MATH 510 Mathematical Reasoning
Tentative Schedule Spring 2008
Polya’s Problem Solving Process
Counting the Number of Games in a Round Robin Tournament
Counting the Number of Squares in an Array of Squares
Mathematical Representations
Inductive Reasoning
Deductive Reasoning
Difference Equations
Recursion
(Explicit) Functional Equations
NCTM Reasoning and Proof Standard for Grades 6–8
Session 2 (February 6): Sequences & Figurate Numbers
Sequences, Method of Finite Differences, Method of Ratios, Functional Equations
Counting the Number of Triangles in an Array of Triangles
Session 3 (February 13): Introduction to Reasoning, Logic, and Proof
Some Notes on Reasoning Logic and Proof
Session 4 (February 20): Reasoning, Logic, and Proof Continued
Some Notes on Reasoning Logic and Proof
Constructing Segments on a Geoboard
What is the Teacher's Role in Teaching Reasoning and Proof? (NCTM)
Session 5 (February 27): Some Mathematics of Social Choice
Session 6 (March 5): Graphs, Euler Circuits and Paths
Group Election Theory Activity
Two Famous Graph Theory Problems (Konigsberg
Bridges Problem
Graph Theory Versions of Two Famous Problems
Fleury's Algorithm for Euler Paths
Session 7 (March 12): Hamilton Circuits and Paths
The Traveling Salesman Problem; In-Class Worksheet
The Brute-Force and Nearest Neighbor Algorithms
Session 8 (March 26): A Shortest Route Algorithm & Spiral Growth
Arranging Coins, Arrangements of Coins, The Ancestry of a Male Bee and Fibonacci Numbers
Session 9 (April 2): Fibonacci Numbers, Golden Ratio, & Some Mathematics of Population Growth
Some Properties of Fibonacci Numbers
Linear Growth
Exponential Growth
Logistic Growth
Session 10 (April 9): Mathematical Induction and Mathematics of Population Growth
Principle of Mathematical Induction; Proof by Math Induction
Working with Models for Growth
Session 11 (April 16): Independent Work on Sample Lessons (Project)
Session 12 (April 23): Symmetry
Rigid Motions: Reflections, Rotations, Translations, Glide Reflections
Virtual Manipulatives (Grades 6-8)
More General (Motions) Transformations
Session 13 (April 30): Descriptive Statistics; Chances, Probabilities, and Odds
Descriptive Statistics; (Excel, TI Calculator, Histograms, Box Plots)
Random Numbers and Random Sampling
Collecting Trinkets (Collecting Tokens; A Simulation)
Session 14 (May 7): Discussion of Sample Lessons