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
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.

Graduate Mathematics Program | All-University Courses and Descriptions

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