BSU Catalog Home | Graduate Mathematics Program | All-University Courses and Descriptions
College-Program Codes: 7-10
NOTE: Please see your advisor regarding course sequencing and any expected preparation.
5050 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.
5051 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.
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.
5054 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.
5056 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.
5064 NUMBER CONCEPTS FOR ELEMENTARY TEACHERS (4 credits) Designed to provide the student with a background in special number concepts which are pertinent to elementary school mathematics. Topics include: 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. Special emphasis will be given to problem solving techniques as they relate to number concepts. Prerequisite: MATH 5052 or equivalent.
5065 MATHEMATICAL FOUNDATIONS FOR ELEMENTARY TEACHERS (4 credits) Designed to provide students with a foundation in elementary algebraic structures, probability, and elementary statistics. Students will also analyze problem solving strategies and the use of calculators in the elementary classroom. Prerequisite: MATH 5052 or equivalent.
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.
5350 MATRIX ALGEBRA (3 credits) Operations on matrices, solving linear systems of equations, determinants, similar matrices, orthogonalization, and canonical forms. Prerequisite: MATH 5210.
5371 MODERN ALGEBRA I (3 credits) A study of abstract algebraic systems with an emphasis on groups and an introduction to rings. Prerequisite: MATH 5310 or equivalent.
5372 MODERN ALGEBRA II (3 credits) A study of abstract algebraic systems with emphasis on rings, integral domains, and fields. Prerequisite: MATH 5371 or consent of instructor.
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 5410.
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 5410.
5560 ADVANCED EUCLIDEAN GEOMETRY (3 credits) A rigorous examination of secondary school geometry, the interaction of definitions, postulates, and theorems in the study of the structure of geometries. Prerequisite: MATH 5210.
5570 GEOMETRY OF CURVES AND SURFACES (3 credits) An introduction of the geometry of hypersurfaces with the goal of introducing the basic notions of differential geometry through examples of curves, and surfaces. These include vector fields, orientation, Gauss map, geodesics, curvature, surface area and volume, Stoke's Theorem and the Gauss-Bonnet Theorem. Prerequisite: MATH 5310.
5631 PROBABILITY AND STATISTICS I (4 credits) Probability of finite sample spaces, discrete and continuous probability distributions, exploratory data analysis, statistical models. Prerequisite: MATH 5210 or equivalent.
5632 PROBABILITY AND STATISTICS II (3 credits) Multivariable distributions, sampling distribution theory, estimation, hypothesis testing, regression and correlation. Prerequisite: MATH 5631.
5730 MATHEMATICS OF FINANCE (3 credits) A thorough and modern treatment of mathematics of investment, incorporating both theory and applications. Topics to be covered are the measurement of interest, annuities, yield rates, amortization schedules and sinking funds, bonds and other securities.
5741 NUMERICAL ANALYSIS 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, and the method of steepest descent. Prerequisite: Programming competency or consent of instructor.
5742 NUMERICAL ANALYSIS AND OPTIMIZATION II (3 credits) Numerical solutions of differential and partial 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. Prerequisite: MATH 5741.
5750 LINEAR PROGRAMMING (3 credits) Mathematical models applicable to linear programming, systems of linear equations and inequalities, graphical methods, the simplex method and game theory.
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.
5890 SEMINAR IN MATHEMATICS (1-4 credits) Lecture, group discussion, readings in an area or field of mathematics. Prerequisite: MATH 5210 or consent of instructor.
6350 ABSTRACT ALGEBRA FOR SECONDARY TEACHERS (3 credits) For secondary school mathematics teachers. Designed to deepen the algebraic background of the student through the study of the real number system, applications of deduction, functional concepts, and other concepts of an algebraic nature. Prerequisites: MATH 5210 and MATH 5310.
6450 FOUNDATIONS OF CALCULUS (3 credits) Designed to strengthen the students' knowledge and understanding of the logical structure of calculus. Examines the results of calculus and provides a logical development of calculus theories. Prerequisite: Consent of the instructor.
6550 GEOMETRY FOR SECONDARY TEACHERS (3 credits) For pre-service and in-service secondary school teachers. Elementary geometric concepts, special problems, activities, and modern trends in geometry and their implications in secondary school mathematics.