# MATH - Mathematics

## MATH-10200 Aviation Mathematics

This course provides a review of fundamental mathematics required for successful completion of other courses in the aviation curriculum, including algebraic equations, graphs, exponential and elementary trigonometry. 60 contact hours (60 lecture). Meets requirements of 14 CFR 147.

4

## MATH-11500 Introduction to Mathematical Thinking

This study of basic problem solving introduces the following topics: set theory, mathematical logic, basic counting techniques, probability, and descriptive statistics.

3

## MATH-11600 Win Lose or Draw

Why do people play games? Whatever the reason, games are a big piece of life. The world has played games for a long, long time - every time period, every culture. Students in this course will study games and gaming in our culture as well as those in other cultures. To better understand games, the students will study probability theory and its application to gaming. Applications include casino games, lotteries, racing, wagering systems, as well as other games. Some analytical tools that will arise during the course are counting methods, expected values, combinatorics, probability, statistics, tress, gambler's ruin, and distributions.
3

## MATH-11700 Storytelling with Data

This data analytics course is presented in the service of a project which will offer students an intensive hands-on experience in the quantitative research process. Students will develop skills in generating testable hypotheses, understanding large data sets, formatting and managing data, conducting descriptive and inferential statistical analyses, and presenting results for expert and novice audiences. This course is designed for students who are interested in developing skills that are useful for working with data and using statistical tools to analyze them. No prior experience with data or statistics is required.
3

## MATH-11900 College Algebra

This course provides a preparation for further study in mathematics and related fields in which fluent skills in algebra are necessary for successful use of mathematical analysis. Topics include simplifying algebraic, rational, radical, exponential, and logarithmic expressions; solving quadratic, rational, radical, exponential, logarithmic, and absolute value equations; solving compound and absolute value inequalities, and graphing functions.
3

## MATH-12300 Modeling our World with Mathematics

This course will provide students with an overview of how mathematics can be used to model behavior and phenomena in a variety of fields including the natural sciences, social sciences, and business. It introduces students to the basics of mathematical modeling and the importance of how the modeling process can be used to draw conclusions and make predictions about systems. Some examples discussed will include how to model the spread of infectious disease, the dynamics of predators and prey, gerrymandering, and the spread of information on social media. This course will also discuss how to use mathematical modeling and their results to make decisions and advocate change. Additionally, students will learn how to use computer software at an introductory level to develop and simulate models.
3

### Prerequisites

3 years of high school Mathematics

## MATH-13100 Algebra and Number Concepts for Educators

Provides a foundation in algebra and number concepts appropriate for elementary and middle school teachers. Topics include numeration systems, number theory rational numbers, and integers. Emphasis is placed on conceptual understanding, problem solving, mental arithmetic, and computational estimation. A graphing calculator is required; the model is specified by the instructor.
3

## MATH-14100 Geometry and Measurement Concepts for Educators

Provides a foundation in geometry and measurement concepts appropriate for elementary and middle school teachers. This course explores the fundamental ideas of planar and spatial geometry. Content includes the analysis and classification of geometric figures; the study of geometric transformations; the concepts of tessellation, symmetry, congruence, and similarity; and an overview of measurement. The course includes an introduction to the use of Geometer's Sketchpad in the teaching and learning of informal geometry. A graphing calculator is required; the model is specified by the instructor.
3

## MATH-17000 Finite Mathematics

This course covers mathematical procedures for business problems and applications; set theory; functions; graphics of functions; permutations and combinations; probability distributions; linear equations; solutions by matrices; computer and/or simplex solutions to linear programming models; and the mathematics of finance.
3

## MATH-19000 Workshop in Mathematics

A series of workshops intended to enhance the study of Mathematics, Mathematics instruction, or Mathematics history.

1

## MATH-19900 Precalculus

This course provides an analysis of the real number system, functions, graphing, exponential and logarithmic functions, trigonometric functions and topics in analytic geometry.

4

### Prerequisites

MATH 11900 or two years of high school Algebra

## MATH-20200 Business Calculus

This course covers concepts in applied calculus. We will explore functions and linear models, derivatives, techniques of differentiation, logarithm functions, the integral, functions of several variables, and trigonometric models. The main goal of this course is to make calculus relevant and interesting to the business student applying real data/cases with interesting examples and exercises.

3

## MATH-20400 Calculus for the Life Sciences

This course presents the tools of calculus using applications and models germane to the life sciences.

4

### Prerequisites

MATH 19900 recommended, or 3 years of high school Mathematics

## MATH-20600 Applied Calculus

This course provides a study of the concepts in differential and integral calculus, including sequences and series, continuity, limits, differentiation, and integration, with a focus on scientific and engineering applications.  Students use mathematical software packages such as Maple or MATLAB for solving Calculus-based problems.

