5052 MATH MODELS, GAMES, AND ACTIVITIES FOR THE ELEMENTARY CLASSROOM (3 credits) An intensive introduction to activities, models, projects, and ideas needed to effectively teach using contemporary text materials. Material usable at every ability level will be included. Set theory; numeration; and the systems of whole numbers, integers, rational numbers, and real numbers. Prerequisite: Teaching experience or consent of instructor.

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. Prerequisite: MATH 5052 or equivalent.

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. Prerequisite: MATH 5052 or equivalent.

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.

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.

5210 FOUNDATIONS AND DISCRETE MATHEMATICS (4 credits) Symbolic logic, quantifiers, predicate calculus, methods of proof, set theory, relations and functions, graphs, trees, networks, recurrence relations, and complexity of algorithms.

5230 MATHEMATICS CONCEPTS FOR MIDDLE SCHOOL TEACHERS (3 credits) A study of mathematics concepts pertaining to middle school based on the current Curriculum and Evaluation Standards established by the National Council of Teachers of Mathematics and the Minnesota Graduation Standards. Prerequisite: MATH 5210.

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. Prerequisite: MATH 5210.

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. Prerequisite: MATH 5210.

5310 LINEAR ALGEBRA (4 credits) Systems of linear equations, linear transformations, matrix operations, vector spaces, eigenvalues and eigenvectors, orthogonality, and applications. Prerequisite: MATH 5210 or consent of instructor.

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. Prerequisite: MATH 5210.

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. Prerequisite: MATH 5210.

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. Prerequisite: MATH 5210.

5480 COMPLEX ANALYSIS (3 credits) Complex number system, polar form, analytic functions, differentiation and integration, series, residues, conformal mapping, Schwarz-Christoffel transformations, and applications. Prerequisite: MATH 5210.

5560 CLASSICAL AND MODERN GEOMETRY (3 credits) Euclidean and non-Euclidean geometry, axiomatic systems, the geometry of solids, transformations, measurement, and fractal geometry. Prerequisite: MATH 5210.

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.

5741 NUMERICAL METHODS AND OPTIMIZATION I (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.

5742 NUMERICAL METHODS AND OPTIMIZATION II (3 credits) Numerical solutions of differential equations, methods for finding eigenvalues and eigenvectors, classical numerical methods for optimization of functions of one or more variables, various search techniques for optimization of functions of several variables, topics chosen from operations research, wavelets, neural networks, and other areas of application. Prerequisite: MATH 5741 or consent of instructor.

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 5052 or MATH 6061.

6300 PATTERNS AND FUNCTIONS FOR ELEMENTARY AND MIDDLE LEVEL TEACHERS (3 credits) Concepts of equality, variable, patterns, sequences, and functions. Students examine activities, models, and techniques for introducing and developing algebra topics in the elementary and middle school classrooms. Prerequisite: MATH 5064 or MATH 6062.

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 5210 or equivalent.

6501 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.

6502 GEOMETRY WITH TECHNOLOGY FOR ELEMENTARY AND MIDDLE LEVEL TEACHERS (3 credits) This class uses technology to explore the concepts of location, symmetry, tiling, congruence, similarity, and the use of transformations. Emphasizes instructional strategies, manipulatives, and tools to enhance student understanding. Prerequisite or Corequisite: MATH 6501.

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. Prerequisite: MATH 5210 or equivalent.

6601 DATA INVESTIGATIONS FOR ELEMENTARY AND MIDDLE LEVEL TEACHERS (3 credits) Study of the collection, display, and analysis of data for the classroom. Emphasizes instructional strategies to help all students learn. Topics include identification of questions, collection of data, organization of data, representations of data, measures of central tendency, measures of spread, and analysis and reporting of results. Prerequisite: Teaching experience or consent of the instructor.

6602 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 or Corequisite: MATH 6601.

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.

5899 DESIGN OF EXPERIMENTS (3 credits) This course focuses on the planning, execution, and analysis of industrial experiments. Topics include, but are not limited to, the analysis of variance, fitting of regression models, factorial experiments, blocking, confounding, fractional factorial experiments, response surface methodology, nested and split-plot experiments, mixed-level experiments, and experiments with random factors.

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