MATHEMATICS (MAT)

Margaret F. Symington, Chair/Professor of Mathematics

Jeffrey K. Denny, Professor

Kedrick Hartfield, Professor

Curtis D. Herink, Professor

Keith E. Howard, Professor

Yuanting Lu, Assistant Professor

Joshua Holloway, Lecturer

Hope McIlwain, Professor

David G. Nelson, Professor

Kedar Nepal, Associate Professor

Jeffrey Pullen, Associate Professor

Lee Troupe, Assistant Professor

Carolyn A. Yackel, Professor

The Department offers Mathematics majors leading to a Bachelor of Arts or a Bachelor of Science degree. It also offers a minor in Mathematics and a minor in Statistics.

Major in Mathematics: B.S. degree 48 semester credit hour minimum • CSC 204. Programming I • MAT 133. Precalculus (may be exempted by achieving a specific score on the Math Index or Math Placement Test) • MAT 191. Calculus I • MAT 192. Calculus II • MAT 260. Introduction to Abstract Mathematics • MAT 293. Multivariable Calculus • MAT 340. Linear Algebra • One proof-emphasis course from: • MAT 326. Graph Theory and Combinatorics • MAT 350. College Geometry • MAT 360. Elementary Number Theory • MAT 380. Introduction to Complex Variables • One applications-emphasis course from: • MAT 320. Probability and Mathematical Statistics • MAT 330. Introduction to Differential Equations • MAT 335. Numerical Methods • MAT 345. Applied Mathematical Modeling • Three courses from: • MAT 461. Abstract Algebra I • MAT 462. Abstract Algebra II • MAT 481. Real Analysis I • MAT 482. Real Analysis II • MAT 499. Senior Seminar in Mathematics • PHY 161. General Physics I • PHY 162. General Physics II • One additional MAT course numbered 320 or above |

Major in Mathematics: B.A. degree 34 semester credit hours minimum • CSC 204. Programming I • MAT 133. Precalculus (may be exempted by achieving a specific score on the Math Index or Math Placement Test) • MAT 191. Calculus I • MAT 192. Calculus II • MAT 260. Introduction to Abstract Mathematics • MAT 293. Multivariable Calculus • MAT 340. Linear Algebra • One proof-emphasis course from: • MAT 326. Graph Theory and Combinatorics • MAT 350. College Geometry • MAT 360. Elementary Number Theory • MAT 380. Introduction to Complex Variables • One applications-emphasis course from: • MAT 320. Probability and Mathematical Statistics • MAT 330. Introduction to Differential Equations • MAT 335. Numerical Methods • MAT 345. Applied Mathematical Modeling • One sequence from: • MAT 461—462. Abstract Algebra I-II • MAT 481—482. Real Analysis I-II • MAT 499. Senior Seminar in Mathematics |

Those students planning to pursue a doctoral degree are also strongly advised to take GER 111-112 or FRE 111-112.

Majors may attain Departmental Honors in mathematics by meeting the following requirements: (1) apply for Honors during the second semester of the junior year; (2) attain a grade point average of 3.50 in the mathematics courses applied toward the major; (3) enroll in MAT 402 and complete a research paper under the direction of a faculty member in the department; (4) present the results of the research in colloquium; (5) receive departmental approval for the entire project.

Secondary Teacher Certification Program in Mathematics

A major in secondary mathematics education with certification for teaching grades 6-12 is available in mathematics as a separate Bachelor of Science in Education degree through the College of Education. Students planning to teach mathematics in secondary schools should notify their advisor and contact the chair of teacher education in the College of Education. Please consult the COLLEGE OF EDUCATION section of this catalog for complete degree requirements. This certification is approved by the Georgia Professional Standards Commission.

Students who want a major in mathematics as well as certification for teaching in grades 6-12 may either (1) complete the requirements for two bachelor’s degrees or (2) qualify for certification through a post-baccalaureate program such as the Master of Arts in Teaching. See the requirements for dual degrees in the ACADEMIC INFORMATION section of this catalog (under Second Degree); see the GRADUATE STUDIES section of this catalog, College of Education, for information about the M.A.T. program.