4

### Prerequisites

MATH 19900 or three years of high school Mathematics including Trigonometry

## MATH-20900 Calculus 1

This course provides a study of the concepts in differential calculus, graphs, continuity, differentiation, and applications for algebraic and trigonometric functions. Antiderivatives and definite integrals are introduced at the end of the course.

IAI: M1 900-1

4

### Prerequisites

Grade of C- or higher in MATH 19900 or three years of high school Mathematics including Trigonometry

## MATH-21000 Discrete Mathematics

An introduction to discrete structures, this course covers such topics as basic logic, sets, basic proof techniques, relations, functions, the basics of counting and probability, graphs and trees.

4

### Prerequisites

MATH 11900 or successful completion of three years of high school Mathematics, including Trigonometry

## MATH-21500 Probability and Statistics Concepts for Educators

This course covers concepts of statistics and probability appropriate for elementary and middle school teachers. This course is an introduction to the fundamental principles and procedures of statistical methods, including a study of frequency distribution, measures of central tendency, probability, statistical decision-making, testing hypotheses, estimating, and predicting. Microsoft Excel is used to reinforce major course concepts.

3

## MATH-22000 Applied Probability and Statistics

This course introduces the concepts of statistics and probability, including measures of center and spread, correlation coefficients, regression, random variables, discrete and continuous distributions, confidence intervals, and hypothesis testing. Students will also learn to use technology to complete statistical analyses.
3

### Prerequisites

MATH 20600 or MATH 20900. MATH 21000 is recommended.

## MATH-23500 Calculus 2

This course provides a study of the concepts of integral calculus. Applications of the definite integral, exponential and logarithmic functions and methods of integration are studied in detail. Sequences, infinite series, and power series are presented at the end of the course.

4

### Prerequisites

Grade of C- or higher in MATH 20400, 20600, or 20900

## MATH-25000 Calculus 3

This course provides a study of Euclidean vector spaces, conic sections, other coordinate systems, parameterized curves and functions of several variables. Differential and integral calculus for functions involving vectors, along with their applications, is presented.

4

### Prerequisites

Grade of C- or higher in MATH 23500

## MATH-27000 History of Mathematics

This course surveys the historical development of mathematics spanning from the pre-Greek period to modern times. Biographical information on mathematicians and historical analysis of each era are included, with an emphasis on famous results and theorems.

3

MATH 21000

## MATH-30000 Differential Equations

This course focuses on ordinary differential equations. It includes variable separable equations, equations with homogeneous coefficients, exact equations, first order linear equations, applications, homogeneous linear equations with constant coefficients, undetermined coefficients, variation of parameters, power series solutions, linear systems of equations and Laplace transforms.

3

MATH 23500

## MATH-30500 Linear Algebra

This course provides a foundation in linear algebra together with applications. Topics include systems of linear equations; linear transformations and their properties; matrices, matrix algebra, and properties of special matrices; vector spaces (with a focus on real-valued vectors) and their properties. Applications may include computer graphics, radiography, ranking algorithms, Markov processes, and other problems from computer science.

3

### Prerequisites

MATH 20600 or MATH 20900 or MATH 21000

## MATH-30600 Advanced Linear Algebra

This course provides a theoretical understanding of the foundations of linear algebra. Topics include vector spaces (including those with complex numbers), linear maps, eigenvalues/vectors/spaces, and inner product spaces.
3

MATH 30500

## MATH-31500 Probability Theory

This course is a continuation of the probability concepts learned in Applied Probability and Statistics. It covers key concepts related to discrete and continuous univariate random variables and multivariate random variables and their applications. Topics include probability density functions, cumulative distribution functions, expectation, variance, covariance, jointly distributed random variables, moment generating functions, and conditional distributions. This course addresses topics found on Exam P for actuarial credentialing.

3

### Prerequisites

MATH 22000 and MATH 25000

## MATH-31600 Advanced Statistics

This course is a continuation of the statistical methods introduced in Applied Probability and Statistics. Students will perform nonparametric hypothesis tests and hypothesis tests on categorical data, compute statistical power and significance, perform multiple regression analysis, complete a one-way analysis of variance, apply percentile matching and maximum likelihood, and perform likelihood ratio tests. Students will also use statistical software to solve complex problems.

3

MATH 22000

## MATH-32000 Theories of Geometry

The study of Euclid’s geometry, its strengths and weaknesses, famous and advanced theorems and its impact on the development of geometry. This latter includes axiomatic systems and proofs, the parallel axiom and the analysis of constructions and transformation geometry.

