# Mathematics (MTH) Courses

Descriptions of courses offered in the Mathematics Department

#### MTH 0153 Intermediate Algebra

#### Three hours

A course designed for students who need to improve their mathematical understanding and skills prior to taking Core Curriculum or major field math courses. This course covers the fundamentals of algebra, including simplification of algebraic expressions, solving and graphing equations and inequalities, solving linear systems, and exponential operations. Intermediate Algebra does not satisfy any college math requirements; credit does not apply toward minimum hours required for graduation.

Offered fall semester

#### MTH 1113 College Algebra

#### Three hours

Topics include solving equations and systems of equations, functions and graphing, inequalities, logarithms, exponentials, sequences, and series. An emphasis is placed on applied problems in physical, life, and social sciences. Meets the Mathematics requirement of the Core Curriculum. Prerequisite: minimum ACT math score of 19, or SAT math score of at least 480, or MTH 0153.

Offered each semester

#### MTH 1122 Trigonometry

#### Two hours

Foundations and applications, including the trigonometric functions and their graphs, proving identities, analytic trigonometry, solution of triangles, two-dimensional vectors, and dot products. Prerequisite: minimum ACT math score of 19, or SAT math score of at least 480, or MTH 0153.

Offered fall semester

#### MTH 1123 Survey of Calculus

#### Three hours

An introduction to the concepts of differentiation and integration. An emphasis is placed on applied problems in physical, life, and social sciences. A student may not earn credit in both MTH 1123 and 1134. Meets the Mathematics requirement of the Core Curriculum. Prerequisite: minimum ACT math score of 24, or SAT math score of at least 580, or MTH 1113.

Offered spring semester

#### MTH 1134 Calculus I

#### Four hours

A study of the foundational principles of calculus with an emphasis on derivatives of functions of one variable and an introduction to integrals. A strong emphasis is placed on application to problems in science and engineering. Meets the Mathematics requirement of the Core Curriculum. Prerequisites: four years of high school mathematics, and a minimum ACT math score of 24, or SAT math score of at least 580, or MTH 1113 and MTH 1122.

Offered fall semester

#### MTH 1144 Calculus II

#### Four hours

A continuation of the study of fundamental calculus concepts, with special emphasis on integration and the use of infinite series. Applications to problems in physics, probability theory, and engineering are emphasized. Prerequisite: MTH 1134.

Offered spring semester

#### MTH 2003 Introduction to Statistics

#### Three hours

A course to give students an understanding of the concepts of statistics and tools to become critical readers of current issues involving quantitative data. Applications of the use of data from a wide variety of professions, public policy, and everyday life are made. The course focuses on methods of producing data, organizing data, and drawing conclusions from data. Topics include descriptive statistics, frequency distributions, correlation, regression, inference, and significance. Selected topics in research design and the consumer price index are also taught. Meets the Mathematics requirement of the Core Curriculum. Prerequisite: minimum ACT math score of 19, or SAT math score of at least 480, or MTH 0153.

Offered each semester

#### MTH 2103 Applied Statistics for Scientists

#### Three hours

A study of the essential statistical techniques needed to analyze your own experiments and understand the work of others with applications in medicine, biology, chemistry, and other scientific fields. Topics include descriptive statistics, probability distributions, sampling techniques, hypothesis testing (t-tests, z-tests, chi-square tests, and ANOVA), correlation, and regression. Extensive use of statistical software packages is included. Meets the Mathematics requirement of the Core Curriculum. Prerequisite: minimum ACT math score of 23, or SAT math score of at least 560, or MTH 1113.

Offered spring semester

#### MTH 2111 Problem-Solving Seminar

#### One hour

A presentation of mathematics in a format that increases students' problem-solving skills and prepares them to communicate mathematical content effectively. The course is designed to build a cohort of mathematics and secondary mathematics education students and covers a variety of topics from different branches of mathematics. The course must be taken at least twice by Mathematics majors and once by Mathematics Education majors.

Offered fall semester

#### MTH 2114 Linear Algebra and Differential Equations

#### Four hours

A continuation of the study of differential equations as begun in Calculus II with special emphasis on applications to problems in physics and engineering. The course also includes an introduction to linear algebra as this subject forms the basis for the study of higher dimensional systems of differential equations. In preparation for MTH 2123, the course ends with an introduction to vectors in two- and three-dimensional space. Prerequisite: MTH 1144.

