# MATH - Mathematics

## MATH-10600 Topics in Mathematics

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

3

## MATH-11000 Introductory Algebra

A study of the essentials of high school algebra, this course prepares students for further study in mathematics.

3

## MATH-11500 College Mathematics

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

3

## MATH-11900 Intermediate Algebra

Terms, expressions, functions, and equations; factoring expressions; solving linear equations; solving quadratic equations; using factoring to solve equations; solving exponential and logarithmic equations, graphing functions, absolute value, and applications.

3

## MATH-12000 Mathematical Analysis

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-12500 Modern Algebra for Elementary School Teachers

This course is designed to meet the needs of teachers in the elementary school. Topics include the algebra of matrices, mathematical systems, modular arithmetic, axiomatic systems, systems of numeration, and the nature of proof.

3

### Prerequisites

MATH 11900 or 3 years of high school Mathematics including Algebra 2

## 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-13500 History of Mathematics for Elementary School Teachers

This course is designed to meet the needs of teachers in the elementary school. The course will explore the historical contributions of many different cultures including Egyptian, Greek, Chinese, Indian and others. The course will focus on the development of the notion of numbers and how they have been denoted as well as well as the progression of the development of geometry and algebra.

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-19000 Workshop in Mathematics

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

1

## MATH-19200 Math Skill Review Workshops for Elementary Education Majors

A set of workshops that review essential mathematics skills from arithmetic, number theory, algebra, and geometry taught in the elementary schools.

1

## MATH-19500 Mathematical Foundations for Secondary School Teachers

This course will give prospective secondary school mathematics teachers increased proficiency in the mathematical skills and concepts they will teach at the secondary level, helping bridge the gap between the mathematics learned in college and the mathematics taught in high school. Prospective Mathematics for Secondary Education majors must earn an A or B in this course or have earned a Math ACT subscore of 25 or higher to apply for undergraduate admission to the College of Education. Required of Secondary Education/Mathematics majors.

3

### Prerequisites

MATH 12000 and 3 years high school Mathematics

## MATH-20000 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.

4

### Prerequisites

Grade of C- or higher in MATH 12000 or three years of high school Mathematics including Trigonometry

## MATH-20100 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 20000, MATH 24000, or MATH 21100

## MATH-21100 Calculus for the Life Sciences

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

4

### Prerequisites

MATH 12000 or 3 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-24000 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 12000 or three years of high school Mathematics including Trigonometry

## 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 20100

## 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 25000

## MATH-30500 Linear Algebra

The study of matrices and matrix algebra, systems of linear equations, matrix inverse and elementary matrices, properties of determinants, vector spaces, especially Rn vectors, linear independence, basis sets, inner products and orthogonality.

3

### Prerequisites

MATH 20100 or MATH 24000

This course begins with the Gram-Schmidt process. Other topics of study are Eigenvalues and Eigenvectors, change of basis, linear transformations, diagonalization, symmetrical and similar matrices. Applications of these concepts include quadratic forms and linear programming.
3

MATH 30500

## MATH-30700 Applied Linear Algebra

The study of matrices and matrix algebra, systems of linear equations, determinants, and vector spaces with a focus on applications. Topics include LU-decomposition, inner products, orthogonality, the Gram-Schmidt process, and eigenvalue problems. Applications include differential equations, Markov processes, and problems from computer science.
3

### Prerequisites

MATH 20100 or MATH 24000

## MATH-31000 Discrete Mathematics

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

4

### Prerequisites

MATH 12000 or successful completion of three years of high school Mathematics including Trigonometry

## MATH-31100 Mathematical Techniques for the Sciences

This course prepares science students to organize, analyze, visualize, and interpret their data using mathematical techniques. Students learn to use a variety of computer applications to model systems and process measurement data specific to their discipline. They also learn the mathematics that powers these applications.

4

### Prerequisites

Senior status and MATH 20100, MATH 21100 or MATH 24000

## MATH-31400 Applied Probability and Statistics

Random variables, conditional probability and independence, mathematical expectation, discrete and continuous distributions, introduction to estimation theory and hypothesis testing. This course is required for the mathematics major. Offered every semester.
3

### Prerequisites

MATH 20100 or MATH 24000

## MATH-31500 Probability and Theory

The course covers the basic principles of probability and statistics, with applications. Topics include descriptive statistics, the axioms of probability, counting techniques, conditional probability, independence, discrete and continuous random variables, expected value, variation, normal, binomial and Poisson distributions, probability density functions, joint distributions, and point estimation. This course is an elective that completes the statistics sequence. Offered every Fall.

3

### Prerequisites

MATH 20100 and MATH 32500

## MATH-31600 Probability and Statistics 2

A continuation of MATH 31500. This course covers confidence intervals for mean, proportion, and standard deviation, hypothesis testing, inferences based on two samples, analysis of paired data, analysis of variance, and linear regression and correlation

3

MATH 31500

## 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 20100

## 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 brief introduction of set theory, symbolic logic, complex numbers, and relations especially as they apply to proof. The course also introduces methods of mathematical proof such as direct proof, indirect proof, proof by contradiction, and proof by induction.
3

MATH 20100

## 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 20000 or MATH 24000

## MATH-33000 History of Mathematics 1

The history of Mathematics from the Babylonian period to the early 17th century. The mathematical emphasis is on famous theorems of each era. Biographical information on mathematicians and historical analysis of each era are included.

3

MATH 20100

## MATH-33100 History of Mathematics 2

The history of mathematics beginning with the 17th century to modern time. The mathematical emphasis is on famous theorems of each era. Biographical information on mathematicians and historical analysis of each era are included.
3

MATH 20100

## 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 20100 or MATH 24000 and CPSC 21000 or CPSC 31500

## MATH-36000 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-36100 Real Analysis 2

A continuation of MATH 36000, 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 36000

## MATH-42000 Sets and Logic

This course studies sets and their properties, set operations, cardinality, ordered sets, well ordering, finite and infinite sets, and the axiom of choice. Also studied are formal deductive systems especially propositional and predicate logic, properties of deductive systems such as consistency and completeness, and Boolean algebra.
3

### Prerequisites

Grade of C- or higher in MATH 32500

## MATH-42500 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 20100 or MATH 24000

## MATH-43000 Complex Analysis

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

3

### Prerequisites

Grade of C- or higher in 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-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-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 36000 or MATH 44000

## 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.