# Mathematics

## Professors

Christina C. Carroll, Chair

Crystal Hall

John Iskra

Xiaoxue Li

## Classes

### MATH 100 : Fundamental Algebra

Introduction to variable expressions and equations, simplifying expressions, solving linear equations and inequalities, graphing linear equations and inequalities, solving systems of equations graphically and by substitution, exponents, operations on polynomials, factoring polynomial equations, solving quadratic equations, and quadratic functions. In addition, students will learn to address math anxiety, math study skills, and how studying mathematics will benefit future career and academic opportunities. Placement into 100 is determined by an algorithm based on SAT (or equivalent ACT) math scores and high school GPA. This course does not fulfill the mathematics requirement for any major. A student in Mathematics 100 must earn a grade of at least C- in order to take Mathematics 121.

3

### MATH 120 : Math for an Informed Citizenry

Introduction to the nature of mathematical thought. Fundamental structure of mathematical systems and basic quantitative skills required for functioning in modern society. Intended as a terminal course for non-majors.

3

### MATH 121 : College Algebra

Introduction to factoring and polynomial equations; working with equations and functions of the following types: linear, quadratic, polynomial, rational, radical, exponential, and logarithmic; functions and their inverses; properties of radicals and logarithms, and inequalities. Prerequisite for students as indicated by an algorithm based on SAT (or equivalent ACT) math scores and high school GPA, C- or better in Mathematics 099, or results of a placement exam.

3

.

### MATH 123 : Pre-Calculus

Precalculus is designed to help students develop the computational and problem solving skills needed to succeed in calculus. Topics covered will include: Solving and graphing equations of exponential, logarithmic, and trigonometric functions, trigonometry including analytical trigonometry, and an introduction to limits. This class is not intended as a terminal mathematics course. Prerequisites can be satisfied by a C or better in 121 or placement as determined by a departmental placement exam. This course is taught in Fall and Spring semesters.

3

.

### MATH 151 : Calculus I

Graphical, numerical, and symbolic study of functions and limits; fundamental concepts of differentiation and integration. Differentiation formulas. Applications to exponential growth and decay, velocity and acceleration. Use of a CAS.

4

#### Prerequisites

C or higher in 123 or permission of instructor.

### MATH 152 : Calculus II

A continuation of Mathematics 151. Applications of integration to physics, statistics and engineering including finding volumes, arc lengths, surface area. Sequences and series, parametrically defined functions including those defined in the polar plane. Introduction to vectors, vector spaces and operations on vectors, including the cross and dot products, norms and linear transformations.

4

#### Prerequisites

C or higher in 151 or permission of instructor.

### MATH 161X : Introduction to Statistics

Descriptive and inferential statistics, probability, and research design with a broad range of applications to various disciplines; statistical software.

4

### MATH 201 : Intro to Mathematical Reasoning

Topics in discrete mathematics; mathematics topics and processes essential to proper understanding of material to be covered in advanced courses; emphasis on techniques of mathematical reasoning. This course satisfies the proficiency requirement for Critical Thinking in the disciplines.

3

#### Prerequisites

151 and sophomore status or departmental permission.

### MATH 253 : Calculus III

Infinite series; two- and three-dimensional vectors, vector calculus; partial derivatives; multiple integrals. Use of a CAS.

4

#### Prerequisites

C or higher in 152 or permission of instructor.

### MATH 311 : Fundamentals of Mathematics I

Content and pedagogy of elementary and middle school mathematics. Problem solving, logic, sets, number theory, and structure, algorithms of rational numbers, geometry, probability, and statistics. Not applicable toward mathematics major.

3

#### Prerequisites

one college level mathematics course and junior status.

### MATH 312 : Fundamentals of Mathematics II

Content and pedagogy of secondary school mathematics. Problem solving, logic, sets, number theory, and structure, algorithms of rational numbers, geometry, probability, and statistics. Not applicable toward mathematics major.

3

#### Prerequisites

one college level mathematics course and junior status.

### MATH 321 : Linear Algebra

Vector spaces, linear dependence, linear mappings, the algebra of matrices over a field, characteristic equations, characteristic roots.

3

201.

### MATH 340 : Geometry

Topics from Euclidean geometry, using transformational approach; general axiomatic systems leading to finite and non-Euclidean geometries.