Minor in Mathematics 17 semester credit hours minimum • MAT 133. Precalculus (may be exempted by achieving a specific score on the Math Index or Math Placement Test) • MAT 191. Calculus I • MAT 192. Calculus II • One option from: • Option (a): • MAT 260. Introduction to Abstract Mathematics • Two additional courses numbered 320 or above • Option (b): • MAT 225. Discrete Mathematics • MAT 340. Linear Algebra • One additional course numbered 320 or above |

Certificate in Actuarial Science

Students may complete a Certificate in Actuarial Science either separately from or in conjunction with the Mathematics major or minor. Actuaries assess financial risk and must be broadly educated in mathematics and statistics, analytical and problem-solving skills, business sense, communication skills, and computer skills. Becoming an actuary requires taking a series of exams. Students who wish to pursue a career as an actuary should take the first two exams in Probability and Financial Mathematics during their undergraduate career. Companies that employ actuaries give time, support, and bonuses for completing the rest.

Certificate in Actuarial Science 12 semester credit hours • MAT 320. Probability and Mathematical Statistics • MAT 321. Problems in Actuarial Science: Probability • MAT 322. Problems in Actuarial Science: Financial Mathematics • MAT 398. Internship in Mathematics (a minimum of 50 hours of internship with an approved business, typically with an actuary department of an insurance company) In addition, the following courses are recommended by the Society of Actuaries (SOA) as good preparation for a career as an actuary: ECN 150, 151; ACC 204; FIN 362, 463; MAT 293, 340; STA 126, 227, 330, 340; CSC 204; COM 210; TCO 141; MKT 361. |

MAT 095. Intermediate Algebra (3 hours)

Credit earned in MAT 095 does not count toward the minimum number of hours required for graduation. An introductory course in algebra which includes the study of the fundamental algebraic operations, factoring, algebraic fractions, equations and inequalities, exponents and radicals. (Every semester)

MAT 104. Mathematical Ideas (3 hours)

An introduction to mathematical ideas that teaches rigorous, precise, effective thinking. Topics will include classical proofs (e.g., Infinitude of Primes, Pythagorean Theorem, Platonic Solids), real world manifestations (e.g., basic probability, codes, Fibonacci numbers, risk), abstractions (e.g., infinite sets, fourth dimension, graph theory, knots), and patterns (e.g., symmetry, fractals). (Every semester)

MAT 121. Concepts in Calculus (3 hours)

Prerequisite: MAT 095 or a specific score on the Math Index or Math Placement Test.

The course emphasizes the concepts in differential and integral calculus and applications of those concepts. The material is made accessible to students with a limited mathematical background by restricting attention to a simple class of functions—polynomial functions in most cases and rational functions where appropriate. (Occasionally)

MAT 131. College Algebra: Functions and Graphs (3 hour)

Prerequisite: MAT 095 or a specific score on the Math Index or Math Placement Test.

Topics include graphs and functions (linear, quadratic, polynomial, rational, exponential, and logarithmic). Credit cannot be earned in both MAT 131 and MAT 133. (Every semester)

MAT 133. Precalculus (4 hours)

Prerequisite: a grade of C or better in MAT 095 or a specific score on the Math Index or Math Placement Test.

Topics include graphs, functions (linear, quadratic, polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric), and trigonometric identities. Credit cannot be earned in both MAT 131 and MAT 133. (Every semester)

MAT 141. Calculus for the Social Sciences (3 hours)

Prerequisite: MAT 131, 133 or a specific score on the Math Index or Math Placement Test. Students who have not completed MAT 131 or 133 and who plan to register for this course should take the Math Placement Test. A high score on this test will meet the prerequisite for the course.

A study of the derivative of algebraic, exponential, and logarithmic functions and an introduction to integration. Business applications are stressed. Both MAT 141 and 191 can be taken, but credit will be granted for only one, which is to be determined by written permission from the Mathematics Department. Students who plan to major in mathematics, chemistry, computer science, or physics should take MAT 191. (Occasionally)

MAT 191. Calculus I (4 hours)

Prerequisite: a grade of C or better in MAT 133 or a satisfactory score on the Math Index or the mathematics placement exam. Students who have not completed MAT 133 and who plan to register for this course should take the mathematics placement exam. A high score on the exam will meet the prerequisite for the course.

