Table of topics and assignments

Table of topics and assignments

It is essential that you read the corresponding sections from the book, review the examples I presented in class and do all of the suggested assignments. For exams (midterm 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. 23	1.2 Intuition vs. Proof	1.2# 1, 2, 4-8all, 10, 13, 15, 16, 17*	Problems denoted with * are more challenging
Aug. 25	1.3Types of Proofs Worksheet week 1	1.3# 1-3, 6-19, 21-24	Homework: Worksheet week 1 is due on Tuesday, Aug. 30. Homework rules: -- your work should be neatly written and logically correct; -- number the pages and staple, if necessary; -- acknowledge joint work, ideas from external sources; -- most of all, your work should not be a copy/paste act from somewhere else.
Aug. 30	2.2 Odd/even, decimal representation 2.3 Divisibility rules	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.
Sep. 1	2.4 Facts on primes 8.3 Math. Induction Worksheet week 2	2.4# 1-15all 8.3# 2, 3, 6, 7, 8, 11, 13, 14	Worksheet week 2 becomes a homework which is due Thursday, Sep. 8.
Sep. 6	Well ordering principle 2.5 The division algorithm	2.5# 1-5all, 7
Sep. 8	2.6 The Euclidean algorithm, gcd & lcm Worksheet week 3	2.6# 1-9all
Sep. 13	2.9 Modular arithmetic	2.9# 1-18 all	Read on your own the subsection on RCA Encryption.
Sep. 15	2.8 Base change Worksheet week 4	2.8# 1-7all	You have two homework assignments, both due on Thursday, Sep. 22. Homework A: Finish all problems in worksheet week 4. Homework B (review of Chapter 2 homework): Do from the textbook the following problems: #2 and #18 section 2.2; #16 section 2.3; #5 section 2.5 and #15 section 2.9 (these two are very related); #5 and #6* section 2.8. (#6 has a star because it is a bit more challenging).
Sep. 20	2.7 Long Division 3.2 Polynomials - Factor Theorem	2.7# 1-6 all 3.2# 1-20all
Sep. 22	3.5 Rational Root Theorem. Applications. Worksheet week 5	3.5# 1-6all	Homework due Thursday, Sep. 29. #2a and 2e, section 3.5 #9, 15, 20, section 3.2.
Sep. 27	3.6 Quadratics	3.6# 1, 2, 5, 9-14all	Note: You can read on your own Section 3.7. I will not require it, but remind me to mention the theorem of Abel and Ruffini showing the impossibility of finding a formula using roots for solving all 5th degree equations (or higher).
Sep. 29	3.4 Fundamental Thm. of Algebra. Worksheet week 6	3.4# 1-8all	Homework: All of the worksheet week 6 is due Thursday, October 6.
Oct. 4	6.5 Density of rationals and irrationals	6.5# 3-11all
Oct. 6	No class - Matthew
Oct. 11	Viete's relations Worksheet week 8	#11, 12 in section 6.4	Midterm on Thursday, Oct. 20, covers all material done until Oct. 11. Any of the problems in the worksheets or on the suggested assignment list can be an exam question. In addition, you should know the following proofs (one or two questions will be chosen from these): Section 1.3: Theorems 1.1, 1.3; Section 2.4: Theorem 2.18; Section 2.6: Theorem 2.30; Section 2.9: Theorem 2.41; Section 3.2: Example 3.5; Section 3.5: Theorem 3.12; Section 3.6: Example 3.18; Section 6.5: Theorem 6.5.
Oct. 13	4.3 The circle	4.3 #1-10 (do these after the midterm)
Oct. 18	Review for midterm
Oct. 20	Midterm exam	Solution key for midterm
Oct. 25	5.6 The circle revisited	5.6 #1-5, 9, 11-20all	Due Thursday, October 27, Problem 10 (a), (b), section 4.3. Add also the following part (c) for the problem: (c) Find a formula for the perimeter P_n of the regular n-gon inscribed in the circle and then take the limit as n goes to infinity to obtain the expression for the circumference of a circle.
Oct. 27	More on 5.6 Worksheet week 10	same as above	Homework due Thursday, Nov. 3: Problem 3 in this worksheet week 10. It has double weight (20 pts).
Nov. 1	5.2 Law of Cosines 5.3 Law of Sines (extended) 5.10.1 Heron's formula	5.2 #1-7all 5.3 #1-9all 5.10 #1-5
Nov. 3	More Geometry Worksheet week 11
Nov. 8	Compound interest, the number e and exponential functions	6.10 #13, 14, 15
Nov. 10	Calculus and Geometry Worksheet week 12	Read also Exp. 10.31 (page 508) 10.9 #1, 2

Nov. 15	7.2 Complex Numbers 7.7 Euler's identity	7.2 #1-8 all 7.7 #3, 5, 7	You should know the proof of Euler's identity and also how you can derive from it various other identities
Nov. 17	7.3 Operations with cx. numbers and Geometry 7.4 Polar form of cx. numbers. Roots of cx. numbers	7.3 #4-15 all 7.4 #2-14 all	Your projects are due on Tuesday, Nov. 29th. (no exceptions). Suggested exercises related to your project: For Geometric Probability/Monte Carlo method - 12.10 # 6, 7, 9, 11, 13, 14, 15(a), (b) For Geometric Transformations -- 10.4 #14, 19 10.5 #10, 11, 14 10.6 #1, 3, 5, 6 You should try to include solutions to a couple of these exercises (two or three) in your project.
Nov. 22	7.5 Complex numbers and geometric transformations Worksheet week 13	7.5 #1-8all, 12
Nov. 24	Happy Thanksgiving!
Nov. 29	Project presentation
Nov. 31	Review for Final Project presentation		The final exam has a take home component: Pb. 2 of Worksheet week 13 (Napoleon's triangle) and one of the Calculus and geometry problems of Worksheet week 12 (you can choose one). These are due on Thursday, Dec. 8. (strict deadline). The in-class part of the final will cover all we did starting with section 4.3 and after, plus sections 1.2, 1.3, 8.3 (types of proofs and induction). All problems from the suggested homework, plus the worksheets could be exam questions.You will also have one problem specific to your project from the list given above (see Nov. 17 row).
Dec. 6	Final Exam		Special office hours for the final exam: Monday, Dec. 5, 10-12noon, 1-3pm.
			Here are the grades (last column in the excel file). In the first column, in increasing order, there are the first 4 digits of your Panther ID. Happy Holidays!