Southeast Missouri State University

MA 523. Probability and Statistics I.

 Introduction to probability and statistics using the tools of calculus. Algebra of probability, random variables, discrete and continuous distributions. Prerequisite or Corequisite: MA 240. (3)  

MA 524. Probability and Statistics II.

Continuation of MA 523 with emphasis on applications, sampling, estimation, hypothesis testing, regression, experimental design, nonparametric methods. Prerequisite: MA 523. (3)  

MA532. Foundations of Geometry.

Historical development of the axiomatic approach to Euclidean geometry and non-Euclidean geometries, coordinate systems for affine and projective planes, and metric postulates for Euclidean, hyperbolic, and elliptic planes. Prerequisite: MA250 with a grade of ‘C’ or higher. (3)    

MA538. History of Mathematics.

A historical account of mathematics from the time of Newton and Leibniz to its twentieth century developments.  Prerequisite: MA139 or MA140 with a grade of ‘C’ or higher. (3)  

MA 540. Projective Geometry.

Noneuclidean geometries, study of projective geometry and its relation to other geometries. Prerequisite: MA 340 or 10 hours of mathematics courses numbered above MA 140. (3)  

MA 544. Numerical Analysis.

Approximation procedures, numerical differentiation and integration, numerical solution of equations, systems of equations and differential equations with reference to computers. Prerequisites: MA 240; MA 334. (3)  

MA 545. Linear Algebra and Matrices.

Introduction to vector spaces, linear transformations, matrices, eigenvalues, eigenvectors and numerical methods in linear algebra. Prerequisite: MA 445. (3) 

MA 546. Advanced Calculus I.

Elementary set theory and topology, sequence and series, continuity and differentiability of functions on Euclidean nspace. Prerequisites: MA 240; MA 250. (3)  

MA 547. Advanced Calculus II.

Convergence of series of functions, Implicit Function Theorem, integration. Prerequisite: MA 546. (3)  

MA548. Enumerative Combinatorics.

A study of basic enumeration techniques, recurrence relations, generating functions, the inclusion-exclusion principle, Ramsey theory, partially-ordered sets, and combinatorial designs. Prerequisite: MA145 and MA250. (3)    

MA549. Graph Theory.

Basic parameters and properties of graphs, representations, trees, connectedness, Eulerian and Hamiltonian cycles and paths, matchings, edge and vertex colorings, independent sets and cliques, planar graphs, directed graphs, multigraphs. Prerequisite: MA145 and MA250. (3)  

MA 550. Differential Equations II.

Theory and techniques of solving ordinary differential equations, partial differential equations and boundary value problems. Applications, numerical methods and stability. Prerequisite: MA 350. (3)  

MA 560. Research Methods in Mathematics.

An overview of research methods. Practice in the methods for the formulation and solution of problems. Prerequisite: MA 240 or MA 445. (3)  

MA580. Experimental Design and Analysis of Variance.

Completely randomized design and analysis, randomized block design and analysis, factorial experiments, split-plot design and analysis, repeated measurement experiments and analysis, analysis of covariance. Prerequisites: MA223 (Elementary Probability and Statistics) or consent of instructor. (3) 

MA625. Applied Regression Analysis.

Learn how to use regression to represent a relationship between explanatory variables and their associated response. Emphasis will be on analyzing actual datasets. The following topics will be covered: simple linear regression, multiple regression, prediction, variable selection, residual diagnostics, auto-regression, and logistic regression. Prerequisites: MA223. (3)  

MA630. Basic Concepts of Modern Mathematics.

An introduction to logic and sets, algebraic systems, and elementary concepts in geometry. Designed for elementary school teachers. (3)  

MA632. Foundations of Geometry.

Historical development of the postulational approach to geometry, coordinatization of affine and projective planes and metric postulates for Euclidean, hyperbolic, and elliptic planes. (3)  

MA633. Differential Geometry.

Basic properties of curves and surfaces in three dimensional space, arc length, curvature, torsion. Frent-Seret formulas, surface normal, tangent plane, fundamental forms of surface theory. Prerequisite: MA240. (3)  

MA635. Topology.

Study of sets, relations, functions, products, cardinality, metric spaces, topological spaces, convergence, continuity, separation axioms, connectedness, compactness, homotopy, and fundamental group. (3)  

MA636. The Nature of Mathematical Thought.

