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Mathematics (MATH)

Check with department for semester when these courses are offered. Read each course description for prerequisites

1011 MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS I (3 credits) This course meets the new BOT fundamental topics in arithmetic competencies. These topics include addition, subtraction, multiplication, and division of whole numbers; number theory related to fractions; fractions; decimals; and integers. This is the first of two mathematics courses providing the background for teaching in the elementary school. Emphasizes the use of mathematics manipulatives for modeling the basic operations. Prerequisite: Elementary education major or consent of instructor.

1012 MATHEMATICS FOR THE MINNESOTA GRADUATION STANDARDS-ELEMENTARY (1 credit) A second mathematics course for elementary education majors. Provides background in mathematics which is essential for preparing students to meet the Minnesota Graduation Standards. Real numbers, ratio and proportion, percentiles, and probability and statistics will be considered. Prerequisite: Elementary education major or consent of the instructor. Note: Course should be taken concurrently with or subsequent to MATH 1011.

1013 MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS II (3 credits) This course meets the new BOT introduction to higher mathematics competencies. These topics include geometry, discrete mathematics, probability, and statistics. This is the second of two mathematics courses providing the background for teaching in the elementary school. Emphasizes the use of mathematics manipulatives for modeling the basic concepts. Prerequisite: MATH 1011.

1100 ALGEBRA AND MATHEMATICAL REASONING (4 credits) Algebraic concepts, including linear and quadratic equations and functions. Descriptive statistics; an introduction to probability and inferential statistics. Mathematical reasoning as applied to a selection of topics, which may include the mathematics of social choice, the mathematics of management, geometry, and problem solving. A graphing calculator is required. Not open to students who have completed MATH 1110. Prerequisites: Two years of high school algebra and an appropriate score on the Mathematics Placement Test or completion of MATH 0800 with a grade of C or better. Liberal Education Category 4

1107 INTRODUCTION TO MATHEMATICAL SCIENCES (3 credits) This course integrates the study of algebra, statistics, and computing in a laboratory-instruction environment. Topics include functions, graphical and tabular analysis, rate of change, syntax and semantics, the process of computing, data manipulation, sampling, statistical measures, basic probability, and correlation. Examples are drawn from a wide range of disciplines and content is taught within the framework of discipline-specific examples. Students learn to use the software package Microsoft Excel. Prerequisites: Two years of high school algebra and an appropriate score on the Mathematics Placement Test or MATH 0800 with a grade of C or better. Liberal Education Category 4

1110 BEGINNING COLLEGE ALGEBRA (3 credits) Algebraic concepts including linear, quadratic, rational and absolute value equations and inequalities; function notation; complex numbers; graphs of relations and functions including lines and parabolas. A graphing calculator is required. Not open to students who have completed MATH 1100. Prerequisite: Two years of high school algebra and an appropriate score on the Mathematics Placement Test or MATH 0800 with a grade of C or better. Liberal Education Category 4

1170 COLLEGE ALGEBRA (3 credits) Functions including polynomial, rational, inverse, exponential, and logarithmic functions; systems of equations and inequalities, matrices, sequences and series, binomial theorem, permutations and combinations. Prerequisites: Successful completion of MATH 1110, or three years of high school mathematics (including two years of algebra) and an appropriate score on the Mathematics Placement Test. Liberal Education Category 4

1470 PRECALCULUS (5 credits) Intended to provide the essential mathematical background needed in calculus. Topics include equation solving, functions (including polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric), identities, applications, and parametric equations. A graphing calculator is required. Prerequisites: Three years of high school mathematics (including two years of algebra with a half year of trigonometry strongly recommended) and an appropriate score on the Mathematics Placement Test, or completion of MATH 1110 with a grade of B or better. Liberal Education Category 4

2171 CONCEPTS OF CALCULUS I (5 credits) A broad overview of both differential and integral calculus with applications in the areas of business, life, and behavioral sciences. This course has less rigor than MATH 2471 and is for students majoring in non-mathematically orientated disciplines. A graphing calculator is required. Prerequisite: A grade of C or better in MATH 1170 or MATH 1470 (Not open to majors in mathematics, computer science, physics, chemistry, or students who have successfully completed MATH 2471.) Liberal Education Category 4

