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 groupwork 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, 48all, 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# 13, 619, 2124  
Aug. 28 
2.2 Odd/even, decimal
representation 2.3 Divisibility rules Worksheet 8/28 
2.2# 116 all 2.3# 116 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 2829 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# 15all, 7 2.6# 19all 

Sep. 6 
2.4 Prime decomposition Theorem Facts on primes 
2.4# 115all  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# 14all, 6*, 7  
Sep. 13  2.9 Modular arithmetic 
2.9# 118 all 
Exam 1 is moved to Tuesday, Sep. 25. It
covers
sections 1.2, 1.3, 2.22.6, 2.82.10, 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# 16 all (do after exam 1) 3.2# 120all (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# 18all 

Oct. 2  3.6 Quadratic formula  3.6# 1, 2, 5, 914all  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, 11am1pm. 
Oct. 4 
3.5 Rational Root Theorem. Applications Worksheet 10/04 
3.5# 16all  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 0130402613). 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 #18 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 #415 all  
Oct. 23  7.4 Polar form of cx. numbers. Roots of cx. numbers  7.4 #214 all  
Oct. 25 
7.5 Complex numbers and geometric
transformations Worksheet 10/25 
7.5 #18all, 12  Worksheet 10/25 is a homework due Thursday, Nov. 1. 
Oct. 30  7.9 Log's of cx. numbers  7.9 #1, 2, 49all  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 classnotes) 
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 #19, 10* 5.6 #15, 9, 1120all 

Nov. 13  4.2 Areas and Pythagorean Thm Geometry and optimization worksheet 
4.2 #123all 
