Post date: Jan 22, 2018 7:57:12 PM
We are learning more number theory, particularly solving Diophantine equations, performing modular arithmetic, and solving systems of linear congruences. Our next topic will include strong induction and recurrence relations.
Diophantine Equations
Tuesday, 1/30 - we solved Diophantine equations. Here are the slides from class. Your HW is p. 45 (Ex. 4B) #5, 6 & p. 47 (Ex. 4C) #1a, 3.
Wednesday, 1/31 - we solved Diophantine equations in context. Here are the slides from class. Here are the problems we worked on in class. Your HW is to check out your comments on ManageBac.
Modular Aritmetic
Thursday, 2/1 - we learned about congruence of numbers with modular arithmetic. Here are the slides from class. Your HW is p.52 (Ex. 5A) #1-5.
Friday, 2/2 - we learned about arithmetic rules (addition, subtraction, multiplication, and exponentiation) in modular arithmetic. Here are the slides from class. Your HW is p.55 (Ex. 5B) #2abcd(i only), 3-5.
Solving Linear Congruences & Systems of Linear Congruences
Monday, 2/5 - we solved linear congruences and saw how division with congruences and modular arithmetic behaves slightly differently than we expect. Here are the slides from class. Your HW is p.59 (Ex. 5C) #1(ii only), 2-6.
Tuesday, 2/6 - we solved systems of linear congruences with Chinese Remainder Theorem problems. Here are the slides from class. In case you didn't get to finish it, here is a picture of the solution to the robbers problem that we tried in class. Your HW is p.62 (Ex. 5D) #3-7.
Wednesday, 2/7 - we learned and used Fermat's Little Theorem. Here are the slides from class. Your HW is p.64 (Ex. 5E) #1(ii only) #2-5.
Thursday, 2/8 - we practiced Chinese Remainder Theorem problems and Fermat's Little Theorem problems. Here are the practice problems from class, including the answers on the last page. Here is the worked out solution to #1c.
Strong Induction
Friday, 2/9 - we started a new topic (not on your test next week) called strong induction. We did not finish the lesson. We will finish on Monday. If you would like to finish on your own, here are the slides from class and here is your HW, which is p. 11 (Ex. 1C) #2 & #3, with #4 & #5 as optional challenges.
Monday, 2/12 - we practiced strong induction problems. Here are the slides from class. Here is the worksheet from class, including your HW which is p. 11 (Ex. 1C) #2 & #3, with #4 & #5 as optional challenges.
Number Theory Exam
Tuesday, 2/13 - we did practice problems to review for our exam tomorrow, which will include Diophantine equations (both particular and general solutions), modular arithmetic, solving systems of linear congruences (Chinese Remainder Theorem), and applying Fermat's Little Theorem. Here are some practice problems you've seen before (and here is the worked out answer to #1c) and here are the new practice problems you got in class.
Wednesday, 2/14 - we have an exam on Diophantine equations (both particular and general solutions), modular arithmetic, solving systems of linear congruences (Chinese Remainder Theorem), and applying Fermat's Little Theorem.
Recurrence Relations
Thursday, 2/15 - we continued our new topic and learned about recurrence relations. Here are the slides from class.
We'll continue learning about recurrence relation after our Mid-Winter Recess. Reminder that your Math Exploration is due at 11:59PM on Friday, March 2nd.
Have a nice break!