**About**
**Why should I major in mathematics?**
Your choice of a mathematics major gives you tools for lifelong learning and a wide variety of careers. Recent advances in physics, chemistry and astronomy rely heavily upon mathematical ideas, and the biological sciences increasingly use mathematical models. Mathematics is being utilized more and more in the social sciences, particularly in economics and psychology, and is the foundation of actuarial science. There are substantial interactions between computer science and mathematics, and the exchange of ideas between these two disciplines has been extraordinarily fruitful.

**What can I do with a mathematics degree from the University of Pikeville?**

A graduate with a degree in mathematics can qualify for a broad range of highly paid positions in business, industry, government and education. Companies in the computer and communications industries, oil companies, banks, insurance companies and consulting firms employ many mathematicians. University and college teaching and research have always attracted mathematicians. Many mathematicians with a bachelor’s or master’s degree teach at the K-12 level. Other job titles apply to mathematicians who have specialized in an applied branch of mathematics. Actuaries assemble and analyze statistics to calculate probabilities and set rates in the insurance industry, operations research analysts apply scientific methods and mathematical principles to organizational problems and statisticians design, carry out and interpret the numerical results of surveys and experiments. All of these careers begin with an education in mathematics and a curiosity about the use of mathematics to solve problems.

**Mathematics at the University of Pikeville**

The mathematics program is part of the Division of Mathematics and Natural Sciences. This program is designed to promote critical thinking and analytical reasoning and to prepare students for mathematical careers in business, government, teaching and industry.

**Mathematics Degree Options**
Bachelor of Science (B.S.) or Bachelor of Arts (B.A.)

**Communication Careers**

Actuary

Bank Manager

Computer Programmer

Credit Analyst

Financial Analyst

Insurance Salesman

Investment Analyst

Investment Banker

Mathematician

Professor

Research Analyst

Retail Manager

Statistician

Teacher

Underwriter

**Courses**

**MTH 091 Fundamentals of Mathematics **

(See Developmental Studies)

**MTH 093 Beginning Algebra **

(See Developmental Studies)

**MTH 095 Intermediate Algebra **

(See Developmental Studies)

**MTH 105 Contemporary College Mathematics**

This course is designed to meet the University’s General Education Mathematics requirement for students who are not majoring in mathematics or science. The goal of this survey course is to develop competency in analytical reasoning, problem solving, and multi-step decision making as well as exposing students to some current trends in mathematical thought. The emphasis is on mathematical reasoning and the solving of real-life problems involving mathematics. The course covers counting techniques and probability, topics in geometry, and financial/consumer mathematics. Additionally, one to three of the following topics will be covered: graph theory, logic/set theory, linear programming, game theory, or elementary number theory. Prerequisite: Grade of “C” or better in MTH 093 or placement beyond.

**MTH 113 Precalculus Algebra**

Further study of topics in algebra including linear and quadratic equations, functions, relations, and their graphs, polynomials and rational functions, exponential and logarithmic functions, systems of linear equations, and applications. Prerequisite: MTH 111 or placement by examination.

**MTH 114 Trigonometry**

A study of concepts and applications of circular and trigonometric functions. Includes graphs of trigonometric functions, inverse trigonometric functions, circular motion, solution of triangles, and trigonometric identities. Should be taken concurrently with MTH 113.

**MTH 115 Fundamentals of Geometry**

A study of plane and solid geometry, including properties of triangles, quadrilaterals, regular polygons, and circles, and congruence, similarity, area, volume, and transformations and symmetry. Prerequisite: MTH 111 or higher.

**MTH 121 Calculus I**

A study of functions, limits and continuity, derivatives, and an introduction to integrals. Applications to finding tangent lines, solving maximum and minimum problems, solving related rate problems, and finding areas. Prerequisites: MTH 113 and 114 or placement by examination.

**MTH 200 Elementary Probability and Statistics **

A study of the basic concepts of probability and statistics including permutations, combinations, binomial distributions and standard deviations, with emphasis on interpretations and hypothesis testing. Prerequisite: MTH 111 or higher. Cannot be used for the Mathematics Minor.

**MTH 222 Calculus II **

A study of exponential and logarithmic functions, applications of the integral to finding volumes, arc lengths, surface areas, and centroids, techniques of integration, polar coordinates, and indeterminate forms. Prerequisite: MTH 121.

**MTH 223 Calculus III**

A study of infinite series, parametric equations, vectors in the plane, curves and surfaces in space, partial derivatives, and multiple integrals. Prerequisite: MTH 222.