Topics include: a study of functions, involving limits, continuity, derivatives, and antiderivatives; the definite integral; and Fundamental Theorem of Calculus. Both MAT 141 and 191 can be taken, but credit will be granted for only one, which is to be determined by written permission from the Mathematics Department. (Every semester)

MAT 192. Calculus II (4 hours)

Prerequisite: a grade of C or better in MAT 191 or consent of instructor.

Topics include: methods of numerical integration, applications of the definite integral, techniques of antidifferentiation, improper integrals, infinite series, differential equations, and polar coordinates. (Every semester)

MAT 198. Special Introductory Topics in Mathematics: (Subtitle) (1-4 hours)

Study of an introductory topic in mathematics not covered in any of the departmental offerings. Students must engaged in projects or assignments requiring at least one contact hour, or equivalent, per week for every hour of credit. This course may be applied to the Mathematics major or minor. (Occasionally)

MAT 225. Discrete Mathematics (4 hours)

Prerequisite: MAT 191.

An introduction to fundamental concepts and methods of proof in discrete mathematics. Topics include sets, functions, Boolean algebra, elementary graph theory, techniques of counting, and methods of proof (including induction and contradiction). (Every semester)

MAT 260. Introduction to Abstract Mathematics (3 hours)

Prerequisite: MAT 192.

A course designed to facilitate the transition to mathematics courses in which the student is expected to prove theorems. Topics include sets, logic, methods of proof, relations, and number systems. (Every fall semester)

MAT 293. Multivariable Calculus (3 hours)

Prerequisite: MAT 192.

Topics include: vector calculus, limits and continuity of functions of several variables, partial derivatives and applications, and multiple integrals and applications. (Every semester)

MAT 320. Probability and Mathematical Statistics (3 hours)

Prerequisite: MAT 192.

Concepts and basic properties of some special probability distributions, independence, moment generating functions, sampling distributions of statistics, limiting distributions. (Every spring)

MAT 321. Problems in Actuarial Science: Probability (3 hours)

Prerequisite: MAT 320 or consent of instructor.

This course teaches the content and problem-solving skills that support the successful completion of SOA Exam P. Emphasis will be placed on solving the large set of problems associated with the exam. Additional instruction will be given on the mathematics needed to solve these problems. (Occasionally)

MAT 322. Problems in Actuarial Science: Financial Mathematics (3 hours)

Prerequisite: MAT 192 or consent of instructor.

This course teaches the content and problem-solving skills that support the successful completion of SOA Exam FM. Emphasis will be placed on solving the large set of problems associated with the exam. Additional instruction will be given on the mathematics needed to solve these problems. (Occasionally)

MAT 326. Graph Theory and Combinatorics (3 hours)

Prerequisite: MAT 260 or 225.

A study of two distinct, though related, concepts in discrete mathematics—graph theory and combinatorics. Topics from graph theory will include cycles, coloring, trees, networks, and planarity. General counting methods of combinatorics will be covered, along with generating functions, and recurrence relations. This course develops the student's logical reasoning and basic methods of proof. (Every four years)

MAT 330. Introduction to Differential Equations (3 hours)

Prerequisite: MAT 192.

A study of ordinary differential equations using qualitative, numerical, and analytic approaches. Topics include first-order differential equations, second-order linear differential equations, systems of differential equations, Laplace transformations and applications. (Every semester)

MAT 335. Numerical Methods (3 hours)

(Same as CSC 335)

Prerequisites: MAT 192 and ability to write programs in a high-level computer language.

A study of numerical methods for the solution of mathematical problems and computer application of those methods. Topics include: methods such as the bisection algorithm and fixed point iteration for the solution of equations with a single variable, interpolation and polynomial approximation, numerical differentiation and integration, solution of systems of linear equations, and least squares approximation. (Every two years)

MAT 340. Linear Algebra (3 hours)

Prerequisite: MAT 225 or 260 or consent of instructor.

