Mon

Tues

Weds

Fri

Jan 25 Introduction, division and Time to Complete a Project (1.1)
HW:  1.1 # 3, 5, 11, 15, 17, 18
Long divide to get a repeating decimal for 2/7, 3/11, 5/12 (due Weds)

Matching Problem (1.2)
1.2 #7 (do twice: by calculator and simplify by hand), 11, 17, 21, 25, 27, Write the best solution you found to the example prob (pg 11) and how you got it (due Friday)

More about fractions, decimals and algorithms.

Knapsack problem (1.3)
1.3 # 15, 19, 21, 23, 24, 25, 29. Answer these fraction to decimal questions

Feb 1 Algorithms and efficiency 1.4 # 8, 9 (due Weds)

1.4 # 23-26 and 27-30 (done in class)
Review of PERT diagrams (1.1)

Sets: 2.1 # 4, 9-16, 26-28. Bring questions on Friday (due Monday unless no-one has questions, in which case due Friday!)
Set notation sheet

A.1 Statements and connectives pg 582 # 13, 14, 15, 16, 17, 19, 21, 23, 24, 25, 26, 27

Feb 8 A.2 Logical equivalence

A.2 # 3, 6 (pg 586)
A.3# 5, 7 (pg 592) Note: "a divides b" means "a is a factor of b".

more logic and proof
A.3 # 10, 11, 19 and prove that the square root of 3 is irrational.

Equivalence relations (2.2)
2.2 # 1, 3, 5, 9 Transitivity mini-lecture. Due Tuesday.
More, predictable, proofs (like 19) due Monday

Feb 15 Equivalence relations and functions 2.2# 11, 13, 15, 16, 21 (prove only one part of 21: if xRy is false then the intersection is empty) 

Congruence

Computing including finding exponents mod n.
Homework
Video help part 1, part 2, part 3

Appreciating RSA public key cryptography
Test 1

Feb 22 More with sets.
Homework

More with truth tables
A.2 # 1, 11, 13, 17, 19

Functions 2.4 # 15, 25, 29, 39, 44, 35-52 odd

More with functions
2.4 # 53-60 odd, 65, 66
Study this for the text next Friday

Feb 29 More practice problems. No new homework

Some solutions to the practice problems (complete)
Condensed version (only 5 pages) (you can skip 23 and 24--we'll talk about them Weds)
Homework 2.5 # 1, 2, 3, 4, 6

More induction: 2.5 # 11, 13, 15

Test on App A, 2.1, 2.2, 2.4 and 3.1

March 7 More induction 2.5 # 18, 19

Graphs
4.1 # 1, 2, 5, 5, 6, 16, 18, 28, 29, 31, 33

4.1 # 19, 21, 39, 40, 41, 42, 43

March 14
Spring

Break

March 21
Invariants and Isomorphisms
Homework

Intro to Euler Circuits and Paths (see 4.2 and this practice)

Two videos on 1-1 functions on the integers: intro and basic ideas; how to prove it.

Homework on Euler paths
More homework.

Two videos on onto functions: how to prove a function is onto; how to prove a function is not onto.
Do these Hamiltonian circuit problems: 1, 3, 6, 8
Prove that f : Z -> Z defined as f(x)=x+7 is onto and g : Z -> Z defined by g(x)=3x+1 is not onto (as a function from the integers to the integers).

March 28 Review Induction proofs for series. Video 1: what is a series, and proving; Vid 2: 2 proof examples.
New content: Recurrence relations.
Homework:  9.1 # 1, 5, 7, 9, 13 and these induction proofs
Test 3 topic list

Review induction proofs for inequalities: Video 1: squared>linear; vid 2: exponential > squared; vid 3: !>exponenetial.
Practice problems
Chapter 9 homework
9,2 # 1, 2, 11, 13

Review function composition proofs (1-1 and onto) see numbers 25 and 26

Test

April  4 9.2 # 4, 15, 17, 19

9.3 # 2, 3, 7, 10

9.2 # 3
9.3 # 13, 17, 20, 22
Scanned notes from class

No class

April 11 Fill in Pascal's triangle down to at least the row the starts 1, 7...
8.1 #  2, 3  (write out and cancel factors), 19-24
Hint-through of 9.2 # 3 and 9.3 # 13

8.1 # 9, 10, 17, 18

8.1 # 25-30

8.2 # 2, 3, 6, 7, 9, 12, 13, 15

April 18 8.2 # 17, 20, 21, 23, 26, 29, 31

8.3 # 13-16, 22, 24, 25, 18, 26, 29, 30

8.4 Find and solve 3 problems of the first 10 exercies that can be solved using theorem 8.7

8.4 # 5-21 odd

April 25 Class cancelled

8.5 # 1-4

8.5 # 5, 7, 9, 11, 17, 19, 21, 23

8.5 # 13, 15, 25, 26, 27, 29

May 2 8.6 # 1, 5

8.6 # 3, 6, 11, 22

What to study for the final exam

May 9

Final exam Weds May 11 1-3 pm.