Illinois State University Mathematics Department

MAT 409: Topics in Algebra and Combinatorics for K-8 Teachers

Dr. Roger Day (day@ilstu.edu)



Content Notes
Addition Principle
Finite Differences
Perfect Covers of Chess Boards
Total Number of Possible Arrangements
Arranging Elements When Repetition Is Allowed
Generating Functions
Permutations
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Basic Counting Techniques
Inclusion/Exclusion Principle
Pigeonhole Principle
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Binomial Expansion
Mathematical Induction
Product Notation
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Circular Permutations
Multinomial Expansion
Proof by Induction
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Combinations
Multiplication Principle
Recursion Relationships
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Derangements
Number of Subsets of a Set
Solving Equations over the Nonnegative Integers
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Factorial Notation
Pascal's Formula
Solving Equations over the Positive Integers
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Fibonacci Sequence
Pascal's Triangle
Summation Notation
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Review: Binomial Expansion
Review: Multinomial Expansion
Review: Pigeonhole Principle
Review: Product Notation
Review: Summation Notation

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