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• Printing Suggestions for Typed Files

I recommend two-page-to-a-side and/or double-sided printing to save paper. If the typed print is too small, try something like Page Setup: Scale: 110%, unless print gets cut off (100% may be better for handwritten notes). Color printing is nice, but B&W printing is cheaper.

These are pdf files. You can get the free Adobe Reader at Get a version that is compatible with your system!

• Class Notes


Creative Commons License

For “attribution,” simply mention my name and/or web URL somewhere if you’re using huge chunks of the notes. I simply want due credit.

Chapter 1: Logic, Sets, and FunctionsBig File 1 (if this doesn’t work, try the small files below)

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 TheoryBig File 2 (if this doesn’t work, try the small files below)

Section 2.3 (Part 1) Notes: Integers and Division; Prime Factorizations

Sieve of Eratosthenes (Primes) Notes

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: ProofsBig File 3 (if this doesn’t work, try the small files below)

Section 3.1 Notes: Methods of Proof

Section 3.2 Notes: Mathematical Induction

Section 3.3 Notes: Recursive Definitions

Chapter 4: Counting IBig File 4 (if this doesn’t work, try the small files below)

Section 4.1 Notes: Counting: Basics

Section 4.2 Notes: Pigeonhole Principle

Section 4.3 Notes: Permutations and Combinations


QUINCUNX ("PLINKO") APPLETS AND SITES (This applet's better.) (Wikipedia article) (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 IIBig File 5 (if this doesn’t work, try the small files below)

Section 5.1 Notes: Recurrence Relations I

Section 5.2 Notes: Recurrence Relations II

Section 5.5 Notes: Inclusion-Exclusion

Chapter 6 on: Relations, Graphs, and Favorite TopicsBig File 6 (if this doesn’t work, try the small files below)

Chapter 6 Notes: Relations

Chapter 7 Notes: Graphs


• Syllabus (Summer 2000): Syllabus

• Exams and Solutions (Summer 2000)

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

• Textbooks / Resources

• Textbook I used: Rosen

(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)

• 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.

• Free online notes and books: (by Charles Wells from Case Western) (by Miguel Lerma from Northwestern); description: (by Marcel Finan from Arkansas Tech) (PowerPoint slides by Zeph Grunschlag from Columbia) (lots of examples and exercises; by David Santos from Community College of Philadelphia) (a variety of texts from Ed Bender and Gill Williamson from UCSD)

• Tutoring Sites … online tutoring … online tutoring … like Google for tutors

• For Mesa College only:

Tutoring at Mesa College (getting one / becoming one): Click here

Various subjects: Tutoring114SubjectList.pdf

• More Web Sites

(Discrete Math and Combinatorics)

(Great review notes on math.)

(Frequently asked questions and extensions…)

(A wonderful collection of games, puzzles, interesting math, and other neat stuff!)

(Interesting topics in a variety of mathematical fields!)

• 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)

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