## MTHC - Mathematics for Educators |

**2017-2018 GRADUATE STUDIES CATALOG**

**Effective 1 June 2017 through 31 May 2018**

*Please see the Graduate Catalog Archives for PDF versions of past catalogs.*

## Course Descriptions

### MTHC 5040 Number Theory (3)

Students examine the basic concepts of number theory with an emphasis on modular systems and their application to a variety of empirical problems.

### MTHC 5080 Puzzles and Proofs (3)

This course examines a variety of materials useful in developing reasoning skills. Included are attribute block puzzles, Lewis Carroll puzzles, logic puzzles, and a variety of games which require deductive reasoning.

### MTHC 5100 Functions and Structure (3)

This course investigates a variety of mathematical systems and functions.

### MTHC 5110 Perspectives in Elementary Geometry (3)

This course focuses on geometry for grades 5-8. May be repeated for credit if content varies.

### MTHC 5120 Topics for the Middle School Teacher (3)

This course covers areas of mathematics and/or mathematics education of particular interest to middle school teachers. Content varies according to the interests of faculty and students. May be repeated for credit if content varies. Not offered at the St. Louis campus.

### MTHC 5130 Probability and Graphs (3)

Part of this course covers topics from probability and statistics with applications to gambling and game theory. The other part covers graphs, trees, and finite state automata.

### MTHC 5150 Number Systems (3)

This course provides middle school teachers with a deeper understanding of the real number system. Topics covered include arithmetic algorithms in negative and whole number bases; rational and irrational numbers; arithmetic and geometric progressions; number properties; mental arithmetic; factorization and divisibility of integers and of Gaussian integers; and number puzzles and games.

### MTHC 5200 Independent Study (1-6)

Students with special interests or needs that are not met by existing curricula may request that a member of the faculty supervise an independent study. Together the student and faculty member decide the content of the independent study and the criteria for evaluation. In no case may an independent study be set up when an existing course already covers the subject. May be repeated for credit if content varies.

### MTHC 5210 In-Service Education (1-4)

Webster offers various graduate in-service courses that are not part of the existing curricula but provide experiences important to the academic and professional development of educators. Consult the semester course listings for specific topics. May be repeated for credit if content varies. This course does not apply toward an MA in mathematics for educators.

### MTHC 5230 Discrete Mathematics (3)

This course covers mathematical structures pertinent to an understanding of computers, including graphs, Boolean algebra, and finite state machines.

### MTHC 5250 Vector Geometry (3)

Basic concepts pertaining to vectors in the plane are developed. Proofs of theorems of plane geometry, using a synthetic approach, an analytic approach, and a vector approach are compared. The class introduces vector spaces.

### MTHC 5260 Algebra for Secondary Teachers (3)

Students examine and extend topics in secondary school algebra. Techniques and materials for teaching algebra are also discussed.

### MTHC 5280 Calculus for Teachers (3)

The course reviews the basic concepts of differential and integral calculus, with special focus on central ideas,theory, and applications. Computers and/or graphing calculators are used to help investigate ideas. Students enrolling in this course are assumed to have completed the undergraduate calculus sequence with grades of B or higher.

### MTHC 5300 History of Mathematics (3)

This course is based on selected readings that examine the history and philosophy of mathematics. An important goal is to provide students with a perspective on the relationship between mathematics and culture as well as an insight into how and why mathematical ideas have evolved. May be repeated for credit if content varies.

### MTHC 5310 Geometry for Secondary Teachers (3)

This course deals with areas of geometry relevant to high school teachers. Content varies according to the interests of the faculty and students. May be repeated for credit if content varies.

### MTHC 5320 Topics in Mathematics (3)

Typically this course introduces areas of mathematics not covered in other courses. Content depends upon the interests of the faculty and students. May be repeated for credit if content varies.

### MTHC 5330 Probability (3)

Participants study probability on finite sample spaces along with applications to gambling and game theory.

### MTHC 5340 Topics in Mathematics Education (1-3)

The content of this course will include an analysis of curricular materials, teaching methods, and/or issues in mathematics education. May be repeated for credit if content varies. Not offered at the St. Louis campus.

### MTHC 5350 Logic (3)

This course includes propositional and predicate logic, with the objective of increasing students’ understanding of what constitutes valid reasoning, as well as increasing their ability to express formal mathematical arguments.

### MTHC 5360 Algebraic Structures (3)

Students examine the algebra of various mathematical structures with the goal of gaining a broader and more sophisticated understanding of ordinary algebra. Relevant theory is developed.

### MTHC 5370 Linear Algebra (3)

Concepts and techniques of linear algebra are developed.

### MTHC 5390 Statistics (3)

This course covers the basic concepts (including applications) of the binomial and normal distributions, the chi-square test, analysis of variance, and nonparametric statistics. Emphasis is placed on educational applications as well as the abuses and misuses of statistical ideas. Computers and/or graphing calculators are used to investigate ideas.

### MTHC 5410 In-Service Topics (1-3)

In-service courses are designed to provide teachers with practical applications of contemporary research and methodology to improve classroom effectiveness. May be repeated for credit if content differs. This course does not apply toward an MA degree in mathematics for educators.

### MTHC 5430 The Real Number System (3)

The course covers the algebraic and topological properties of the real number system and several of its subfields and subrings.

### MTHC 5450 Topics in Number Theory (3)

This course covers selected topics in number theory, such as modular systems, quadratic reciprocity, number-theoretic functions, Pythagorean Triples, and perfect numbers. Specific topics to be determined by instructor. Relevant theory will be developed.

### MTHC 5480 Problem-Solving Strategies in Mathematics (3)

The primary objective of this course is to help students develop reasoning strategies that are powerful tools in solving problems.

### MTHC 5500 Studies in Mathematics (1-6)

Courses in this category are offered on an irregular basis. May be repeated for credit if content varies.

### MTHC 5900 Final Reflections (0)

All math students are required to register for this zero-credit hour course during their penultimate semester. Students write an essay describing how they have changed as a result of their participation in the math program. For specific guidelines see the math coordinator. This course is graded on a credit/no credit basis only.

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