Table of topics and assignments 

This is a partially flipped class. This means that you are required to read and take notes from the corresponding sections of the book before the date listed in the table below. I will still go over some important points in class, but lecture time is minimized, so that there is time for group-work in class. Most important: you have to constantly solve at home all of the suggested exercises from the sections we cover. For exams (midterms and final), most of the questions will be very similar (or even identical) with problems from the suggested assignment, from the worksheets or from the examples presented in class.

Date Topics covered Suggested Assignment Comments
Aug. 21 1.2 Intuition vs. Proof

Worksheet 8/21
1.2# 1, 2, 4-8all, 10, 13, 15, 16, 17*
Symbol * denotes more difficult, or more theoretical problems.
Exams contain mostly standard problems, but one or two
may be like the * ones.
Aug. 23 1.3 Types of Proofs
1.3# 1-3, 6-19, 21-24  
Aug. 28 2.2 Odd/even, decimal representation
2.3 Divisibility rules
Worksheet 8/28
2.2# 1-16 all
2.3# 1-16 all, 18*
Fun puzzles for your future students in pbs. 17 and 18 in 2.2!
For Pbs 15&16 in 2.3, read the UPC label example on pages 28-29 in the text. 
Worksheet 8/28 is a homework due Thursday, Aug. 30.
Aug. 30 8.3 Math. Induction and Well ordering principle

Worksheet 8/30
8.3# 2, 3, 6, 7, 8, 11, 13, 14

Homework due Tuesday, Sep. 4: Pbs 1 and 2 from Worksheet 8/30
(deadline extended to Thursday, Sep. 6)
Sep. 4
2.5 The division algorithm
2.6 The Euclidean algorithm, gcd & lcm
Worksheet 9/04
2.5# 1-5all, 7
2.6# 1-9all
 
Sep. 6 2.4 Prime decomposition Theorem
Facts on primes
2.4# 1-15all Quiz 1 on Tuesday, Sep. 11 covers sections 2.2 through 2.6.
Be sure to go over the suggested problems from these sections.
Sep. 11 More on 2.4
2.8 Base change
2.8# 1-4all, 6*, 7  
Sep. 13 2.9 Modular arithmetic
2.9# 1-18 all

Exam 1 is moved to Tuesday, Sep. 25. It covers sections 1.2, 1.3, 2.2-2.6, 2.8-2.10, 8.3.
Be sure to go over the worksheets and over all suggested problems from these sections.
Possible theoretical topics for Exam 1 (one of these proofs will be an exam question): 
Theorem 2.18, Theorem 2.30 (with Corollary 2.31), Theorem 2.16 (proof uses Corollary 2.31),
Theorem 2.32 (see pb. 4 in worksheet 9/04 for an outline of the proof).

Sep. 18 2.10 Linear Diophantine Equations 2.10# 4, 8, 10 textbook and
pbs 12a, 13a, 14, 15
from this handout
The handout is from the book "Exploring the Real Numbers" by Frederick W. Stevenson.
(second page is the one I gave you earlier in class).
Sep. 20 2.7 Long Division
3.2 Polynomials - Factor Theorem
2.7# 1-6 all (do after exam 1)
3.2# 1-20all (do after exam 1)
 
Sep. 25 Exam 1 Solution key of Exam 1  
Sep. 27 3.4 Fundamental Thm. of Algebra
Viete's relations
Worksheet 9/27
3.4# 1-8all

 
Oct. 2 3.6 Quadratic formula 3.6# 1, 2, 5, 9-14all Worksheet 9/27 is a homework due Thursday, Oct. 4
No office hours on Tuesday, Oct. 2.
Instead, I have office hours on Wed. Oct. 5, 11am-1pm.
Oct. 4 3.5 Rational Root Theorem. Applications
Worksheet 10/04
3.5# 1-6all Both worksheets 9/27 and 10/04 are now homework assignments due Tuesday Oct. 9.
Oct. 9 6.16.1 Algebraic vs. Transcendental Numbers
6.16 #9, 10, 11
and Pbs. 5, 6 handout
(for 6, assume n is not a perfect square)
This handout is one section from the wonderful book Exploring the Real Numbers,
by Frederick W. Stevenson (ISBN 0-13-040261-3). In particular, I will ask you to know
Gelfond's theorem 4.4.18 and to apply it.
Oct. 11 7.2 Complex Numbers
7.2 #1-8 all
 
Oct. 16 7.7 Euler's formula
Worksheet 10/16
7.7 #3, 5, 7 You should know the series proof of Euler's formula and 
also how you can derive from it various other identities.
Oct. 18 More on Euler's formula
7.3 Operations with cx. numbers and Geometry
7.3 #4-15 all  
Oct. 23 7.4 Polar form of cx. numbers. Roots of cx. numbers 7.4 #2-14 all  
Oct. 25 7.5 Complex numbers and geometric transformations
Worksheet 10/25
7.5 #1-8all, 12 Worksheet 10/25 is a homework due Thursday, Nov. 1.
Oct. 30 7.9 Log's of cx. numbers 7.9 #1, 2, 4-9all Exam 2 on Tuesday, Nov. 6, covers material done between Sep. 20 and Oct. 30. All problems in the worksheets and all suggested exercises are potential exam questions.
Theoretical topics for Exam 2 (one of these proofs will be an exam question): 
Factor Theorem (Thm. 3.1 textbook);
Fundam. Thm. of Algebra (the easy part) (Thm 3.7 - proof of (c) as in textbook):
Rational Root Thm. (Thm. 3.12 textbook);
Quadratic formula (Example 3.18 textbook);
Derive from Euler formula other identities (see your class-notes)
Nov. 1 Mostly review for Exam 2    
Nov. 6 Exam 2    
Nov. 8 4.3 The circle, Archimedes and pi
5.6 The circle revisited
4.3 #1-9, 10*
5.6 #1-5, 9, 11-20all
 
Nov. 13 4.2 Areas and Pythagorean Thm

Geometry and optimization worksheet
4.2 #1-23all