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 on the Wednesday 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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HW1 Propositions,binary 1.1 & 1.3
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Kahn Academy video on Binary Numbers Learning About Computers Binary Tutorial Vi Hart's Binary Hand Dance (Silly, but I like it)
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1.1: 1 ,4, 11, 18, 27, 30, 37, 43 Quiz will include questions about duality and DNF (sum of products normal form) Solution to even problems |
January 13 |
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HW2 Equivalencies 1.3 Sets 2.1 |
Khan academy video on implications 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) |
1.3: 6, 9ade, 11ade, 13, 34, 40, 41, 55 SOlutions to even problems in forum post 2.1: 4, 7, 8, 9, 15, 19, 21, 35, 39 Solution to even problem |
Jan 23 (quiz on monday following usual friday because of inauguration) |
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HW3 Set Operations 2.2 Predicates and Quantifiers 1.4, 1.5 |
The Khan academy video on intro to sets and set operations is still pertinent. |
2.2:3, 5, 15, 25, 27 1.4: 1, 5, 7, 11, 17, 30, 43, 50 1.5 1, 21, 27, 30, 45, 48 |
Jan 27 |
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HW4
Rules of Inference and Proofs 1.6-1.8 Functions and Cardinality 2.3 and 2.5 |
The Khan academy section on rational and irrational numbers is pertinent The Khan academy section on absolute value is pertinent |
1.6: 3, 19, 33 1.7: 1, 9, 21, 38 Even problems 1.8: 7, 29 Chapter one supplemental problems: 21, 23 2.3:1, 3, 7, 9, 10, 11, 23, 29, 49, 54, 69, 73 |
February 3 |
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HW5 Functions and Cardinality 2.3 and 2.5 Sequences and Summations 2.4
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Diagonalization explained with Pokémon Khan academy introduction to exponents Khan academy introduction to logarithms Khan academ on sequences and summations
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We have repeat problems because I got ahead of myself: 2.3:1, 3, 7, 9, 10, 11, 23, 29, 49, 54, 69, 73 Even problems 2.4: 3, 9, 25, 29, 35, 44 even problem 2.5: 1, 11, 16 even problem |
Feb 10 |
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HW6 Divisibility and Mod 4.1 primes and divisors 4.3 Induction 5.1 |
Khan academy on modular arithmetic and congruence Page discussing modulus of a negative number Wikipedia on the Fundamental Theorem of Arithmetic Proof by contradiction that there must be an infinite number of primes This is beyond the class, but if you are interested in how important prime numbers are for cryptography, follow this Khan academy unit |
4.1: 1, 6, 9abc, 15, 18, 21, 26, 34, 37 Even problem 4.3: 1,5,6,25 even problem 5.1: 3, 5, 7, 14, 21, 23, 33, 49 even problem |
Feb 17 |
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HW7 More Induction 5.2 & 5.3 |
Another video with a Proof by induction example Proof on harmonic numbers, but not the one I do in class (good for proof examples using sums) Proof by induction that something is divisible by 8 Hour and a half video on Induction. Strong induction starts at the hour mark. |
5.2: 3,9,29 and prove the harmonic series diverges
5.3: 1,5,7,13,14,25,39,40,43 |
Feb 24 | |
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HW 8 Counting 6.1-6.3 |
Proof of the Binomial Theorem by Induction. |
5.3: 1,5,7,13,14,25,39,40,43 even problems 6.1:3,5,8,10,11,21,35,40,51,53,63 even problems 6.2:5,9,17,35 |
March 3 | |
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HW9 Binomials and Probability 6.4 7.1-7.2 |
Video on Pascal's triangle |
6.4:1,7,15,19,27,32
7.1: 1,5,15,16,17,19,21,37,39 |
March 10 | |
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HW10 Recurrence Relations 8.1-8.2 |
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March 17 |