# Catalogue: Traditional Program: Mathematics

## Mathematics (MAT)

Assistant Professor Estes, Chair

Assistant Professor Oakley

Mathematics is a source of intrinsic beauty of numbers, shapes, structures, and interrelationships; it is also a tool to help solve practical problems in many fields of human endeavor. The history of mathematics was shaped through interaction with Christianity, and course work reflects the enormous usefulness of mathematics to describe the universe created and sustained by God. The program for mathematics majors is the traditional mathematics undergraduate program. Coursework for non-majors is designed to help students acquire and refine computational and analytical skills needed to function well in their chosen vocations. Mathematics students will have real-world experience through student teaching, EDU 200, MAT 209, 399 or 499.

Mathematics faculty advise mathematics majors and pre-engineering students.

The **Bachelor of Science degree in mathematics** requires 40 hours: MAT 207, 208, 209, 210, 303, 304, 305, 311, 315, 410, and 490 plus six additional hours of MAT at the 300 level or above, and 3 hours of CSC electives.

The **Bachelor of Arts degree in mathematics** requires 40 hours: MAT 207, 208, 209, 210, 303, 304, 305, 311, 315, 410, and 490, 3 hours of CSC electives, plus six additional hours of 300 level or above from ART, BIB, HIS, DAN, EDU, ENG, MUS, PHI, PSC, PSY, SOC, THE, or foreign language.

Physics is recommended to fulfill the core science requirement. Students who choose the pre-engineering option can take the following requirements of (ABET) engineering: MAT 207, 208, 209, 210, 304, and CHE 111-112. (Some engineering disciplines also require CHE 113-114. The pre-engineering student should consult with his advisor and check the engineering school catalog for other specific courses.)

The **mathematics minor** requires 18 hours. Fifteen hours must be at the level or MAT 207 and higher.

**Honors Program**: The mathematics department offers opportunities for students to enroll in honors courses from its department. The following are mathematics general education, elective, and major courses that may be taken as honors courses: MAT 101, 207, 208, 209, and 210. For students majoring in Mathematics, one must pass a minimum of nine hours of honors courses within the discipline and a minimum of nine hours from the honors courses of other departments. Each course must be passed with a B or better. No more than 18 hours are required for the honors degree. For other honors program policies, see “Honors Program” found in the “Administration of the Curriculum” section of this catalogue.

099 |
Beginning Algebra (3). Institutional credit only.For students whose mathematics ACT score is below 17 (SAT math score below 440). Elementary mathematical concepts and procedures. This course does not fulfill the core requirement nor does it count toward the 124 hours required for graduation. (Fall only) |

100 |
Intermediate Algebra (3). Institutional credit only.For students whose mathematics ACT score is 17-21 (SAT math score is 440-490). A study of real numbers, algebraic expressions, algebraic fractions, linear equations/inequalities, quadratic equations, and Pythagorean theorem. This course does not fulfill the core requirement nor does it count toward the 124 hours required for graduation. (Fall and spring) |

101 |
College Algebra (3).For students whose mathematics ACT score is 22 or above (SAT math score is 500 or above). A study of the real number system, equations, inequalities, functions, graphs, zeros of polynomials, conic sections, and the binomial theorem. (Fall and spring) |

102 |
Plane Trigonometry (3). Prereq: MAT 101 or consent of instructor.Trigonometric functions and graphs, identities, equations, inverse functions, vectors, and applications of these concepts. (Spring only) |

110 |
Quantitative Reasoning (3). Prereq: ACT score of 22 or above (SAT math score of 500 or above).A general core alternative to MAT 101, designed primarily for non-science majors. (Not for students planning to take trigonometry or calculus.) Topics include statistical reasoning, probability, logic, problem-solving, estimation, and other analytical skills useful in real-world situations. (Fall and spring) |

131, 132 |
Concepts of Mathematics (3, 3). For majors in elementary education.The problem-solving process, sets, logic, integers, number theory, rational numbers as fractions, decimals and percents, probability and statistics, plane and coordinate geometry, and measurement. (131, fall only; 132, spring only) |

201 |
Mathematics for Business and Economics (3). Prereq: MAT 101 or 110.An introduction to the basics of mathematics tools used in business and economics. Topics include an algebra review, mathematics of finance, probability computations, and introductory calculus with applications. (Fall and spring) |

207 |
Calculus and Analytic Geometry I (3). Prereq: MAT 102, or consent of instructor.Open to freshmen with mathematics ACT score of 26 or above (SAT math score is 610 or above). Concepts of analytic geometry, functions, limits, derivatives, and applications of derivatives. (Fall only) |

208 |
Calculus and Analytic Geometry II (3). Prereq: MAT 207.Integration, applications of the definite integral, logarithmic and exponential functions with their derivatives and applications. (Spring only) |

209 |
Calculus and Analytic Geometry III (3). Prereq: MAT 208.Further techniques of integration, infinite series, and topics in analytic geometry. (Fall only) |