2172 CONCEPTS OF CALCULUS II (3 credits) Investigate Taylor's series, and its applications, indeterminate forms and L'Hopital's Rule, numerical techniques, root approximations, interpolating polynomials, numerical integration, discrete and continuous probability functions, simulation and application. A graphing calculator is required. Prerequisite: Successful completion of MATH 2171. Liberal Education Category 4

2471 CALCULUS I (5 credits) Limits, differentiation and integration of algebraic and trigonometric functions; applications of the derivative and curve sketching; applications of integration. A graphing calculator is required. Prerequisite: An appropriate score on the Mathematics Placement Test or a grade of C or better in MATH 1470. Liberal Education Category 4

2472 CALCULUS II (5 credits) Differentiation and integration of transcendental functions, techniques of integration, infinite sequences and series, parametric equations, polar coordinates, analytic geometry, and vectors. A graphing calculator is required. Prerequisite: A grade of C or better in MATH 2471. Liberal Education Category 4

2480 MULTIVARIABLE CALCULUS (4 credits) Three dimensional analytic geometry, spherical, and cylindrical coordinate systems, vectors, partial derivatives, and multiple integrals. A graphing calculator is required. Prerequisite: Successful completion of MATH 2472.

2490 DIFFERENTIAL EQUATIONS (4 credits) Ordinary differential equations including first order and second order linear equations, series solutions, Laplace transformations, existence and uniqueness theory, systems of linear and nonlinear equations, dynamical systems and applications. A graphing calculator is required. Prerequisite: MATH 2472.

3010 MATHEMATICS FOR PRE-K TO GRADE 3 (3 credits) Students gain understanding of appropriate mathematics and pedagogy for young children from pre-K through the primary grades. Prerequisite: Liberal Education Math course and ED 3670.

3050 MATH MODELS, GAMES, AND ACTIVITIES FOR THE PRIMARY GRADES (2 credits) For teachers of grades K-3. Mathematical background including teaching-aids, games, projects, and activities that relate to the primary level will be presented. The basic mathematical operations will be presented from a "concrete" standpoint. Set theory, numeration, and the systems of whole numbers and rational numbers will be considered. Prerequisite: Teaching experience or consent of instructor.

3051 MATH MODELS, GAMES, AND ACTIVITIES FOR THE INTERMEDIATE GRADES (2 credits) For teachers of grades 3-6. Mathematical background including teaching-aids, games, projects, and activities that relate to the intermediate level will be presented. The basic mathematical operations will be presented from a "concrete" standpoint. The systems of integers, rational numbers, and real numbers; ratio and proportion; percentiles; and elementary functions will be considered. Prerequisite: Teaching experience or consent of instructor.

3052 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.

3054 MATH ACTIVITIES FOR THE JUNIOR HIGH/MIDDLE SCHOOL CLASSROOM (3 credits) Presents and analyzes mathematical activities, models, games, and related background material that can be used to supplement textbook instruction. Prerequisite: Teaching experience or consent of instructor.

3056 MATH ACTIVITIES FOR THE SECONDARY CLASSROOM (3 credits) Presents and analyzes mathematical activities, models, games, and related background material that can be used to supplement textbook instruction. Prerequisite: Teaching experience or consent of instructor.

3064 NUMBER CONCEPTS FOR ELEMENTARY AND MIDDLE SCHOOL TEACHERS (4 credits) This course meets or helps meet the new BOT rule with respect to number sense and concepts of patterns, relations, and functions. 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 1011 or equivalent. (Might not be offered every year)

3065 MATHEMATICAL FOUNDATIONS FOR ELEMENTARY AND MIDDLE SCHOOL TEACHERS (4 credits) This course meets or helps meet the new BOT rule with respect to concepts of patterns, relations, and functions; discrete mathematics; probability; and statistics that are pertinent to middle school mathematics. Prerequisite: MATH 1011 or equivalent. (Might not be offered every year)

3066 UTILIZING TECHNOLOGY IN THE ELEMENTARY AND MIDDLE SCHOOL MATHEMATICS CLASSROOM (4 credits) This courses meets the licensure rule with respect to concepts of patterns, relations, and functions; shape and space; limits and derivatives; and appropriate use of technology in the classroom. Prerequisites: MATH 1011 and MATH 1100 or MATH 1110 or equivalent; Recommended: CS 1107 or computer competency. (Might not be offered every year)

3210 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. Prerequisites: Sophomore status and MATH 2471.

