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Selected Topics from Number Theory

The course engages teachers in investigations with instructional materials to formulate and prove conjectures. The course points out, discusses and enriches multiple intersection points with the elementary and middle school curricula. It discusses the topics of prime and composite numbers, divisibility rules, strategies for determining the LCM and GCD (including the Euclidean algorithm and Fermat’s factoring), Goldbach’s conjecture, Gauss’s theorem, arithmetic progressions, relatively prime numbers, other classification of numbers such as Fibonacci numbers, figurate numbers, abundant, deficient, and perfect numbers, divisibility rules, number bases and the origin of numeration systems, to name a few. The course also introduces participants to Pascal’s triangle and modular arithmetic.

Suggested Text: Number Treasury2  by Bezuszka and Kenney