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