Historical evaluation of mathematical concepts. Selected topics related to elementary geometry and algebra, analytic geometry and calculus, and the modern postulational viewpoint.
3 hr./wk.
Extensions and generalization of elementary geometry; higher geometry of triangles, circles, quadrilaterals; constructions, classical problems.
3 hr./wk.
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 hr./wk.
Survey of mathematical computer software. Using Geometer's Sketchpad to learn advanced geometry theorems. Sample programming problems drawn from scientific and mathematical applications.
3 hr./wk.
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 hr./wk.
Frequency histograms, measures of location and dispersion, correlation and least squares, testing hypotheses, confidence intervals and estimation.
A course in probability.
3 hr./wk.
Vector spaces, matrices, systems of linear equations, determinants, linear transformations.
3 hr./wk.
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 hr./wk.
Solution of algebraic equations by iteration interpolation; numerical integration; solution of ordinary differential equations.
One year of calculus.
3 hr./wk.
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 hr./wk.
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.
Requires sponsorship by an appropriate faculty member and approval of the Advisory Committee.
VARIABLE 1-3 CR./SEM. Hours to be arranged.
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
Requires sponsorship by an appropriate faculty member and approval of the Advisory Committee.
Hours to be arranged.
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.
Calculus, Linear Algebra and at least one proof-intensive course such as Abstract Algebra, Number Theory, Logic or Real Analysis
3 hr./wk.
Examples and classifications of surfaces; metric and topological spaces.
3 hr./wk.
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 hr./wk.
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 hr./wk.
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 hr./wk.
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 hr/wk
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 hr./wk.
Focuses on the mathematics content knowledge needed to teach mathematics from birth to grade 6, and the development of children's numerical and logical reasoning. Includes topics such as problem solving, sets, operations with sets, functions, numerical systems with different bases, and topics in number theory. All topics are connected to children's developing mathematics understandings. Reasoning and proof, problem solving, connections, communication, and representation are threaded through all instruction. Includes 15 hours of fieldwork.
3 hr./wk.
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.
One proof intensive course and Calculus II, Linear Algebra.
3 hr./wk.
The course is designed for teachers to explore a wide range of problems in various areas of mathematics, including but not limited to the different aspects of the secondary curriculum: number theory, set theory, functions, Euclidean and non-Euclidean geometry. By engaging with problem solving in various mathematical topics, teachers will understand the process of mathematical reasoning and will be able to transfer this knowledge to their own practice within secondary schools.
3 hr./wk.
The course is designed for teachers to explore a wide range of problems in non-traditional topics of mathematics. Teachers will engage in solving these problems and subsequently will discuss issues of implementation in secondary classrooms
3 hr./wk.
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 hr./wk.
The basic concepts of Euclidean Geometry and the underpinnings of non-Euclidean Geometry.
3 hr./wk.
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 hr./wk.
Further applications will be taken from fields of population growth, electrical circuits, interest rates, planetary motions, and others.
3 hr./wk.
Sets, mappings, equivalence relations, operations, rings, integral domains, isomorphisms. Mathematical induction fields and groups.
3 hr./wk.
The study of geometric transformation groups in the complex plane including similitudes, isometries, translations, rotations, dilations. Applications of cosets and normal subgroups, invariants.
3 hr./wk.