Offered fall semester

#### MTH 2123 Vector Calculus

#### Three hours

An introduction to the study and application of multivariable and vector calculus. Prerequisites: MTH 1134 and MTH 1144.

Offered spring semester

#### MTH 2143, 2183 Mathematical Structures I, II

#### Each course, three hours

A presentation of mathematics in a format that prepares teachers of elementary school mathematics. Topics include problem-solving, sets and logic, functions, the mathematical meaning and background of arithmetic through real numbers, number theory, probability and statistics, introductory geometry, geometric constructions, congruence, similarity, measurement, and coordinate geometry. Prerequisite for 2143: minimum ACT math score of 19, or SAT math score of at least 480, or Passing Score (State Level) on Praxis I Math, or MTH 0153 with grade of 'C' or better. Prerequisite for 2183: MTH 2143.

2143 offered fall semester

2183 offered spring semester

#### MTH 3101 Mathematics Teaching Practicum

#### One hour

Practical experience in mathematics instruction. Three hours per week. May be repeated once for credit. Prerequisites: Junior standing and consent of instructor.

Offered upon sufficient request

#### MTH 3103 Foundations of Mathematics

#### Three hours

Introductory predicate logic, set theory, and methods of mathematical proof. The general techniques learned are applied to topics from discrete mathematics, cardinality, metric spaces, algebraic structure, and field properties of real numbers. Prerequisite: MTH 1144.

Offered fall semester

#### MTH 3113, 4113 Selected Topics

#### Each course, three hours

Topics are chosen from various branches of mathematics such as set theory, number theory, complex variables, history of mathematics, combinatorics, and topology. May be repeated for credit when content differs. Prerequisite: consent of instructor.

Offered upon sufficient request

#### MTH 3143 Topics in Mathematics Education

#### Three hours

An introduction to the philosophy and practice of teaching mathematics. Discussion and analysis of current trends and an introduction to the literature. Prerequisites: MTH 1134 or MTH 1123 and MTH 2183.

Offered fall semester (even-numbered years)

#### MTH 3153 Foundations of Geometry

#### Three hours

An introduction to the theory of Euclidian, neutral, Lobachevskian, Riemannian, incidence, and affine geometrics, together with linear, planar and spatial order properties. Designed primarily for prospective secondary teachers of mathematics. Prerequisites: MTH 1134 or MTH 1123 and MTH 2183.

Offered spring semester (odd-numbered years)

#### MTH 3173 Mathematical Modeling and Simulation

#### Three hours

A study of the building of mathematical models and computer simulations to describe selected topics from physical, biological, and social sciences. Prerequisites: MTH 2123 and CS 1113.

Offered upon sufficient request

#### MTH 3183 Probability and Statistics

#### Three hours

An introduction to the theory of probability and statistical inference including discrete and statistical inference, discrete and continuous random variables, sampling distributions, the Central Limit Theories, estimation, and hypothesis testing. Prerequisite: MTH 1144; MTH 2123 is strongly recommended but not required.

Offered spring semester

#### MTH 4123 Abstract Algebra

#### Three hours

An introduction to modern algebra and algebraic structures such as groups, rings, integral domains, and fields. Prerequisites: MTH 2114 and MTH 3103.

Offered spring semester (even-numbered years)

#### MTH 4143 Real Analysis

**Three hours**

A systematic study of topics in mathematical analysis such as the real number system, sequences, limits, continuity, differentiation, and integration. Prerequisites: MTH 2123 and MTH 3103.

Offered fall semester (odd-numbered years)

#### MTH 4221, 4222, 4223 Mathematics Research

**One to three hours**

Research projects in an area of mathematics of interest to the student and supervising faculty. May be repeated for credit up to a total of three hours counted toward fulfillment of upper-division elective credits in mathematics required for the Mathematics major.

Offered each semester

#### MTH 4501 Mathematics Capstone

#### One hour

Structured review of key concepts and problem-solving approaches in multiple disciplines of mathematics to foster the development of cross-connections between these disciplines while aiding students in preparing for the standardized achievement test required for completion of the Mathematics major. One hour lecture-discussion per week. Prerequisites: senior standing and completion of, or current enrollment in, all (or most) mathematics courses specified by the department for the Mathematics major.

Offered spring semester