**MATH 245 – DISCRETE MATHEMATICS **

*• 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 http://www.adobe.com.
Get a version that is compatible with your system!

*• Class Notes*

**• FRONT PAGES**

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 Functions** … Big 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 Theory** … Big 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:
Proofs** … Big
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 I** … Big
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

**•
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**
… Big 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 Topics**
… Big 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 (4 ^{th} 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:**

http://www.abstractmath.org/MM/dm.pdf
(by Charles Wells from Case Western)

http://www.math.northwestern.edu/~mlerma/papers/discrete_mathematics-2005.pdf
(by Miguel Lerma from Northwestern); description: http://www.freetechbooks.com/notes-on-discrete-mathematics-t732.html

http://faculty.atu.edu/mfinan/main2.pdf
(by Marcel Finan from Arkansas Tech)

http://www.cs.columbia.edu/~zeph/3203s04/lectures.html
(PowerPoint slides by Zeph Grunschlag from Columbia)

http://opensourcemath.org/books/santos/santos-discrete_math_lecture_notes1.pdf
(lots of examples and exercises; by David Santos from Community College of
Philadelphia)

http://cseweb.ucsd.edu/~gill/BWLectSite/
(a variety of texts from Ed Bender and Gill Williamson from UCSD)

*• Tutoring Sites*

• http://www.tutorvista.com … online
tutoring

• http://www.akaritutoring.com … online
tutoring

• http://www.ziizoo.com … like Google for tutors

• For Mesa College
only: http://www.sdmesa.edu/tutoring-center/about.cfm

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

Various subjects: Tutoring114SubjectList.pdf

*• More 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!)

*• 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)