3

MATH 21000

## MATH-32500 Foundations of Advanced Mathematics

This course provides a gateway into the more abstract and theoretical expectations of upper-level mathematics courses. The course includes a more in-depth study of set theory, propositional logic, predicate logic, and relations especially as they apply to proof. The course also continues the experience of reading, writing, and analyzing mathematical proof. Furthermore, this course introduces technology that is used to solve complex mathematical problems.
3

MATH 21000

## MATH-32700 Introduction to Number Theory

Number theory is the study of the integers. Topics include divisibility, primes, congruences, number theoretic functions, quadratic residues, and primitive roots, with additional topics selected from among Diophantine equations, Pythagorean triples, Fermat's Last Theorem, sums of squares, continued fractions, cryptography, primality testing, and Pell's equation.
3

### Prerequisites

MATH 20600 or MATH 20900

## MATH-33000 History of Mathematics

This course surveys the historical development of mathematics spanning from the pre-Greek period to modern times. Biographical information on mathematicians and historical analysis of each era are included, with an emphasis on famous results and theorems.

3

MATH 23500

## MATH-35000 Numerical Analysis

Students examine floating point arithmetic, polynomial interpolation, numerical methods of integration, numerical solution of non-linear equations and numerical linear algebra.

3

### Prerequisites

MATH 20600 or MATH 20900 and CPSC 20000 or CPSC 21000 or CPSC 31500 or DATA 20000

## MATH-35500 Financial Mathematics

This course will provide students with an understanding of the fundamental concepts of financial mathematics and how those concepts are applied in calculating present and accumulated values for various streams of cash flows as a basis for future use in: reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and valuing contingent cash flows. These are all topics covered on the financial mathematics actuarial exam (Exam FM).

3

### Prerequisites

MATH 23500 and MATH 22000 or MATH 21000

## MATH-36500 Mathematical Modeling

This course studies the process of creating models for real world applications from a wide variety of areas such as physics, chemistry, biology, economics and social sciences. It introduces the students to the basics of mathematical modeling with a focus on model construction, fitting and optimization, analysis, evaluation, and application. This course will make use of computer software in developing models.
3

### Prerequisites

MATH 20600 or MATH 23500

## MATH-37500 Complex Analysis

A study of complex numbers, analytic functions, integration, power series and calculus of residues is presented.

3

### Prerequisites

MATH 30000 or MATH 32500

## MATH-396XX Topics in Mathematics

This course provides students the opportunity to study topics of interest to mathematicians. Subject matter will vary.

1-3

## MATH-43000 Complex Analysis

A study of complex numbers, analytic functions, integration, power series and calculus of residues is presented.

3

### Prerequisites

MATH 30000 or MATH 32500

## MATH-44000 Abstract Algebra 1

This course focuses on binary operations, groups, subgroups, permutations, cyclic groups, cosets, and group homomorphisms.
3

### Prerequisites

Grade of C- or higher in MATH 25000 and MATH 32500

## MATH-44100 Abstract Algebra 2

A continuation of MATH 44000, this course studies rings, fields, Fermat’s Theorem, matrices ideals, ring homomorphisms polynomial rings, vector spaces and linear transformations.

3

MATH 44000

## MATH-45000 Real Analysis 1

This course provides a formal presentation of the real number system and Euclidean vector spaces (inner products, norms and distance functions), compactness and connectedness, continuity, differentiation, and integration.

3

### Prerequisites

Grade of C- or higher in MATH 25000 and MATH 32500

## MATH-45100 Real Analysis 2

A continuation of MATH 45000, this course studies uniform convergence, sequences and series of functions, differential and integral calculus for functions of several variables, the Implicit Function Theorem and the Inverse Function Theorem.

3

MATH 45000

## MATH-47000 Workshop in Mathematics

This course provides opportunities for the presentation and discussion of a variety of concepts, principles, literature, and other topics important to the discipline.

1

### Prerequisites

In some cases, students will be required to obtain the permission of the instructor or chair.

## MATH-47500 Mathematics Research

Students work under faculty supervision on a research project in mathematics, statistics, or a related area chosen in consultation with the faculty member. This course may be repeated multiple times for credit.

1-6

## MATH-48000 Senior Seminar

This course fulfills the advanced writing requirement for the mathematics major. In this course the student will study a topic related to the algebra, analysis, or statistics sequence required by the mathematics major. The student will complete a written report and an oral presentation based on his/her study.
2

### Prerequisites

MATH 31500, MATH 44000, or MATH 45000

## MATH-49800 Mathematics Internship

Students can acquire practical related experience through placement in selected settings. Students submit an internship proposal in advance for approval, maintain a daily task log and submit a five-page written summary report at the conclusion of the internship. A minimum of 210 clock hours and an interview with the on-site supervisor are required.

3

### Prerequisites

Junior or Senior status, Mathematics major, GPA of 3.00 or above and consent of the department chairperson

## MATH-49900 Independent Study in Mathematics

This course is designed to meet the needs of mathematics majors wishing to study an advanced topic not found in the curriculum.

1-4

### Prerequisites

Consent of department chairperson. To qualify for an Independent Study, a student must have successfully completed 60 credit hours, at least 12 of which were earned at Lewis, and have earned at Lewis University a minimum 3.0 cumulative GPA.