Recitation CS 205, Summer 2009

Recitation CS 205 - Introduction to Discrete Structures 1, Summer 2009

Solved Quiz 8
For your final exam preparation:
- Make sure you know how to solve Quiz 7 and 8. If you have any questions (anything you don't understand about the solution or the method) email me
- Understand the concepts and definitions from chapter 3, 9 and 10. For graphs and trees, knowing the definitions is very important (planar, connected, hamiltonian, eulerian etc). Try to do at least one example for each concept. For complexity, knowing the increasing order of complexity will make your life easier (look here for: a good list of increasing complexity of functions - you won't need all for the exam but it is a good reference).
Good luck for the final!

Solved midterm problems 20,23
Solved Quiz 7
Counted the number of edges for a complete graph. A quick continuation to that is exercise 54 from section 9.2
Examples DFS and BFS to generate spanning trees - section 10.6, exercises 14,16

Example 9.1 (chapter 9). Try to do exercise 31
From section 9.3 - exercises 34, 36, 42
From section 9.6 - exercise 56 and some variants. Try to fill an 8X8 chess grid starting in the corner using knight moves (this is a nice puzzle)
From section 9.4 - exercise 26

Solved Quiz 6
Exercises 24 and 44 from section 5.1
Exercises 8 and 30 from section 5.5
Exercise 32 from section 8.3
As a general rule, try to make as much counting exercises as you can (chapter 5) - you'll find skills linked to that useful in your computer science studies. Don't forget, in a counting problem, understanding what is asked (permutation (the order of elements matters) vs. combination (the order of elements doesn't matter), repetions allowed vs. no repetions allowed) is half of the work.
Make sure you know the definitions for relations (reflexive, symmetric, etc) - besides helping you for the exams, you'll encounter them over and over again in the future.
Last but not least, good luck with your midterm!

Examples of valid arguments that make weird claims
Exercise 6 from section 1.5
Proved by contradiction that sqrt(2) is an irrational number
Discussed some logical fallacies: ad hominem, hasty generalization - see here an extreme example from mathematics (Polya Conjecture), deductive fallacies. You can find here for instance a list of the most common fallacies with examples; it is an interesting and useful read both for your mathematical background and for real-world rational skills.

Discussed Quiz 4 and 5
Exercises 33(e) and 34 from section 1.4
Exercises 6(b) and 14(d) from section 11.4
Suggestions: try exercises 6(c), 12, 14(a,b,c) from 11.4 and read "Don't care conditions" from page 774 (1 page, very clear explanations)

Solved Quiz 3
Extended Quiz 3, question 10 to design a half adder using NOR gates - exercise 18 from section 11.1
Discussed about translating English to First Order Logic - examples in the spirit of examples 23 - 26 from section 1.3

Solved Quiz 2 problems
Example 15 from chapter 2.4 (modified)
Exercises from chapter 2.4: 2.19, 2.20
Documentary (part 1) about proving Fermat's last theorem. Parts: 2, 3, 4, 5 - about 45 minutes