210 |
Calculus and Analytic Geometry IV (3). Prereq: MAT 209.Vectors and vector calculus, three-dimensional space, partial derivatives, and multiple integrals. (Spring only) |

230 |
Puzzles and Riddles (3). Prereq: MAT 101, 102, 110, 200 or 207.Puzzles and Riddles is an exploration in different mathematically based games, puzzles, and logic riddles. Students will spend time playing with these concepts before delving into developing strategies for success. Topics include but are not limited to Latin Squares, Sudoku, Karuko, Rubik’s Cubes, and Logic Puzzles. (Preference in availability will be given to juniors and seniors. This course does not satisfy a General Education Math requirement nor a Mathematics Major elective.) |

303 |
Discrete Mathematics (3). Prereq: MAT 201 or 207 or consent of instructor.Logic, sets, functions, algorithms, counting, graphs, and selected topics. (Fall 2013, Spring 2015) |

304 |
Differential Equations (3). Prereq: MAT 210 or consent of instructor.Theory and application of ordinary differential equations. (Spring, even years) |

305 |
Introduction to Mathematical Statistics and Probability (3). Prereq: MAT 208 or consent of instructor.Frequency distributions, statistical constants, curve fitting, correlation and sampling, and basic laws of probability. (Fall 2012, spring 2014, Fall 2015) |

306 |
Advanced Statistics and Probability (3). Prereq: MAT 305.Continuation of MAT 305 for the further study of various standard probability distributions, moments, moment generating functions, sampling theory, and statistical inference. |

308 |
Introduction to Higher Geometry (3). Prereq: MAT 208.Advanced topics in Euclidean geometry; introduction to non-Euclidean geometries. |

311 |
Linear Algebra (3). Prereq: MAT 208.Vectors, vector spaces, matrices and determinants, systems of linear equations, and linear transformations. (Fall only) |

314 |
College Geometry (3). College Geometry serves as a study of axiomatic systems in geometry, including affine, projective, Euclidean, and non-Euclidean geometries and the historical background of their development. Additionally, the course is developed to assist in proof writing and reasoning. |

315 |
Proof Exposition (1). Co-req: MAT 303. Proof writing is a critical tool and discipline for one to correctly approach higher mathematics. As a continuation of the proof techniques discussed in MAT 303, students will conduct a self-paced study on tackling proof-based problems through a written lab book with an aim to further develop critical thinking and creative problem solving. (Fall and Spring) |

329 |
History of Mathematics (3). Co-req: MAT 303. History of Mathematics approaches the development of the broad field of mathematics from a historical perspective. The student will retrace through works of ancient cultures and mathematical giants in chronological order in order to understand the origins of mathematical thought and to develop a deeper appreciation of the current state of the mathematical field. |

399 |
Selected Topics in Mathematics (1-3). Prereq: MAT 209.Topics chosen from such areas of mathematics as number theory, probability, topology, graph theory, mathematical modeling, mathematics internship, and others. Course can be taken more than once. |

402 |
Operations Research (3). Prereq: MAT 209 or consent of instructor.Application of quantitative methods such as linear and dynamic programming, decision theory, simulation, queuing theory, and network analysis; used to solve problems in the areas of mathematics, business, and computer science. |

409 |
Modern Algebra (3). Prereq: MAT 303 or consent of the instructor.Sets, relations, functions, groups, rings, and fields. (Fall, odd years) |

410 |
Advanced Calculus (3). Prereq: MAT 210 or consent of instructor.Advanced treatment of functions, limits, continuity, differentiability, and the definite integral. (Spring only) |

418 |
Number Theory (3). Prereq: MAT 303 Number Theory takes an encouraging and theoretical look at number systems that are often taken for granted. A course in Number Theory introduces the student to classic mathematical ideas in order to develop a stronger understanding of methods of higher mathematics as well as discover truth in a world created by God (Jeremiah 51:15, Isaiah 41:20). |

421 |
Topology (3). Prereq: MAT 303, Co-req: MAT 410 or consent of instructor. Topology provides a mixture of concrete and abstract mathematics through which students can further development their creative reasoning skills. Topics from general topology covered will include set theory and logic, topological spaces and continuous functions, metric spaces, connectedness and compactness, separation axioms and the Urysohn lemma. Other topics may include classification of surfaces and an introduction to the fundamental group. |

478 |
Graph Theory (3). Prereq: MAT 303. Graph Theory studies networks and relationships between objects from the perspective of theoretical mathematics. The course is designed to introduce students to introductory topics of graph theory such as trees, graph coloring, independence, connectivity, planar graphs, walks, and cycles. |

490 |
Mathematical Investigation (3). Prereq: MAT 210, 304, and 305 or consent of the instructor.Synthesizing mathematical concepts, investigating open-ended problems, and justifying results of analysis of advanced problems through written, oral, and graphic explanation. Utilization of the computer algebra system Mathematica. (Fall only) |

499 |
Selected topics in Mathematics (1-3). Prereq: MAT 304 or consent of the instructor.Topics to be chosen from such areas of mathematics as number theory, topology, complex variables, and advanced differential equations. |