In our next part of Number Theory, we're studying Diophantine equations, modular arithmetic, and linear congruences.
Thurs, 2/13 - we studied linear Diophantine equations more in depth, taking our solutions from the Euclidean algorithm and expanding them to find a general solution to this type of equation. Here are the slides from class. Your HW is p. 45 (Ex. 4B) #5, 6 & p. 47 (Ex. 4C) #1a, 3.
Fri, 2/14 - we used linear Diophantine equations and their general solutions to reason about contextual word problems. Here are the slides from class and here is the worksheet from class. Your HW is to make plans to hang out with your friends - see a movie, play a board game, get bubble tea, whatever - it's only the connections that matter.
Enjoy Mid-Winter Recess!
Mon, 2/24 - we were introduced to integer congruence and the idea of modular arithmetic. Here are the slides from class. Your HW is p. 52 (Ex. 5A) #1-5.
Tues, 2/25 - we used the basic rules of modular arithmetic to simply expressions. Here are the slides from class. Your HW is p. 55 (Ex. 5B) #2abcd (i only) and #3-5.
Wed, 2/26 - we used division in congruences and solved linear congruences. Here are the slides from class. Your HW is p. 59 (Ex. 5C) #1 (ii only) and #2-6.
Thurs, 2/27 - we practiced solving linear congruences. Here are the practice problems from class.
Fri. 2/28 - we solved systems of linear congruences and also used the Chinese Remainder Theorem. Here are the slides from class. Your HW is p. 62 (Ex. 5D) #3-7.
Mon, 3/2 - we practiced solving systems of linear congruences. Here are the problems we practiced in class.
Tues, 3/3 - we used Fermat's Little Theorem to reason about congruences when the modulus is prime. Here are the slides from class. Your HW is p.64 (Ex. 5E) #1 (ii only) and #2-5.
Wed, 3/4 - you went bowling. Hooray!
Thurs, 3/5 - we took a group practice quiz that will be very much like your actual exam, which will be on Monday on Diophantine equations and linear congruences. Here is the group quiz you took in class + the markshcheme. Here are the exam details as well as some extra practice problems.
Fri, 3/6 - we took another group practice quiz. Here is the group practice quiz and the markscheme.
Mon, 3/9 - you have an exam on Diophantine equations (finding the gcd of two integers with the Euclidean algorithm, performing the Euclidean algorithm backwards to solve Diophantine equations and finding both particular and general solutions, using modular arithmetic and linear congruences, using Fermat's Little Theorem, and solving systems of linear congruences.