Required Readings
For each week, I will list what part of the book we are addressing and what you should look into to prepare for the quiz. Homeworks are due on the Homework Submission page by midnight (11:59pm) on the Wednesday before the quiz. That is, on the Wednesday associated with but before the quiz.
Homeworks always due Wednesday before Quiz
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Official Reading |
Possibly helpful online pages | Assigned Problems | Quiz date |
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Sets Chapter 1 (all 10 sections) |
Khan academy video on intro to sets and set operations (Everything on that page is good--poke the "practice this concept" button and watch all the videos if the first one helps you)
Khan academy introduction to exponents
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1.1: 1, 3, 5, 6, 19, 21, 29, 31, 33, 35 1.2: 1 1.3: 1, 3, 5, 13, 15 1.4: 1, 3, 5, 13, 15 1.5: 1, 3, 9 1.6: 1 1.7: 1, 3, 7, 11, 13 1.8: 1a, 3, The question of the day from Tuesday Lecture. |
Oct 4 (HW due 11:59pm on Oct 3) |
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Logic Chapter 2 Sections 2.1-2.6
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Kahn Academy video on Binary Numbers Squirrel Girl explains counting in Binary Learning About Computers Binary Tutorial Vi Hart's Binary Hand Dance (Silly, but I like it) Video about making truth tables Khan academy video on implications
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2.1: 1, 3, 5, 9, 11, 13 2.2: 1, 3, 5, 7 2.3: 3, 5, 7 2.4: 3, 5 2.5: 1, 3, 5, 9, 11 2.6: 1, 3, 5, 9, 11
The questions of the day from Tuesday Lecture. |
Oct 11 (HW due 11:59pm on Oct 10) |
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Logic Chapter 2 Sections 2.7-2.12 Some stuff on functions and Number Theory |
2.7: 1, 3, 5, 7, 9 2.9: 1, 3, 5, 7, 13 2.10: 1, 3, 5, 7, 11 (more assignments may be added here, but I am trying to give you something to look towards) Prove that if a | b ^ c | d, ac | bd. Prove that if a ≡ b (mod m) ^ c ≡ d (mod m), then ac ≡ bd (mod m) |
Oct 18 (HW due 11:59pm on Oct 17) |
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Intro to Proofs Chapter 4, 5, 6 |
The Khan academy section on rational and irrational numbers is pertinent The Khan academy section on absolute value is pertinent Khan academy section on one-to-one and onto functions
Diagonalization explained with Pokémon Khan academy introduction to exponents |
Chapter 4: 1, 3, 5, 7, 9, 11 (from the problems for Chapter 4) Extra problems: 1) Prove that you can conclude e from the following 3 hypotheses: H1= (a ∨ ¬c) ∧ ¬c H2= ¬c → (d ∧ ¬a) H3= a ∨ e 2) Use a formal proof to show that (p ∨ q) ∧ (¬p ∨ q) ∧ (p ∨ ¬q) ∧ (¬p ∨ ¬q) leads to a contradiction |
Quiz is Oct 30, and HW is due 11:59 pm Oct 24
There will be two quizzes the last week of October/first week of November (because of the strike the previous week). |
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More on Proofs Chapters 4,5,6,7,8,9 |
Proof by contradiction that there must be an infinite number of primes Khan academy on the square root of 2 is irrational Wikipedia on the Fundamental Theorem of Arithmetic This is beyond the class, but if you are interested in how important prime numbers are for cryptography, follow this Khan academy unit A short video of a formal proof using modus ponens. A video on formal proofs, with slightly different notation (like ⊃ for →) A video about resolution theorem provers. (mostly beyond this class, but it shows how important this stuff is to AI) Proof by contradiction that there must be an infinite number of primes A short video of formal proof specializing in proofs by contradiction. |
Chapter 5: 1, 3, 5, 9, 13, 15, 17, 19, 21, 25 (this one is harder than some of the others), 29 Chapter 6: 1, 3, 5, 7, 9, 11, 15, 19, 21 Chapter 7: 1, 3, 7, 13, 17, 27, 31 Chapter 8: 1, 9, 11, 15, 31 Chapter 9 (remember the title of the chapter): 1, 3, 7, 11, 15, 21 |
Quiz date is Nov 1
HW is due 11:59 pm Oct 31 (Scary!) |
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Induction Chapter 10 (the first section, before strong induction) |
Sal Khan does a basic induction proof Another video with a Proof by induction example Proof using induction to prove divisibility |
Chapter 10: 1, 3, 5, 7, 9, 13, 15, 17, 19, 21 plus the Questions of the Day plus, prove that the harmonic series diverges in the way that Tracy will demonstrate on Tuesday, Nov 6. |
Quiz date is November 8 HW due 11:59pm November 7 |
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Counting Chapter 3 |
3.1: 1, 3, 7 3.2: 3, 5, 3.3: 1, 3, 5, 9, 11, 13 3.4: 1, 3, 5, 7 3.5: 1, 3, 5, 6, 10 Chapter 10: 23, 25, 27, 29 |
Quiz date is Nov 15 HW due 11:59pm Nov 14 Quiz on Nov 20 will also be induction |
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Relations and Functions Chapters 11 and 12 |
Khan academy on relations and functions |
Section 11.0: 1, 5, 9 Section 11.1: 1, 3, 7, 11, 15 Section 11.2: 1, 5, 7 (Read 11.3-11.5, but no assigned problems) 12.1: 3, 5 12.2:1, 5, 15 12.3: 1, 3 12.4: 1, 3, 9 12.5: 1, 9 12.6: 3 |
Quiz date is Nov 29 HW is due 11:59 Nov 28 |
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Recurrence Relations and Review |
Your final HW is here. A couple of useful slides to do this homework are here and here. |
Quiz date is Dec 6 HW is due 11:59 Dec 5 |