This course will examine the nature of mathematics along with its historical, social, and cultural aspects. Students will become familiar with the national as well as state principles and standards for teaching and learning mathematics. Students will explore current issues and trends in mathematics education. Credit only for The Missouri Cooperative Online Masters Degree in Teaching and Learning-Elementary Education. Prerequisites: Successful completion of the program's core courses. (3)  

MA637. Mathematical Processes.

This course will examine both finite and infinite mathematical processes used when solving problems involving discrete or continuous data. The course connects experiences from the concepts of numbers, algebra, and data analysis. Credit only for The Missouri Cooperative Online Masters Degree in Teaching and Learning-Elementary Education. Prerequisites: Successful completion of the program's core courses and MA636. (3)  

MA638. History of Mathematics.

A historical account of mathematics from the time of Newton and Leibniz to its twentieth century developments. (3)  

MA640. Seminar in Contemporary School Mathematics.

A survey of the major issues and curricular trends in mathematics for secondary schools (7-12). Prerequisites: Secondary mathematics teaching experience or consent of instructor. (3) 

MA641. Geometry and Measurement.

In this course, students will use geometric concepts and relationships to describe and model mathematical ideas and real world constructs and understand measurable attributes of objects and the units, systems, and processes of measurement. The student will formulate questions that can be addressed with data and collect, organize, and display relevant data. Credit only for The Missouri Cooperative Online Masters Degree in Teaching and Learning- Elementary Education. Prerequisites: Successful completion of the program's core courses and MA636. (3)  

MA642. Groups and Fields.

Groups, Group Actions, Sylow Theorems, Abelian Groups, Field Extensions, Galois Theory. Prerequisites: MA445. (3)  

MA643. Number Theory.

A study of prime numbers, congruences, quadratic residues, and numerical functions. Prerequisites: MA 443 Elementary Number Theory or consent of instructor. (3)  

MA644. Rings and Modules.

Rings, Ideals, Quotient Rings, Domains, Polynomial Rings, Modules, Modules over PIDs, Commutative Rings. Prerequisites: MA445. (3)  

MA645. Algebra.

A study of the basic algebraic (number) systems including groups, rings, modules, and categories. Prerequisites: MA445 and either MA345 or MA545 or consent of instructor. (3)

 MA646. Modern Real Analysis.

Sets, metric spaces, Lebesgue integral, Hilbert spaces. Prerequisites: MA546 Advanced Calculus I. (3)  

MA647. Complex Analysis.

Complex numbers, analytic function, integrals, power series, residues and poles, and conformal mapping. Prerequisites: MA240. (3)  

MA648. Independent Study in Mathematics.

Study of topics in specialized area not covered by regular course offerings. (1)  

MA649. Independent Study in Mathematics.

Study of topics in specialized area not covered by regular course offerings.(2)  

MA650. Independent Study in Mathematics.

Study of topics in specialized area not covered by regular course offerings.(3)  

MA651. Mathematics Capstone.

In this course students will synthesize and demonstrate their understanding of mathematical concepts learned in the three prerequisite mathematics courses by successful completion of a final independent paper/project. Other activities will be assigned to connect and extend the student's existing mathematical knowledge and experiences. Credit only for The Missouri Cooperative Online Masters Degree in Teaching and Learning-Elementary Education. Prerequisites: Successful completion of the program's core courses and MA636, MA637, and MA641. (3)  

MA664. Mathematical Cryptography.

Basic concepts of secure communication, classical cryptography and cryptoanalysis, monoalphabetic and polyalphabetic ciphers. Shannon’s theory of secrecy. Modern private-key cryptosystems such as DES, and public-key cryptosystems such as RSA. Prerequisites: One of the following (with a minimum grade of ‘C’): MA223, MA250, MA338, MA345, or MA443. (3)  

MA694. Thesis.

A written report based upon investigation of some subject or the completion of a creative project. See Thesis Plan for additional information. (3)  

MA695. Thesis.

A written report based upon investigation of some subject or the completion of a creative project. See Thesis Plan for additional information. Second semester. (3)  

MA696. Thesis.

A written report based upon investigation of some subject or the completion of a creative project. See Thesis Plan for additional information. Second semester. (2)  

MA697. Thesis.

A written report based upon investigation of some subject or the completion of a creative project. See Thesis Plan for additional information. Second semester. (1)

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