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

Mathematics (MATH)

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 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.

**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** (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.

**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: MATH
5631.

**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.

**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 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.

**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.

Graduate Mathematics Program | All-University Courses and Descriptions

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