3230 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 3210.

3260 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 3210. (Might not be offered every year)

3310 LINEAR ALGEBRA (4 credits) Systems of linear equations, linear transformations, matrix operations, vector spaces, eigenvalues and eigenvectors, orthogonality, and applications. Prerequisites: MATH 2472 and MATH 3210 or consent of instructor.

3410 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. Prerequisites: MATH 2472 and MATH 3210.

3440 INTRODUCTION TO FRACTALS AND CHAOS (3 credits) An introduction to 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. Prerequisites: MATH 2472 and MATH 3210. (Might not be offered every year)

3560 CLASSICAL AND MODERN GEOMETRY (3 credits) Euclidean and non-Euclidean geometry, axiomatic systems, the geometry of solids, transformations, measurement, and fractal geometry. Prerequisite: MATH 3210.

3710 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. Prerequisite: MATH 2472. (Might not be offered every year)

3741 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: MATH 2472.

3742 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. Prerequisites: MATH 2480 and MATH 3741 or consent of instructor. (Might not be offered every year)

3820 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. Prerequisites: Junior or senior status and consent of the instructor. (Might not be offered every year)

4240 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 3210. (Might not be offered every year)

4350 ABSTRACT ALGEBRA (3 credits) A study of abstract algebraic systems with an emphasis on the development of number systems, properties of polynomials, rings, integral domains, and fields. Prerequisites: MATH 3210 and MATH 3310. (Might not be offered every year)

4371 MODERN ALGEBRA (3 credits) A study of abstract algebraic systems with an emphasis on groups and an introduction to rings. Prerequisite: MATH 3310.

4470 ADVANCED CALCULUS (3 credits) Properties of limits, vector valued functions, infinite series, Taylor series, uniform convergence, improper integrals, convergence in the mean and Fourier series. Prerequisite: MATH 2480 and MATH 3210. (Might not be offered every year)

4480 COMPLEX ANALYSIS (3 credits) Complex number system, polar form, analytic functions, differentiation and integration, series, residues, conformal mapping, Schwarz-Christoffel transformations, and applications. Prerequisites: MATH 2480 and MATH 3210. (Might not be offered every year)

4890 SEMINAR IN MATHEMATICS (1-4 credits) Lecture, group discussion, readings in an area or field of mathematics. Prerequisite: MATH 3210 or consent of instructor.

4980 RESEARCH PROJECT AND PRESENTATION (0 credits) This research and presentation is part of an approved upper division mathematics course. Students engage in research on a specialized mathematics topic or application selected by the student in consultation with the course instructor; students present the research results in a public forum. This course is graded Satisfactory/Unsatisfactory only. Prerequisite: Junior or senior status; Corequisite: MATH 3310 or MATH 3410 or MATH 3560 or MATH 3742 or MATH 4240 or MATH 4371 or MATH 4470 or MATH 4480 or STAT 3631 or STAT 3632.

Statistics (STAT)

Check with department for semester when these courses are offered. Read each course description for prerequisites

3610 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. Prerequisites: (MATH 2472 and STAT 2610) or STAT 3631. (Might not be offered every year)

3631 PROBABILITY AND STATISTICS I (4 credits) Probability of finite sample spaces, discrete and continuous probability distributions, exploratory data analysis, statistical models. Prerequisites: MATH 2472.

3632 PROBABILITY AND STATISTICS II (3 credits) Multivariable distributions, sampling distribution theory, estimation, hypothesis testing, regression and correlation. Prerequisites: MATH 2480 and STAT 3631. (Might not be offered every year)

3650 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. Prerequisite(s): MATH 2471.

3660 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. Prerequisite: MATH 1170 or consent of instructor.

4899 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. Prerequisite: STAT 2610 or consent of instructor. (Might not be offered every year)