Topics/ Team Logic Presentation Format
3 students per team working on the same proof.
10 minutes of in-class preparation time at the beginning of class on
presentation day.
New groups will be formed and presentations given in small groups of 7-8
students. This will take place over two weeks. One week you will present
individually, another week you will not.
Ten minute (maximum) presentation time per group beginning at 3:35 PM.
Topics will present in order of chapter sections.
Each topic presentation will include the following:
Introduction to topic, section, and "Big Idea".
An analogy or example for given topic to build intuition.
Formal Definitions and a numerical example, where appropriate.
Presentation of Proof
List representative homework problem for class.
One related original exam question.
Solution to original exam question will be provided to the instructor.
Visual Presentation: PowerPoint Presentation
Written material must be readable large, liberal use of white space.
All PowerPoint Presentations will be uploaded to Blackboard by midnight of the
day you present. I expect one presentation uploaded per group of 3.
All team members will participate and present material as part of presentation.
A team evaluation will be completed following this activity.
Format: 3rd edition/4th edition
3.2 /4.2 Rational
1. Cover Proof on page 145 (Thm 3.2.2) /page 166 (Thm 4.2.2)
3.3/4.3 Divisibility
2. Transitivity proof page 151 (Thm 3.3.1) /page 173 (Thm 4.3.3)
3. Primes proof page 151-152 (Thm 3.3.2) /page 174 (Thm 4.3.4)
3.4 Division into Cases & Quotient-Remainder Theorem
4. Quotient-Remainder Theorem proof page 157-158 (div and mod)/page 180
5. Opposite parity proof page 160 (by case, 3.4.2)/Parity Property page184
6. Square of any odd integer has.. ..proof page 162(by case, 3.4.3) / page 186
3.5 Floor and Ceiling
7. Theorem 3.5.1 proof page 167/ 4.5.1 page 194
8. Theorem 3.5.2 Floor of n/2 proof page 168 / 4.5.2 page 195
9. Theorem 3.5.3 proof page 169/ 4.5.3 page 196
10. Ceiling problem #29 page 171 /page 197
Hint: Use the definition of odd number and begin by substituting into the *LS of
equation. Then do the same for the *RS.
3.6 Indirect Proof: Contradiction and Contraposition
Contradiction
11. No greatest integer proof, page 172 (Thm 3.6.1)/4.6.1 page 199
12. There is no integer that is both even and odd, page 173 (Thm 3.6.2) /4.6.2
page 199
13. Sum of any rational and irrational is irrational , page 174 (Thm 3.6.3)/4.6.3
page 201
Contraposition
14.For all integers n, if n2 is even then n is even, page 176 (Thm 3.6.4)/4.6.4 page
202
Fundamental Theorem of Arithmetic
15. Unique Factorization of Integers Theorem, page 153 (Thm 3.3.3)/page 176
(4.3.5)
16. Square root of 3 is irrational, page 180-181 (Thm 3.7.1 good example)/
page 208-209 (Thm 4.7.1 good example)
* left side/ right side