Readings and Homework
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 via gradescope on Canvas 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 the Thursday Quiz
|
Official Reading |
Possibly helpful online pages | Assigned Problems | Quiz date |
|---|---|---|---|
|
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
|
1.1: 1, 3, 19, 21, 29, 31, 35 1.2: 1 1.3: 1, 3, 5, 13, 15 1.4: 1, 3, 5, 13, 15 1.5: 1, 3, 9
The questions of the day from Thursday and Tuesday Lecture. |
September 30 (HW due at 11:59pm Sept 29 |
|
Finish Chapter 1 and start Chapter 2 |
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)
|
1.6: 1 1.7: 1, 3, 7, 11, 13 1.8: 1a, 3, 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 Thursday and Tuesday Lecture. |
October 7 (HW due at 11:59pm Oct 6 |
|
Logic Chapter 2
Sections 2.7-2.12 |
https://www.youtube.com/watch?v=3-J2TCHLg0M&t=5s
The Khan academy section on absolute value is pertinent Khan academy section on one-to-one and onto functions
|
The questions of the day from the last week's Lectures. 2.7: 1, 3, 5, 7, 9 2.9: 1, 3, 5, 7, 13 2.10: 1, 3, 5, 7, 11
The questions of the day from Thursday and Tuesday Lecture.
|
Oct 14 (HW due 11:59 Oct 13) |
|
Counting Chapter 3 |
Video on how many poker hands of various types there are |
3.1: 1, 3, 7 (If you don't have Section 3.1 exercises you have the wrong edition of the book) 3.2: 3, 5, 3.3: 1, 3, 5, 9, 11, 13
3.4: 1, 3, 5, 7 |
Oct 21 (HW due Oct 20) |
|
Intro to Proofs Chapter 4, 5, 6 (and make sure you re-read 2.11) |
The Khan academy section on rational and irrational numbers is pertinent 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 Khan Academy on Congruence and Modulo 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) |
Chapter 4: 1, 3, 5, 7, 9, 11 (from the problems for Chapter 4) Formal proof problems moved to next week
The questions of the day from Thursday and Tuesday Lecture.
|
Oct 28 (HW due Oct 27) |
|
More on Proofs Chapters 4,5,6,7,8,9 |
A video with a formal proof using modus ponens (they use premise instead of hypothesis) A video with a proof example that mostly discusses rules of inference another video on formal proofs |
Chapter 5: 1, 3, 5, 9, 13, 15, 17, 19, 21, 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
Do these formal proof 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 3) Prove that if a | b ^ c | d, ac | bd. 4) Prove that if a ≡ b (mod m) ^ c ≡ d (mod m), then ac ≡ bd (mod m)
Do the QotD problems from the previous week |
Nov 4 (HW due Nov 3) |
|
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, 19, 21 plus the Questions of the Day plus, prove that the harmonic series diverges in the way that Tracy will demonstrate in class |
Nov 9 (HW due Nov 10) |
|
More induction (Chapter 10) and the beginning of relations (Chapter 11) |
Chapter 10: 17, 23, 25, 27, 29, 31, 35 Chapter 11.1: 1, 7, 9 The QotD's are especially important this week |
Nov 18 (HW due Nov 17) |
|
|
Chapter 13 and
solving Linear Homogeneous Recurrence relations of order k with constant coeffiecients |
Diagonalization explained with Pokémon
Video on finding solutions of linear homogeneous Recurrence relations with constant coefficients. (you can find a lot more by googling) |
HW is here . (Don't take the last problem too seriously--its a lot of bookkeeping) A couple of useful slides to do this homework are here and here.
QotDs, as usual |
Nov 23 (HW due Nov 24) |
