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 the Friday 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, 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 Monday and Wednesday Lecture. |
April 5 (HW due midnight April 3) |
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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) Video about making truth tables
Khan academy video on implications Pages and videos on CNF and DNF from truth tables: https://math.stackexchange.com/questions/636119/find-dnf-and-cnf-of-an-expression http://www.mathematik.uni-marburg.de/~thormae/lectures/ti1/code/normalform/index.html
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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 the last week's Lectures. |
April 12 (HW due midnight April 10 |
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Logic Chapter 2 Sections 2.7-2.12
Some stuff on functions and Number Theory |
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
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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)
The questions of the day from the last week's Lectures. |
April 19 (HW due at midnight on April 17) |
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Intro to Proofs Chapter 4, 5, 6
(and makesure 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) 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 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)
The QotD from the last week. |
April 26 (HW due at midnight on April 24) |
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More on Proofs Chapters 4,5,6,7,8,9 |
Chapter 5: 1, 3, 5, 9, 13, 15, 17, 19, 21, 25 (this one is harder than some of the others--think geometric series), 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 any of the "extra problems" from last week that you did not do.
Do the QotD from the previous week. |
May 3 (HW due at midnight on May Day) |
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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 in class |
May 10 (HW due midnight on May 8) |
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More induction (Chapter 10) and Counting Chapter 3 |
Chapter 10: 23, 25, 27, 29 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 3.5: 1, 3, 5, 6, 10 |
May 17 (HW due midnight on May 15) |
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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 (this one is hard, don't worry if you don't get it) 12.4: 1, 3, 9 12.5: 1, 9 (another difficult one--don't stress it)
12.6: 3 |
May 24 (HW due midnight on May 22) |
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While I was gone, Andrea gave permission to turn in Chap 11 and 12 on May 29. |
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| Recurrence Relations |
HW is here. A couple of useful slides to do this homework are here and here.
QotDs, as usual |
June 7 (HW due June 5) |
