MATH 245 (SUMMER 2000)
RELAX, BILL!
Fuzzy theory is wrong, wrong, and pernicious. What we need is more logical thinking, not less. The danger of fuzzy logic is that it will encourage the sort of imprecise fuzzy thinking that has brought us so much trouble. Fuzzy logic is the cocaine of science.
- Prof. William Kahan
(UC Berkeley, Computer Science)
SUMMER 2000
Exams and Solutions
DISCLAIMER: There is no guarantee that your tests will look anything like these!
Quiz 1 (Sections 1.1-1.3: Logic) … Solutions
Quiz 2 (Sections 1.4-1.7: Basic Structures) … Solutions
Quiz 3 (Sections 2.3-2.5: Number Theory) … Solutions
Quiz 4 (Sections 3.1-3.3: Methods of Proof, Inductive Reasoning) … Solutions
Quiz 5 (Sections 4.1-4.3: Counting) … Solutions
Quiz 6 (Sections 5.1, 5.2, 5.5: Recurrence Relations and Inclusion-Exclusion) … Solutions
Final … Solutions not yet available
CLASS NOTES
These are pdf files. Get the free Adobe Reader here: http://www.adobe.com
File title example: "M2450102" means "Math 245, Chapter 01, Section 02."
Textbook I used:
(I later concluded that this text may be too advanced for the beginning discrete math student. It's great for a math or computer science professor, but it may not be clear for students. See OTHER BOOKS below.)
Discrete Mathematics and Its Applications (4th Edition)
by Kenneth H. Rosen. (WCB/McGraw Hill, 1999)
5th edition available 2003.
The Notes:
Email me if you have corrections, comments, or suggestions!
Chapter 1: Logic, Sets, and Functions …
Section 1.1 Notes: Logic I: Intro
Section 1.2 Notes: Logic II: Propositional Equivalences
Section 1.3 Notes: Logic III: Predicates and Quantifiers
Section 1.4 Notes: Sets I: Intro
Section 1.5 Notes: Sets II: Set Operations
Section 1.6 Notes: Functions I: Intro
Section 1.7 Notes: Functions II: Sequences and Summations
Algorithms … Algorithms Notes
Chapter 2: Number Theory …
Section 2.3 (Part 1) Notes: Integers and Division; Prime Factorizations
Section 2.3 (Part 2) Notes: Applications of Prime Factorizations
Sections 2.4 and 2.5 Notes: Integers and Algorithms; Euclidean Algorithm, Binary, and Congruences
Chapter 3: Proofs …
Section 3.1 Notes: Methods of Proof
Section 3.2 Notes: Mathematical Induction
Section 3.3 Notes: Recursive Definitions
Chapter 4: Counting I …
Section 4.1 Notes: Counting: Basics
Section 4.2 Notes: Pigeonhole Principle
Section 4.3 Notes: Permutations and Combinations
• FUN WITH PASCAL'S TRIANGLE
QUINCUNX ("PLINKO") APPLETS AND SITES
http://www.jcu.edu/math/isep/Quincunx/Quincunx.html (This applet's better.)
http://www.ms.uky.edu/~mai/java/stat/GaltonMachine.html
http://en.wikipedia.org/wiki/Bean_machine (Wikipedia article)
http://en.wikipedia.org/wiki/Quincunx (Wikipedia article)
The Beauty of Pascal's Triangle
From Chaos and Fractals by Peitgen, et al: Patterns in Pascal's Triangle
The Magic of Pascal's Triangle (Plinko from The Price is Right and Word Jumbles)
Chapter 5: Recurrence Relations and Counting II …
Section 5.1 Notes: Recurrence Relations I
Section 5.2 Notes: Recurrence Relations II
Section 5.5 Notes: Inclusion-Exclusion
Chapter 6: Relations … Chapter 6 Notes: Relations
Chapter 7: Graphs … Chapter 7 Notes: Graphs
Some favorite additional topics … Faves
OTHER BOOKS
• Discrete Mathematics with Applications by Susanna S. Epp
This text is much clearer than Rosen's, though it doesn't have as many interesting problems. Maybe start with this book, and, if you love the stuff, try Rosen.
WEB SITES
• http://www.combinatorics.net/hyper
(Discrete Math and Combinatorics)
(Great review notes on math.)
• http://www.drmath.com/dr.math
(Frequently asked questions and extensions…)
(A wonderful collection of games, puzzles, interesting math, and other neat stuff!)
• http://www.math.hmc.edu/funfacts
(Interesting topics in a variety of mathematical fields!)