier Analysis, Partial Differentiation, and Laplace Transforms. Prerequisite: MS122.

MS321 Abstract Algebra (4) MS, WI

Sets, functions, equivalence relations, integers, mathematical induction, modular systems, permutations, groups, rings, fields, isomorphisms,and homomorphisms. Prerequisite: MS122, MS232 (MS240 recommended)

MS332 Introduction to Numerical Analysis (3) MS

Numerical methods involving polynomial evaluation, series approximations, numerical integration, interpolation of linear and differential equations, least squares, and minimax approximations. Prerequisite: MS231, MS232 and CS180 or department approval.

MS340 Linear Regression (3)

The study of regression techniques and applications in statistics. Topics include linear regression, analysis of variance (ANOVA), multiple regression, analysis of covariance (ANCOVA), and linear hypotheses. Prerequisites: MS232 and at least one of MS252 and MS494. MS282 is recommended.

MS351 History of Mathematics (3) MS

Survey of the development of mathematics from ancient to modern times. Prerequisite: MS122.

MS375 Methods of Teaching Secondary Mathematics (3)

Provides a detailed examination of the pedagogy for teaching the mathematical content and process strands of secondary mathematics curricula and of appropriate instructional and assessment strategies. Tutoring component required. Prerequisite: EN201 (can be taken concurrently with MS375); MS122; cumulative grade point average of 2.5.This course is not accepted for the General Education Mathematics requirement.

MS397 Field Experience in Mathematics (Variable)

One or two semester hours of internship or experience in a field directly related to mathematics, negotiated between Mathematics Department and student. Prerequisite: approval of the department chairperson.

MS398 Readings in Mathematics (Variable)

Individually-negotiated program of readings on selected topic established by contract between instructor and student. Contracts filed with Registrar. Prerequisite: Department approval.

MS399 Independent Project (Variable)

Individually-negotiated project of defined nature established by contract between instructor and student. Contracts filed with Registrar. Prerequisite: Department approval.

MS401 Introductory Real Analysis (3) MS

Properties of real numbers, Cauchy sequences, series, limits, continuity, differentiation, Riemann integral, sequences, and series of functions. Prerequisite: MS231.

MS433 Topics in Geometry (3) MS

Topics selected from affine, Euclidean, non-Euclidean, and projective geometry. Prerequisite: MS122.

MS440 Data Analytics Project (3) MS

An application of foundational data analytics skills to a real-life project. The course will include explorations of specific examples of data analysis problems that will serve to exercise and integrate students’ backgrounds in linear algebra, applied statistics, probability, and programming. Additionally, students will become familiar with good data visualization practices using appropriate software as well as other software tools for managing data. The course will culminate with an analytics project and presentation using real-world data. Prerequisites: CS180, MS232, MS252, and junior or senior standing.

MS491, 492 Advanced Topics in Mathematics (Variable)

Prerequisite: MS231 or instructor approval.

MS493 Probability (3) MS

Probability theory and distributions, large and small sample theory. Prerequisite: MS231 or department approval.

MS494 Mathematical Statistics (3) MS

Tests of hypotheses, point and interval estimation, non-parametric statistics, regression and correlation, analysis of variance. Prerequisite: MS493

MS495 Mathematics Capstone SC

An in-depth exploration of career options for mathematics majors. Each student, with the instructor’s assistance, will formulate and carry out a plan to gain first-hand knowledge of the kinds of work mathematics majors do after college. The knowledge will come by the way of job shadowing, classroom observations, attendance at career fairs, graduate school visits, conference participation, or other opportunities that will give students the opportunity to see how a degree in mathematics might be used in the world.

MS499A, B, C, D Mathematics Seminar (1 each)

Topics selected to broaden the students’ mathematical background. Prerequisites: MS122 and junior status. Not more than two semester hours may be applied to the major.