An introduction to the algebraic structure of vector spaces, the theory of matrices, the application of matrices to the study of vector spaces, systems of linear equations and linear transformations. (Every spring semester)

MAT 345. Applied Mathematical Modeling (3 hours)

Prerequisite: MAT 330 or consent of instructor.

This course focuses on mathematical modeling of phenomena from biology, chemistry, engineering, medicine, and physics. Students learn the tools and techniques of modeling, using differential equations, matrix algebra, and statistics and learn to formulate a variety of models. Students engage cooperatively and individually in the formulation of mathematical models and in the techniques of investigating those models. Several major projects throughout the semester give the students experience in applying the tools and formulation of models. Class sessions consist of lectures and hands-on experimentation with projects using several computational tools. (Every two years)

MAT 350. College Geometry (3 hours)

Prerequisite: MAT 340.

A rigorous study of the properties of Euclidean geometry, with special attention to incidence and metric properties, and introduction to elementary properties of non-Euclidean geometries. This course develops the student’s logical reasoning and basic methods of proof. (Every two years)

MAT 360. Elementary Number Theory (3 hours)

Prerequisite: MAT 260 or 225.

A study of topics from classical number theory, including discussions of mathematical induction, prime numbers, division algorithms, congruences, and quadratic reciprocity. This course develops the student's logical reasoning and basic methods of proof. (Every four years)

MAT 380. Introduction to Complex Variables (3 hours)

Prerequisites: MAT 260 or 225 and MAT 293.

An examination of properties of complex numbers, elementary functions of a complex variable, complex derivatives and analytic functions, applications to sums and integrals, and conformal maps. This course develops the student's logical reasoning and basic methods of proof. (Every two years)

MAT 390. Topics in Mathematics: (Subtitle) (1-3 hours)

Credit will be determined based on the particular topic studied. A student may receive no more than three hours per course and no more than six hours total. Students must engage in projects or assignments requiring at least one contact hour, or equivalent, per week for every hour of credit. (Occasionally)

MAT 398. Internship in Mathematics (1-3 hours)

Prerequisites: junior or senior standing and permission of department chair.

An intensive practicum experience at an approved business, organization, or academic institution. Students, under the direction of a faculty member and an on-site supervisor, must engage in projects or assignments requiring at least three on-site hours per week for every hour of credit. Students will learn through observation, regular discussions with the on-site supervisor and Mercer faculty member, and written reflection. In addition, students may be required to attend training events, workshops, or weekly seminars. This course may be repeated for a total of 9 hours and does not count toward a major or minor in Mathematics. Graded S/U. (Every year)

MAT 401. Directed Independent Study (1-3 hours)

Prerequisite: consent of instructor.

This course is intended to provide the student with the opportunity to study independently in an area of interest. Arrangement with the department chair and the instructor is required. Students must engage in projects or assignments requiring at least one contact hour, or equivalent, per week for every hour of credit. (Occasionally)

MAT 402. Directed Independent Research (1-3 hours)

Prerequisite: consent of instructor.

This course is intended to provide the student with the opportunity to do supervised research in an area of interest. Arrangement with the department chair and instructor is required. Students must engage in projects or assignments requiring at least one contact hour, or equivalent, per week for every hour of credit. (Occasionally)

MAT 461-462. Abstract Algebra I and II (3 hours each)

Prerequisite: MAT 340.

A study of groups, rings, and fields. Topics will include homomorphisms of groups and rings, quotient structures, polynomial rings, and extension fields. (Every two years)

MAT 481-482. Real Analysis I and II (3 hours each)

Prerequisites: MAT 293 and 340.

A rigorous introduction to the system of real numbers; a study of the consequences of continuity, differentiability, integrability, and the elementary topology of the real numbers. (Every two years)

MAT 499. Senior Seminar in Mathematics (1 hour)

A course designed to help students take a broad view of their mathematics education and to synthesize the disparate components of this education. Students will be expected to organize and deliver a mathematical presentation. (Every fall semester)