# MATHE - Secondary Education Mathematics Course Descriptions

## MATHE 1000E The History of Mathematics

Historical evaluation of mathematical concepts. Selected topics related to elementary geometry and algebra, analytic geometry and calculus, and the modern postulational viewpoint.

3

3 hr./wk.

## MATHE 1100E Advanced Euclidean Geometry

Extensions and generalization of elementary geometry; higher geometry of triangles, circles, quadrilaterals; constructions, classical problems.

3

3 hr./wk.

## MATHE 1200E Fundamental Concepts of Modern Mathematics

Limit, length, area, volume (non-limit/limit developments). Euler's Theorem and consequences, angle-sum formulae (De-Gua) and generalization, isomorphic subdivisions. Pythagorean Theorem and Special Relativity. Combinational concepts. Foundations, axiomatics, proof-theory.

3

3 hr./wk.

## MATHE 1900E Mathematical Computer Software

Survey of mathematical computer software. Using Geometer's Sketchpad to learn advanced geometry theorems. Sample programming problems drawn from scientific and mathematical applications.

3

3 hr./wk.

## MATHE 2100E Probability

Finite sample spaces; probability as set function; permutations, combinations, conditional probability and Bayes' Theorem; independent events; random variables and distribution functions; expected values; Chebyshev's inequality.

3

3 hr./wk.

## MATHE 2200E Mathematical Statistics

Frequency histograms, measures of location and dispersion, correlation and least squares, testing hypotheses, confidence intervals and estimation.

3

### Prerequisites

A course in probability.

3 hr./wk.

## MATHE 2600E Linear Algebra

Vector spaces, matrices, systems of linear equations, determinants, linear transformations.

3

3 hr./wk.

## MATHE 2700E The Theory of Numbers

A study of problems concerning numbers as well as properties of numbers. Included are: divisibility, continued fractions, diophantine equations, primes, congruences. Fermat's and Euler's Theorems, quadratic residues and reciprocity, number theoretic functions.

3

3 hr./wk.

## MATHE 2800E Numerical Analysis

Solution of algebraic equations by iteration interpolation; numerical integration; solution of ordinary differential equations.

3

### Prerequisites

One year of calculus.

3 hr./wk.

## MATHE 2900E Topics in Higher Algebra

Topics include: polynomials and their properties, solution of third and fourth degree equations by formula and approximation, impossibility of solving equations of fifth degree or higher, real and complex roots of nth degree equations; other fundamental concepts of elementary algebra from an advanced standpoint.

3

3 hr./wk.

## MATHE 3200F Indpt Study Resrch Math

Open to qualified graduate students in the School of Education interested in the study of special problems. MAY BE REPEATED FOR A MAXIMUM OF SIX CREDITS.

1-3

### Prerequisites

Requires sponsorship by an appropriate faculty member and approval of the Advisory Committee.

### Contact Hours

VARIABLE 1-3 CR./SEM. Hours to be arranged.

## MATHE 3200F-3203F Independent Study and Research in Mathematics

Open to qualified graduate students in the School of Education interested in the study of special problems. May be repeated for a maximum of six credits.

### Credits

Variable 1-3 cr./sem

### Prerequisites

Requires sponsorship by an appropriate faculty member and approval of the Advisory Committee.

### Contact Hours

Hours to be arranged.

## MATHE 3700E Topology

Examples and classifications of surfaces; metric and topological spaces.

3

3 hr./wk.

## MATHE 4600C Introduction to Mathematical Thinking

This course discusses mathematical thinking and methods for theorem proving. It includes truth tables, basic set theory, equivalence relations and functions, mathematical induction and other techniques for discussing and proving mathematical statements. Material to be proven will be drawn primarily from basic number theory and elementary combinatorics. This course may be required of students with insufficient background in abstract mathematics.

3

3 hr./wk.

