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

Official

Reading

Possibly helpful online pages Assigned Problems Quiz date

HW1

Propositions,binary

1.1 & 1.3

 

 Kahn Academy video on Binary Numbers

 Learning About Computers Binary Tutorial 

 Vi Hart's Binary Hand Dance (Silly, but I like it)

 

1.1:   1 ,4, 11, 18, 27, 30, 37, 43

Even problems

 Quiz will include questions about duality and 

DNF (sum of products normal form)

 

 April 7

 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)

 

A video on Cartesian products

1.3: 6, 9ade, 11ade, 13, 34, 40, 41, 55

 Solutions to even problems on forum

2.1: 4, 7, 8, 9, 15, 19, 21, 35, 39

Solutions to even 2.1 problems (plus a couple more that weren't assigned)

 

 April 14
 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.

A video on Power sets

 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

 April 21
 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

Khan academy section on one-to-one and onto functions

 

Khan academy on the square root of 2 is irrational

 

Vi Hart on Diagonalization

Diagonalization explained with Pok√©mon 

 1.6: 3, 19, 33

1.7: 1, 9, 21, 38

1.8: 7, 29

Chapter one supplemental problems: 21, 23

2.3: 1, 3, 7, 9, 10, 11, 23, 29, 49, 54, 69, 73

 April 28

HW5

Functions and Cardinality

2.3 and 2.5

Sequences and Summations

2.4

4.1 Divisibility and modularity

Khan academy introduction to exponents

Khan academy introduction to logarithms

Khan academ on sequences and summations

Khan academy on modular arithmetic and congruence

Page discussing modulus of a negative number

2.4: 3, 9, 25, 29, 35, 44 

Even probs (+1)

2.5: 1, 11, 16

Even prob

4.1: 1, 6, 9abc, 15, 18, 21, 26, 34, 37

Even probs

May 5
 primes and divisors

4.3

Induction 

5.1

 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

Sal Khan does a basic induction proof

 4.3: 1,5,6,25

Even problem

 

5.1: 3, 5, 7, 14, 21, 23, 33, 49

Even problem

 

 

 May 12

 HW7

More Induction

5.2 & 5.3

 Video on Proof by induction

Another video with a Proof by induction example

 Video on Fibonacci proof

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: 3,9,13, 29, 31 and prove the harmonic series diverges

harmonic series diverges proof

 

 

5.3: 1,5,7,13,14,25,39,40,43

 

even problems

 

 

 May 19

 HW8

Counting

6.1 through 6.3

Khan academy on permutations

Khan academy on combinations

Video on proving the binomial theorem by induction

 

  6.1:3,5,8,10,11,21,35,40,51,53,63

even problems

6.2:5,9,17,35

6.3:1, 3, 7, 11, 17, 29, 33, 37

 May 26
 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

 June 2
 HW10

Recurrence Relations

8.1-8.2

 Josephus problem on Numberphile

Towers of Hanoi on Khan Academy

 

YouTube video on linear homogeneous recurrence relations.

 8.1: 1, 7, 33,34,35,36
 8.2: 1, 3
 June 9