# Graduate Course Offerings Mathematics (MATH)

5064 NUMBER CONCEPTS FOR MIDDLE SCHOOL TEACHERS (4 credits) This course helps meet the new BOT rule with respect to number sense. Provides a background in special number concepts that are pertinent to middle school mathematics. Topics include elementary algebra, properties of integers, prime and composite numbers, divisors, GCDs, LCMs, the number of divisors, the sum of divisors, the Euclidean Algorithm, famous unsolved problems, finite mathematical systems, modular arithmetic and congruences, and sequences. Emphasis given to problem solving techniques as they relate to number concepts and algebraic representation.

UPDATED S13 5064 NUMBER CONCEPTS FOR TEACHERS (4 credits) This course provides a background in number concepts that are pertinent to school mathematics. Topics include scientific notation, number sense, properties of integers, prime and composite numbers, divisors, GCDs, LCMs, the number of divisors, the sum of divisors, the Euclidean Algorithm, famous unsolved problems, finite mathematical systems, modular arithmetic, introductory graph theory and applications, permutations, combinations, sorting, congruences, sequences, direct and indirect proofs, mathematical induction, and traveling salesman problem and algorithms. Emphasis will be given to problem solving techniques as they relate to number concepts.

5065 MATHEMATICAL FOUNDATIONS FOR MIDDLE SCHOOL TEACHERS (4 credits) This course helps meet the new BOT rule with respect to concepts of patterns, relations, functions, and discrete mathematics that are pertinent to middle school mathematics.

UPDATED S13 5065 MATHEMATICAL FOUNDATIONS OF ALGEBRA FOR TEACHERS (4 credits) This course investigates concepts of patterns, relations, and functions.

5066 GEOMETRY AND TECHNOLOGY IN THE MIDDLE SCHOOL MATHEMATICS CLASSROOM (4 credits) This course helps meet the licensure rule with respect to concepts of patterns, shape and space; spatial sense; plane, solid, and coordinate geometry systems; generalizing geometric principals; limits, derivatives and integrals; and appropriate use of technology in the classroom.

UPDATED S13 5066 GEOMETRY AND TECHNOLOGY IN THE MATHEMATICS CLASSROOM (4 credits) This course examines the concepts of patterns, shape and space; spatial sense; plane, solid, and coordinate geometry systems; generalizing geometric principals; limits, derivatives and integrals; and appropriate use of technology in the classroom.

5067 DATA INVESTIGATIONS, PROBABILITY, AND STATISTICS FOR MIDDLE SCHOOL TEACHERS (4 credits) This course meets the new BOT rule with respect to data investigations and concepts of randomness and uncertainty. The collection, display, analysis, and interpretation of data are studied. Additional topics include randomness, sampling, probability in simple and compound events, the prediction of outcomes using a variety of techniques, and the comparison of theoretical and empirical results of experiments.

UPDATED S13 5067 DATA INVESTIGATIONS, PROBABILITY, AND STATISTICS FOR TEACHERS (4 credits) This course explores data investigations and concepts of randomness and uncertainty. The collection, display, analysis, and interpretation of data are studied. Additional topics include randomness, sampling, probability in simple and compound events, the prediction of outcomes using a variety of techniques, and the comparison of theoretical and empirical results of experiments.

5240 NUMBER THEORY (3 credits) Properties of integers, primes and their distribution, linear and quadratic congruences, number-theoretic functions, Diophantine equations, Fibonacci numbers, primitive roots and quadratic reciprocity.

5260 MATHEMATICAL PROBLEM SOLVING (3 credits) Investigation of problems and the process of problem solving across a variety of mathematical areas. Development and application of strategies used to solve problems with emphasis on multistep and nonroutine problems. Application of the process of mathematical modeling to real situations.

5310 LINEAR ALGEBRA (4 credits) Systems of linear equations, linear transformations, matrix operations, vector spaces, eigenvalues and eigenvectors, orthogonality, and applications.

5371 MODERN ALGEBRA (3 credits) A study of abstract algebraic systems with an emphasis on groups and an introduction to rings. Prerequisite: MATH 5310 or equivalent.

5410 INTRODUCTION TO ANALYSIS (3 credits) Functions, sequences, and properties of limits. Topics from calculus including continuity, differentiation, and integration. Open and closed sets, cluster points, and other topological properties.

5440 INTRODUCTION TO FRACTALS AND CHAOS (3 credits) An introduction into the topics of fractal geometry, chaos, and dynamic mathematical systems. Topics included are iteration, fractals and fractal dimension, iterated function systems, Julia set, Mandelbrot set, and bifurcation.

5470 ADVANCED CALCULUS (3 credits) Further properties of limits, vector valued functions, infinite series, Taylor series, uniform convergence, improper integrals, convergence in the mean and Fourier series.

5560 CLASSICAL AND MODERN GEOMETRY (3 credits) Euclidean and non-Euclidean geometry, axiomatic systems, the geometry of solids, transformations, measurement, and fractal geometry.

5710 MATHEMATICAL MODELING (3 credits) Mathematical modeling of applications that involve difference equations, matrices, probability, differentiation, and integration. Applications may be chosen from among the biological and p hysical sciences, economics, the social sciences, or other areas of interest. A graphing calculator is required.

5720 NUMERICAL METHODS (3 credits) Root finding techniques, fixed point iteration, polynomial interpolation, methods for solving linear and nonlinear systems of equations, numerical integration and differentiation, numerical solutions of differential equations, and the method of steepest descent. Prerequisite: Programming competency or consent of instructor.

5760 TOPICS IN APPLIED MATHEMATICS (3 credits) This course focuses on an advanced topic from applied mathematics. Possible foci include operations research, cryptography, computational science, and bioinformatics. May be repeated for credit with instructor permission.