**MTH 251 Discrete Mathematics **

A study of the elements of sets, set operations, mathematical induction, basic counting techniques, and recurrence relations. Prerequisite: MTH 113 or higher.

**MTH 281 Basic Mathematics of Maps, Puzzles and Games**

A basic investigation of mathematics of basic map projections and travel itineraries; familiar puzzles such as Sudoku, the triangular peg puzzle, Rubik’s Cube, and jigsaw puzzles; and board games such as Yahtzee, Risk, Monopoly, and others. Students demonstrate the solving of the Rubik’s Cube using open notes as well as the other puzzles. Meets with MTH 481. Prerequisite: MTH 095, MTH 105, MTH 113, or MTH 121. Cannot be taken if student has already passed MTH 481. May fulfill requirements for the Mathematics minor but not the Mathematics major

**MTH 290 Special Topics**

A study of a selected topic of special interest. The topic may differ each time the course is offered and may be proposed by either the instructor or by the student. May be taken for credit any number of times, provided a different topic is offered each time. Prerequisite: Consent of Instructor.

**MTH 299 Directed Study**

Individual basic study of a selected topic in mathematics, under the direction of a member of the faculty. Normally open only to students who have completed all regularly offered courses in the mathematics major. Prerequisites: Consent of the Instructor, Division Chair, and Dean of the College of Arts and Sciences.

**MTH 303 Introduction to Abstract Mathematics **

An introduction to abstract mathematics and proofs by means of a study of selected topics in elementary number theory. Prerequisite: MTH 222 or a prerequisite of MTH 251 and a co-requisite of MTH 222.

**MTH 305 History of Mathematics**

A chronological presentation of the development of the science of mathematics, with emphasis placed on the significant problems, inconsistencies, and discoveries that led to the growth of the field of mathematics. Prerequisite: MTH 223.

**MTH 307 Complex Variables**

Functions, limits, continuity, differentiation, and integration of functions of a complex variable are examined. Also, contour integration and applications to physics and mechanics are presented. Prerequisite: MTH 223.

**MTH 320 Introduction to Numerical Methods**

Algorithms for the solution of numerical problems implemented on micro-computers; includes discussion of error, polynomial interpolation, solution of nonlinear equations, and numerical integration. Prerequisites: MTH 222 and either CS 112 or 221. Cross-listed as CS 320.

**MTH 322 Differential Equations **

A study of simple types of ordinary differential equations of various orders and their algebraic and geometric solutions, Laplace transforms, systems of differential equations, and applications. Prerequisite: MTH 222.

**MTH 335 Linear Algebra **

A study of vector spaces, linear equations, linear transformations, matrices, determinants, and geometric applications of these concepts. Prerequisite: MTH 222.

**MTH 400 Advanced Geometry**

A study of advanced topics in plane and solid geometry. Topics may include, but are not limited to, methods of proof, constructions, loci, elementary transformations, introduction to non-Euclidean geometry, and introduction to projective geometry. Prerequisite: MTH 303.

**MTH 410 Abstract Algebra**

A study of abstract binary operations, groups, rings, and fields. Prerequisite: MTH 303 or consent of the Instructor.

**MTH 481 Advanced Mathematics of Maps, Puzzles and Games**

An advanced investigation of mathematics of basic map projections and travel itineraries; familiar puzzles such as Sudoku, the triangular peg puzzle, Rubik’s Cube, and jigsaw puzzles; and board games such as Yahtzee, Risk, Monopoly, and others. Students demonstrate the solving of the Rubik’s Cube from memory as well as the other puzzles. Meets with MTH 281. Prerequisite: MTH 222.

**MTH 490 Special Topics**

A study of a selected topic of special interest. The topic may differ each time the course is offered and may be proposed by either the Instructor or by students. Prerequisite: MTH 223 or consent of the Instructor. May be taken for credit any number of times, provided that a different topic is studied each time.

**MTH 495 Seminar in Mathematics**

Study of a variety of mathematical topics of interest to instructor and students, with active student participation emphasized. Prerequisites: Senior standing, Mathematics major, and consent of the Instructor.

**MTH 499 Directed Study**

Individual advanced study of a selected topic in mathematics, under the direction of a member of the faculty. Normally open only to students who have completed all regularly offered courses in the mathematics major. Prerequisites: Consent of the Instructor, Division Chair, and Dean of the College of Arts and Sciences.