Required Readings

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

A video on Power sets

Khan academy introduction to exponents

Khan academy introduction to logarithms

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 question of the day from  Tuesday Lecture.

 Jan 10

(HW due midnight Jan 9)

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

https://www.youtube.com/watch?v=3-J2TCHLg0M&t=5s

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.

Jan 17 (HW due midnight the day before)

video on quantifiers

The Khan academy section on absolute value is pertinent

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

Vi Hart on Diagonalization

Diagonalization explained with Pokémon 

Khan academy introduction to exponents

Khan academy introduction to logarithms

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)

Do the questions of the day from  the last week's Lectures.

Jan 24 (HW due midnight the night before)

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

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

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)

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

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

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

Chapter 10: 23, 25, 27, 29

Khan academy on relations and functions

Khan academy section on injective and surjective functions

Khan academy on invertible 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

HW is here.

A couple of useful slides to do this homework are here and here.

The QotD from T and Th

March 14

(HW due midnight March 13)