3

#### Prerequisites

201 or departmental permission.

### MATH 350 : Special Topics

Topics selected by the instructor for one semester of study based on needs and interests of students, including (but not limited to) number theory, cryptology, real analysis, graph theory, or coding theory.

4

#### Prerequisites

junior or senior status and permission of instructor.

### MATH 353 : Differential Equations

Some first-order methods; second-order constant coefficient equations; series solutions; first-order linear and nonlinear systems and phase-plane analysis. Applications including population growth models, simple and forced harmonic motion, the pendulum, and chaotic behavior. Use of a CAS.

3

201 and 253.

### MATH 360 : Probability & Statistics

An introduction to the mathematical theories of probability and statistics, including some topics such as combinatorial methods, conditional probability and independence, discrete and continuous random variables, expectation, simple and multiple regression, analysis of variance, contingency tables, time series, logistic regression, and experimental design. This course satisfies the proficiency requirements for Ethical Reasoning and Quantitative Literacy in the disciplines.

3

#### Prerequisites

Mathematics 152 and Statistics 161, or permission of instructor.

### MATH 370 : Discrete Structures

Theoretical foundations of computer science, including sets, functions, Boolean algebra, first order predicate calculus, trees, graphs, discrete probability. This course satisfies the proficiency requirement for Oral Communication in the disciplines.

3

#### Prerequisites

201 and knowledge of a high-level programming language or departmental permission.

### MATH 420 : History of Math

The historical development of mathematics over the past 5,000 years, including typical mathematical problems from various historical periods and biographical and philosophical aspects of mathematics. This course satisfies the proficiency requirements for Oral Communication and Written Communication is the disciplines.

3

#### Prerequisites

mathematics major with senior status or departmental permission.

### MATH 421 : Modern Algebra

Binary systems, groups, rings, and fields. Normal subgroups, quotient groups, permutation groups, homomorphisms,isomorphisms, and Lagrange's theorem.

3

201.

### MATH 440 : Mathematical Modeling

Applications of mathematics to a wide variety of problems inherent in a technological society. Emphasis may vary among applications to physical, biological, and environmental systems or linear programming, queueing theory, Markov processes, and other problems of systems engineering. Emphasis on constructing mathematical interpretations of such problems.

3

321 and 360.

### MATH 451 : Real Variable Theory

Introduction to mathematical analysis. Axiomatic development of the real number system. Examination of foundations of the theory of functions of real variable; limits, continuity, differentiation, and integration of functions of a single real variable, an infinite series.

3

201 and 253.

### MATH 455 : Math of the Physical Sciences

Series solutions of differential equations, Fourier analysis, partial differential equations, and functions of a complex variable with emphasis on application to physical systems.

3

#### Prerequisites

353 and Physics 202, or departmental permission.

### MATH 460 : Independent Study

Individual study and research in mathematics, under the supervision of a faculty member.

4

#### Prerequisites

junior or senior status, GPA of 3.

### MATH 470 : Internship I

Work experience related to the student's major, jointly supervised by the department and a professional in the field. Although the usual internship will carry either three or six hours credit, a student may elect to arrange an internship carrying between two and six hours credit with the permission of the department. Each hour of credit will require forty hours at the internship site.

6

2.

### MATH 471 : Internship II

Work experience related to the student's major, jointly supervised by the department and a professional in the field. Although the usual internship will carry either three or six hours credit, a student may elect to arrange an internship carrying between two and six hours credit with the permission of the department. Each hour of credit will require forty hours at the internship site.

6

2.

### MATH 473 : Numerical Analysis

Mathematical theory underlying selected numerical methods and the application of those methods to solving problems of practical importance. Computer programs used to facilitate calculations. Roots of equations, systems of linear equations, interpolation, approximation, and numerical integration.

3

#### Prerequisites

353 and knowledge of a high-level programming language.

### MATH 480 : Senior Seminar

Selected topics in mathematics; presentations by students, faculty, or visiting speakers.

3

#### Prerequisites

mathematics major with senior status or departmental permission.

### MATH 490 : Honors Thesis I

Independent research in a special topic for honors.

3

#### Prerequisites

senior status, GPA of 3.

### MATH 491 : Honors Thesis I

Independent research in a special topic for honors.

3

#### Prerequisites

senior status, GPA of 3.