# Mathmatics Course Descriptions

# Mathematics Courses (MAT)

Placement in mathematics courses for those with no previous college mathematics credit is determined on the basis of high school mathematics credit, high school mathematics GPA, mathematics scores on the SAT or ACT and scores on the mathematics placement test given at registration time each semester.

A review of elementary and intermediate algebra designed to assist students in developing the skills necessary for taking MAT 122. Fundamentals of Mathematics or MAT 141. College Algebra. Prerequisite: placement level 0 (zero). Four hours institutional credit (institutional credit is not applicable to the 126 hours required for graduation). Only offered on a credit/no credit basis.

These courses are a two-course sequence of mathematics content course (not method course) designed to prepare students to teach elementary and middle school mathematics for understanding, as envisioned by the National Council of Teachers of Mathematics, and as described in their document Principles and Standards for School Mathematics. The courses will examine deeply those topics in mathematics which are relevant for elementary and middle school teaching. MAT 111 focuses on the problem solving and arithmetic including why standard algorithms work, properties of arithmetic, and applications of elementary mathematics. MAT 112 focuses on the problem solving and geometry including why various standard formulas and properties in geometry are valid. Prerequisite: MAT 040 or placement level 2 for MAT 111 and MAT 111 for MAT 112. MAT 111 is three hours and MAT 112 is three hours for early grade majors and four hours for middle grade majors. (Note. (1) These courses only fulfill the general education core mathematics requirement for elementary and middle grade education majors. (2) These courses are not equivalent to either MAT 122 or MAT 14

This course will introduce a variety of topics chosen from the following: Number systems, finite and infinite sets, geometry, topology, chaos theory, probability, and game theory. This course aims to help students to develop an appreciation for the beauty of mathematics, and for the usefulness of mathematical thinking, by examining particularly surprising results in classical and contemporary mathematics. Prerequisite: MAT 040 or placement level 1. (Note: This course fulfills the core requirement in mathematics, but does not serve as a prerequisite for any other course.) Three hours.

The course will cover complex numbers, solution of equations and inequalities, techniques of graphing, and the study of various functions: linear, quadratic, polynomial, rational, exponential, and logarithmic. Designed for those who have had two years of high school algebra, but need more depth in algebraic topics to prepare for enrollment in MAT 142, 144 or STA 251. Prerequisite: MAT 040 or placement level 2; not open to students with credit for any mathematics course (or equivalent) numbered 142 or higher unless special permission is granted by the instructor. Four hours.

The course will cover analytical trigonometry, systems of equations, matrices and determinants, linear programming, solution of polynomial equations, conic sections, mathematical induction, the binomial theorem, permutations and combinations, and introductory probability. Designed to meet the requirements of various major programs (including biology, business and elementary education/middle grades certification), and to provide preparation for the calculus sequence. Prerequisite: MAT 141 or placement level 3; not open to students with credit for any mathematics course (or equivalent) numbered 145 or higher unless special permission is granted by the instructor. Four hours.

The course will cover systems of linear equations, matrices, linear programming, mathematics of finance and elementary differential and integral calculus. Emphasis will be placed on applications to finance and management problems. Prerequisite: MAT 141 or placement level 3. Four hours.

The course will cover analytic geometry, functions and limits, the derivative and its applications, antiderivatives, indefinite integrals, transcendental functions, the definite integral and its application, methods of integration, polar coordinates and infinite series. These courses are prerequisites to all courses numbered above 200. Prerequisite: MAT 142 or placement level 4 for MAT 145; MAT 145 or placement level 5 for MAT 146. Four hours each.

A continuation of MAT 145-146. The course will cover vectors, parametric equations, solid analytic geometry, partial differentiation, multiple integration, line and surface integrals. Prerequisite: MAT 146. Four hours.

An introduction to the theory of probability. The course will cover combinatorics, laws of probability, discrete and continuous random variables and distributions, expectation, variance, and if time permits, other topics. Prerequisite: MAT 247. Three hours.

The course will cover first order differential equations, second and higher order linear equations, series solutions, the Laplace transform, systems of first order equations, linear second order boundary value problems. Both analytic and numerical techniques are studied. Prerequisite: MAT 146. Four hours.

The course will cover counting, permutations, combinations, discrete probability distributions, generating functions, Ramsey Theory, the pigeonhole principle, induction, various algorithms, topics in graph theory including: connectivity, trees, Euler tours, Hamilton cycles, edge and vertex coloring, planar graphs and graph algorithms. Prerequisite: MAT 145. Three hours.

Proofs in mathematics are both intimidating and mysterious to most people. This course hopes to dispel some of that mystery as well as equip students to both read and write mathematical proofs. Besides a review of logic and mathematical nomenclature, students will be required to tackle proofs from a variety of different fields of mathematics. Prerequisite: MAT 146. Three hours. ‘S’ ‘W’

This course will develop the algebra of vectors and matrices, including finding the inverse of a matrix, subspaces, basis and dimension of vector spaces, linear transformations, isomorphisms. Inner and cross products will be treated. Special types of matrices will be discussed, such as the Jordan Normal form. Eigenvalues and eigenvectors will be treated. Prerequisite: MAT 146. Three hours.

