﻿ Table of topics and assignments

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. 22 1.2 Intuition vs. Proof 1.3 Types of Proofs Worksheet 08/22 1.2# 1, 2, 4-8all, 10, 13, 15, 16, 17* 1.3# 1-3, 6-19, 21-24 Symbol * denotes more difficult, or more theoretical problems. Exams contain mostly standard problems, but one or two may be like the * ones. Aug. 24 2.2 Odd/even, decimal representation 2.3 Divisibility rules Worksheet 08/24 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. Aug. 29 8.3 Math. Induction and Well ordering principle 2.5 The division algorithm Worksheet 08/29 8.3# 2, 3, 6, 7, 8, 11, 13, 14 2.5# 1-5all, 7 The worksheet for today is now a homework due next class (Aug. 31) Aug. 31 2.4 Prime decom. thm. Facts on primes Worksheet 08/31 2.4# 1-15all Sep. 5 2.6 The Euclidean algorithm, gcd & lcm Worksheet 09/05 2.6# 1-9all The worksheet for today is now a homework due next class (whenever that may be!). Be Irma-safe! Sep. 7 University closed - Irma Sep. 12 University closed - Irma Sep. 14 University closed - Irma Sep. 19 2.7 Division of polynomials 3.2 Factor Theorem Worksheet 09/19 2.7# 1-6 all 3.2# 1-20all Please note the new schedule. Exam 1 is now scheduled  for Oct. 3 and covers all sections done between Aug. 22 and Sep. 26. All problems in the worksheets and all suggested exercises are potential exam questions. Possible theoretical topics for Exam 1 (proofs you need to know): Theorem 2.18, Theorem 2.30, Theorem 2.16 (proof uses thm. 2.30),  Theorem 3.1 and Corollary 3.3, Theorem 3.12. Sep. 21 3.4 Fundamental Thm. of Algebra Viete's relations Worksheet 09/21 3.4# 1-8all The worksheet 09/21 is now a homework due Thursday Sep. 28 (at the start of the class). Sep. 26 3.5 Rational Root Theorem. Applications Worksheet 09/26 3.5# 1-6all Sep. 28 Review for Exam 1 Oct. 3 Exam 1 Oct. 5 6.16.1 Algebraic vs. Transcendental Numbers 6.16 #9, 10, 11 Oct. 10 More on transcendental numbers 7.2 Complex Numbers 7.7 Euler's identity Handout Pb. 5 7.2 #1-8 all 7.7 #3, 5, 7 This attached handout is one section from the wonderful book Exploring the Real Numbers, by Frederick W. Stevenson (ISBN 0-13-040261-3) You should know the proof of Euler's identity and  also how you can derive from it various other identities Oct. 12 7.3 Operations with cx. numbers and Geometry 7.4 Polar form of cx. numbers. Roots of cx. numbers Worksheet 10/12 7.3 #4-15 all 7.4 #2-14 all Worksheet 10/12 is now a homework due Thursday, Oct. 19. Oct. 17 7.9 Log's of cx. numbers 7.9 #1, 2, 4-9all Oct. 19 7.5 Complex numbers and geometric transformations Worksheet 10/19 7.5 #1-8all, 12 Problem 2 (only)  from Worksheet 10/19 is a homework due Thursday, Oct. 26. Oct. 24 8.4 Fractals 8.4 #2-5 Oct. 26 4.3 The circle, Archimedes and the number pi 4.3 #1-9, 10* The worksheet for today was the equivalent of Pb. 10 from this section Oct. 31 Compound interest and the number e You should know the derivation for formulas for balance of bank accounts with interest compounded n-times/year vs. interest compounded continuously. Nov. 2 Conics -- use this review of conics from Stewart Calculus as textbook for this lecture and the next one #3, 6, 16, 29, 49-52 (from Stewart - review of conics) Homework due Thursday, Nov. 9: Obtain the equations in standard form for an ellipse, hyperbola, parabola from their syntetic definitions. Nov. 7 Reflective properties of conics # 59, 60 Exam 2 on Tuesday, Nov. 14 covers all topics done between Oct. 5 and Nov. 7. All problems in the worksheets and all suggested exercises are potential exam questions. Anything marked as "you should know" are also potential (theoretical)  exam questions Nov. 9 Review for exam 2
 Nov. 14 Exam 2 You can do at home any (or even all) of the problems 1, 2, 3, 4, for some bonus. The deadline to turn these in is Thursday, Nov. 16. You are allowed and encouraged to talk about the problems, but each of you should turn in their own work Nov. 16 Geometry and Calculus Worksheet 11/16 #5, 6 page 543 textbook Nov. 21 More Optimization Worksheet 11/21 Homework due Thursday, Nov. 30: Problem 3 from worksheet 11/21 (for uniformity, assume that your eyes are at a height of 4 feet above the floor) Problem 2 from worksheet 11/16. As usual, you are encouraged to collaborate, but each should turn in their own solutions. Nov. 23 No class Happy Thanksgiving! Nov. 28 Motion, parametric curves Worksheet 11/28 Part of your final exam will consist of a lesson plan that you have to prepare at home and a team presentation of your topic on the day of the final (Dec. 12). The topics are: --Rolle's Theorem and the Mean Value Theorem -- team TB, AM, OR; --Local linear approximation; differentials -- team MD, JR, VR. Each one of you should hand in their own lesson plan (before the presentation on Dec. 12), but you'll organize the presentation as a team (you'll have about 1h total time). The other part of your final (also take-home) will be a set of problems which I'll announce on Dec. 5. Nov. 30 More on parametric curves Dec. 5 Related rates Worksheet 12/05 This is the problem part of your take home final A T/F problem added. Exam has 5 problems. Dec. 7 Group work for the final Dec. 12 Final Exam