5820 HISTORY OF MATHEMATICS (3 credits) Historical investigation and presentation of the sources and growth of mathematical knowledge and principles, including Peano's axioms, the Axiom of Choice, and Russell's Paradox. Prerequisite: Consent of instructor.

6050 ASSESSMENT IN THE MATHEMATICS CLASSROOM (3 credits) Examination of two important parts of assessment. First is the assessment of students: changes in assessment, new tools for assessment, implementing new assessments, and using the results of assessment. Second, teachers need to understand and know how to assess their teaching or changes in their teaching practices. Teachers learn to pose measurable questions, collect data, statistically analyze the data, interpret the data, and present conclusions. Teachers are given assistance in transferring this process to analyzing their teaching practices or programs in their school. Prerequisite: Teaching license or consent of the instructor.

6055 PEDAGOGICAL PORTFOLIO EVALUATION (0 credits) This course is the culmination of the student’s coursework, analysis, and study. In MATH 6050, Assessment in the Mathematics Classroom, students examine the current practices in individual and classroom assessment and study the fundamentals of applying statistical methods for instructional analysis. Students construct instructional units in some of the courses needed for their program. Students try at least four instructional unit changes and analyze the units as per the outline from MATH 6050. The portfolio is evaluated by the student’s graduate committee, and the student cannot proceed with the oral defense until the portfolio has been approved by the committee. This course is graded Satisfactory/Unsatisfactory only. Prerequisite: Teaching license or consent of the instructor.

6061 NUMBER SENSE FOR ELEMENTARY AND MIDDLE LEVEL TEACHERS (3 credits) Number sense is the ability to understand numbers, ways of representing numbers, relationships among numbers, and number systems, according to the National Council of Teachers of Mathematics. This course focuses on these issues by examining problems with quantitative information and exploring reasonable solutions. Prerequisite: Teaching license or teaching position or consent of instructor.

6062 NUMBER THEORY FOR ELEMENTARY AND MIDDLE LEVEL TEACHERS (3 credits) Analysis of activities and mathematical games to understand the underlying mathematics. Students also study the division algorithm, prime and composite numbers, greatest common divisor, least common multiple, the Euclidean algorithm, mathematical induction, linear Diophantine equations, famous number theory conjectures, and additional elementary number theory topics. Prerequisite: Teaching license or teaching position.

6200 DISCRETE MATHEMATICS FOR ELEMENTARY AND MIDDLE LEVEL TEACHERS (3 credits) Topics include problem solving, the counting principle, combinations, permutations, graphs, Euler circuits, Hamiltonian paths, Pascal’s triangle, Venn diagrams, scheduling, and voting theory. Students are expected to use the concepts and methods of discrete mathematics to model and solve problems. Emphasizes instructional strategies to help all students learn. Prerequisite: MATH 6061.

6350 ABSTRACT ALGEBRA FOR SECONDARY TEACHERS (3 credits) Designed to deepen the algebraic background of students through the study of elementary number theory and modular arithmetic; the development of the rational, real and complex number systems; and an introduction to rings, integral domains and fields. Prerequisites: MATH 5310 or equivalent.

6500 GEOMETRY IN THE CLASSROOM FOR ELEMENTARY AND MIDDLE LEVEL TEACHERS (3 credits) This course uses typical classroom materials to examine the Van Hiele model, 3-dimensional and 2-dimensional geometric shapes, and measurement concepts. Emphasizes instructional strategies, manipulatives, and tools to enhance student learning. Prerequisite: Teaching experience or consent of the instructor.

6550 GEOMETRY FOR SECONDARY TEACHERS (3 credits) Historical development and theorems of Euclidean and non-Euclidean geometry, properties of polygons and polyhedra, tessellations of the plane, measurement and strategies for teaching geometry in the secondary classroom.

6600 PROBABILITY FOR ELEMENTARY AND MIDDLE LEVEL TEACHERS (3 credits) Introduction to the terms and models of elementary probability. Emphasizes instructional strategies to help all students learn. Topics include definition of terms, the counting principle, event modeling, event analysis, probability determinations, empirical and theoretical probabilities, and use of simulations to analyze real world problems. Prerequisite: Teaching experience or consent of the instructor.

# Graduate Course Offerings Statistics (STAT)

5610 TIME SERIES ANALYSIS (3 credits) Linear time models, seasonal models, stationary models, moving average, autoregressive and ARIMA models, model identification, confidence intervals and testing, forecasting and error analysis.

5631 PROBABILITY AND STATISTICS I (4 credits) Probability of finite sample spaces, discrete and continuous probability distributions, exploratory data analysis, statistical models. Prerequisite: Consent of instructor.

5632 PROBABILITY AND STATISTICS II (3 credits) Multivariable distributions, sampling distribution theory, estimation, hypothesis testing, regression and correlation. Prerequisite: STAT 5631.

5650 PROBABILITY AND STATISTICS FOR SECONDARY TEACHERS (4 credits) Topics include descriptive statistics and graphical representations, basic probability and commonly encountered distributions, random variables, expectation and variance, sampling theory, and inferential statistics including univariate and bivariate data. Calculus is employed in the development of these concepts. Technology is used extensively to motivate and explain concepts and techniques. The course emphasizes and models exercises and pedagogy appropriate for the secondary school classroom.

5660 STATISTICS FOR THE HEALTH SCIENCES (3 credits) Introduction to descriptive and inferential statistics in the context of the health sciences. Covers data types, methods for summarizing and displaying data, measures of central tendency and variability, hypothesis testing including the analysis of variance and nonparametric techniques, correlation and regression. Students learn to use the statistical software package SPSS for data analysis.

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