# 13 - Mathematics

## 13-106 Topics in Mathematics

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

3

## 13-110 Introductory Algebra

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

3

## 13-115 College Mathematics

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

3

## 13-119 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

## 13-120 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

13-119 or two years of high school Algebra.

## 13-125 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

13-119 or 3 years of high school Mathematics including Algebra II.

## 13-130 Mathematics for Elementary School Teachers

This course is designed to meet the needs of teachers in the elementary school. Topics include the real number system (whole numbers, integers, rational numbers, real numbers, decimals) and operations with real numbers, number theory (divisibility, prime numbers, composite numbers, perfect numbers, factors), proportional reasoning (ratio, percent), and patterns.

3

## 13-135 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

## 13-140 Geometry for Elementary School Teachers

This course is designed to meet the needs of teachers in the elementary school. Topics include properties of angles, congruence, similarity, transformations, circles, spheres, triangles, quadrilaterals, constructions, measurement, length, area, and volume.

3

## 13-190 Workshop in Mathematics

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

1

## 13-192 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

## 13-195 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.
3

### Prerequisites

13-120; 3 years high school Mathematics. Required of Secondary Education/Mathematics majors.

## 13-200 Calculus I

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

13-120 or three years of high school Mathematics including Trigonometry.

## 13-201 Calculus II

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

13-200.

## 13-210 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

13-120 or successful completion of three years of high school mathematics including trigonometry.

## 13-211 Calculus for the Life Sciences

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

4

### Prerequisites

13-120 or 3 years of high school Mathematics including Trigonometry.

## 13-240 Applied Calculus

This course teaches the basics of calculus. It is cross-listed as 24-240 Business Calculus and fulfills the calculus requirement for the BA program in Computer Science.

3

### Prerequisites

13-120 or three years of high school Mathematics, including Trigonometry.

## 13-250 Calculus III

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

13-201.

## 13-300 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

13-250.

## 13-305 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

13-201.

## 13-306 Advanced Linear Algebra

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

13-305.

## 13-310 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

13-120 or successful completion of three years of high school Mathematics including Trigonometry.

## 13-311 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

13-200 and 13-201, or 13-211; Senior standing in Biology, Chemistry, Mathematics, Computer Science, or Physics.

## 13-315 Probability and Statistics I

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.

3

13-201.

### Corequisites

Pre or co-requisite 13-325

## 13-316 Probability and Statistics II

A continuation of 13-315. 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

13-315.

## 13-320 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

13-201.

## 13-325 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.
2

### Prerequisites

Prior or concurrent enrollment in 13-201.

## 13-327 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

13-200.

## 13-330 History of Mathematics I

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

13-201.

## 13-331 History of Mathematics II

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

13-201.

## 13-350 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

13-325 and 70-200.

## 13-360 Real Analysis I

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

13-250 and 13-325.

## 13-361 Real Analysis II

A continuation of 13-360, 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

13-360.

## 13-420 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

13-325.

## 13-425 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.
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13-201.

## 13-430 Complex Analysis

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

3

13-325.

## 13-440 Abstract Algebra I

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

3

### Prerequisites

13-250 and 13-325.

## 13-441 Abstract Algebra II

A continuation of 13-440, this course studies rings, fields, Fermat’s Theorem, matrices ideals, ring homomorphisms polynomial rings, vector spaces and linear transformations.

3

13-440.

## 13-470 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.

## 13-480 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.
1

### Prerequisites

13-315 or 13-360 or 13-440.

## 13-498 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 in Mathematics major, GPA of 3.00 or above, and approval of the department chairperson.

## 13-499 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.