## MATHE 4700C Modeling with Algebraic and Trigonometric Functions

In this course, students will use algebra, geometry, and trigonometry to mathematize real life problems. Students will formulate questions, identify assumptions, collect data, and build and revise mathematical models. Students will use multiple representations and methods including formulas, diagrams, graphs, and procedures, and technology in modeling. Particular attention will be paid to linear, polynomial, exponential, logarithmic and trigonometric functions. Students will be asked to interpret models in contexts and will be expected to communicate effectively about connections they see, representations they create, and generalizations they make. Technological tools such as graphing calculators will be used to facilitate the learning. Adolescent certification candidates may not take this course for graduate credit without permission of the mathematics advisor.

3

### Prerequisites

MATHE 4600C or permission.

3 hr./wk.

## MATHE 4800C Foundations of Geometry

Continuation of MATHE 4700C. Further study of the theory of numbers, equations, inequalities, proof in a mathematical system, metric and non-metric geometry, topics in topology, probability and statistics. Senior high school mathematics teachers may not take this course for graduate credit without permission of the mathematics advisor.

3

3 hr./wk.

## MATHE 4900C Fundamental Ideas of Calculus

Through the use inquire and discovery students will apply prior knowledge to explore the ideas and principles of calculus. Topics covered will include sequences and series; functions with a focus on the ideas of limits and continuity; differentiation with a focus on rates of change, optimization, graph sketching and exponential change; integration with a focus on area and volume. Students will also use mathematical tools such as graphing calculators to explore concepts and applications of calculus. Technological tools such as graphing calculators will be used to facilitate the learning.

3

### Prerequisites

MATHE 4700C and MATHE 4800C.

3 hr/wk

## MATHE 5000C Data Analysis, Probability and Statistics

The course aims to develop a deep and flexible understanding of basic data analysis (probability and statistics) concepts and applications. Topics include descriptive statistics such graphs (histograms, box plots), two-way tables, and summary statistics (mean, median, mode, standard deviation, range) to describe data, sampling and study design, probability distributions, conditional probability, combinations, permutations, expected value and introduction to inference. Students will use technology such as spreadsheets to explore and analyze data sets.

3

3 hr./wk.

## MATHE 6000C High School Mathematics from an Advanced Perspective

In this course, students will examine the topics in the high school curriculum through the lens of advanced college level mathematics courses (including Calculus, linear algebra, modern geometry, real analysis, abstract algebra and number theory). Connections between the mathematics taught in high school and college will be stressed, and students will also develop increased understanding of the connections between algebraic, geometric, and logical thinking. Students will be asked to interpret mathematical ideas in contexts and will be expected to communicate effectively about connections they see, representations they create and generalizations they make.

3

### Prerequisites

One proof intensive course and Calculus II, Linear Algebra.

3 hr./wk.

## MATHE 6500C Mathematical Applications in Science and Industry

Mathematics in contemporary science and industry, as illustrated in representative examples ranging through the mathematical subjects taught in secondary schools, but including other mathematics as well. Introduction to mathematics underlying instrumentation in science and technology.

3

3 hr./wk.

## MATHE 7400E Foundations of Geometry

The basic concepts of Euclidean Geometry and the underpinnings of non-Euclidean Geometry.

3

3 hr./wk.

## MATHE 7500E Classic Applications of Calculus I

Development of prediction techniques using various physical models developed by Newton, Leibniz, and their successors. Models using one variable differential and integral calculus will be described and used to make predictions. Applications will be taken from fields of population growth, electrical circuits, interest rates, planetary motions, and others.

3

3 hr./wk.

## MATHE 7600E Classic Applications of Calculus II

Further applications will be taken from fields of population growth, electrical circuits, interest rates, planetary motions, and others.

3

3 hr./wk.

## MATHE 7700E Modern Algebra

Sets, mappings, equivalence relations, operations, rings, integral domains, isomorphisms. Mathematical induction fields and groups.

3

3 hr./wk.

## MATHE 7800E Transformational Geometry

The study of geometric transformation groups in the complex plane including similitudes, isometries, translations, rotations, dilations. Applications of cosets and normal subgroups, invariants.

3

3 hr./wk.