The course will cover integral domains, rings, fields, groups, elementary number theory, and other selected topics. Prerequisite: MAT 290 or permission of instructor for Math Edu majors. Three hours.

The objective of this course is to teach students axiomatic reasoning without the aid of diagrams, explore what can be deduced from neutral geometry (without the Euclidean Fifth Postulate, or, equivalently, the Hilbert Parallel Axiom for Euclidean Geometry), explore aspects of Euclidean Geometry, then, replace the Euclidean Fifth Postulate with the Hyperbolic Parallel Postulate, and show that Hyperbolic Geometry is as self-consistent as Euclidean Geometry. The historical developments, philosophical implications and Hyperbolic Trigonometry should be of particular use to future secondary education mathematics instructors. Prerequisite: MAT 290 or permission of instructor for Math Edu majors for MAT 360; MAT 360 for MAT 361. Three hours each.

The course will cover truth functions and tables, rules of logic, predicate calculus, first order arithmetic, formal set theory, consistency, completeness, recursive functions, and if time permits, Godel Numbers, Godel’s Incompleteness Theorem, algorithms, computability, Church’s Thesis, Turing machines, undecidability of formal systems and the halting problem. Prerequisite: MAT 290. Three hours.

The course will cover set theory, the real number system, functions, sequences, limits, convergence, uniform convergence, Bolzano-Wierstrass Theorem, functions of a real variable, open and closed sets, continuity, uniform continuity, connectivity of the real numbers, the intermediate value theorem, completeness, compactness, the mean value theorem, differentiation, Riemann integration, and if time permits, other topics. Prerequisite: MAT 290 and 258. Three hours.

Review of set theory and logic, defining axioms of topological spaces, bases for topological spaces, order, product and subspace topology, closed sets and limit points, continuous functions, metric topology, connectivity, compactness, the Tychonoff Theorem, and if time permits, other topics. Prerequisite: MAT 290. Three hours.

Topics are considered in number theory, operations research, mathematical statistics, or advanced calculus, depending on student demand. Prerequisite: MAT 290.Three hours per semester. ‘S’ ‘W’

**Spring 2014 Departmental Course Offerings**

(click column title to sort)

Subject | Course# | Course Title | Days | Begin | End | Instructor |
---|---|---|---|---|---|---|

MAT | 040 | Intermediate Algebra | MF | 0900 | 0950 | Mindeman, Barbara |

MAT | 040 | Intermediate Algebra | TR | 0830 | 0920 | Mindeman, Barbara |

MAT | 111 | Mathematics for Educators I | TR | 1300 | 1415 | Donaldson, Sarah |

MAT | 111 | Mathematics for Educators I | TR | 1430 | 1545 | Donaldson, Sarah |

MAT | 122 | Concepts in Mathematics | TR | 0800 | 0915 | Donaldson, Sarah |

MAT | 141 | College Algebra | T | 0830 | 0920 | Park, Heunggi |

MAT | 141 | College Algebra | MWF | 1000 | 1050 | Park, Heunggi |

MAT | 145 | Calculus I | MWF | 1145 | 1250 | Stern, Curt |

MAT | 247 | Calculus III | MWF | 1145 | 1250 | Park, Heunggi |

MAT | 310 | Linear Algebra | MWF | 1300 | 1350 | Park, Heunggi |

MAT | 470 | Topology | MWF | 1500 | 1550 | Petcher, Don |

MAT | 492 | Senior Integration Paper | Park, Heunggi |

# Quantitative Methods Courses (STA)

An introductory course in statistical science used in scientific research investigations. Topics considered include the nature and importance of statistics, quantification, measurement, probability, elementary research design, the collection and scoring of research results, measures of central tendency, the normal distribution, correlational analysis, statistical inference, analysis of variance and the analysis of categories and ranks. Computer applications will be stressed. Prerequisite: MAT 040 or higherlevel mathematics course, or placement level 2 or higher. Four hours.

This course explores methods of data collection and analysis for making decisions related to business, economics, and other organizational issues. Topics include descriptive statistics, correlation, the Normal distribution, sampling, surveys, statistical inference, hypothesis testing, and regression. Applications focus on real data analyzed with statistical software. Students learn to think critically about conclusions drawn from data and to apply statistical methods in their own studies. Prerequisite: MAT 141 or higherlevel mathematics course, or placement level 3 or higher. Four hours.

**Spring 2014 Departmental Course Offerings**

(click column title to sort)

Subject | Course# | Course Title | Days | Begin | End | Instructor |
---|---|---|---|---|---|---|

STA | 252 | Statistics:Concepts & Methods | MWF | 1145 | 1250 | Eames, Kevin |

STA | 253 | Statistics for Decision Making | TR | 0930 | 1045 | Hudson, Ginner |

STA | 253 | Statistics for Decision Making | W | 1000 | 1050 | Hudson, Ginner |

STA | 253 | Statistics for Decision Making | TR | 1300 | 1415 | Hudson, Ginner |

STA | 253 | Statistics for Decision Making | W | 1630 | 1720 | Hudson, Ginner |