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Intermediate Number TheoryNumber theory using algebraic techniques, multiplicative functions, Diophantine equations, modular arithmetic, Fermat's/Euler's Theorem, primitive roots, and quadratic residues. Much of the first half of the class emphasizes using the basic tools of the Introduction class in clever ways to solve difficult problems. In the second half, more theory will be developed, leading students to the beginning Olympiad level.
This course is University of California a-g approved. Click here for more details.
|12 weeks ARE YOU READY? DO YOU NEED THIS?|
Oct 11 - Jan 17
7:30 - 9:00
Oct 11 - Jan 17
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
|Summer 2017||This course will be offered in Summer 2017.to join our mailing list to be notified when the course schedule is available.|
Who Should Take?Students should have a complete understanding of modular arithmetic, and a mastery of algebra through our Intermediate Algebra class (or a typical honors Algebra 2 class and some Precalculus) before taking this class.
|Lesson 4||Divisors and Multiplicative Functions|
|Lesson 5||Prime Factorizations|
|Lesson 6||Algebra in Modular Arithmetic|
|Lesson 7||Linear Diophantine Equations|
|Lesson 8||Perfect Squares|
|Lesson 9||Fermat's Little Theorem and Euler's Theorem|
|Lesson 10||Orders and Primitive Roots|
|Lesson 11||Quadratic Residues and Squares|
|Lesson 12||Sums of Two Squares|