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BSU Catalog Home | Graduate Mathematics Program | All-University Courses and Descriptions

Mathematics (MATH)

**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 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
5052 or equivalent.

**5065
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
5052 or equivalent.

**5066 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.

**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.

**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.

**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.

**6150 SECONDARY SCHOOL MATHEMATICS FROM AN ADVANCED STANDPOINT** (3 credits) Advanced treatment of trigonometry, polar coordinates, complex numbers, conic sections, exponential functions, logarithmic functions, and hyperbolic functions with an emphasis on strategies for teaching these topics in the secondary school classroom.

**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.

**6450 FOUNDATIONS OF CALCULUS** (3
credits) Designed to strengthen the students’ knowledge and understanding of calculus. This course examines the results, historical development and the theory of calculus. Prerequisite:
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.

Graduate Course Offerings

Statistics (STAT)

**NOTE:** Please see your advisor regarding course sequencing and any expected preparation.

**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.

Graduate Mathematics Program | All-University Courses and Descriptions

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