Welcome to the Mathematics 312 Home Page!


Meeting Time: TuTh 12:30-1:45
Meeting Place: Burruss 133


This is the syllabus for the course.



ANNOUNCEMENT   February 3  As I'm sure you know by now, school was cancelled today. The official make-up day is this Saturday, but since I am no more eager than you to have class on Saturday, I thin we will let this one slide. Please notice that there is a new homework assignment. Please print it out and get started on it. It relates to chapter three in the notes, so print those out and read them as well.



I will be writing the textbook for this course. The individual chapters will be made available here as they are written:


Chapter One:   Logic     Sections: 1.1 The Rain vs. The Water Truck, 1.2 Scientific Reasoning, 1.3 Aristotle's Laws of Thought, 1.4 The Rules, 1.5 Quantifiers   (20 Pages)

Chapter Two:   Proof     Sections: 2.1 The Nature of Proof, 2.2 Direct Proof, 2.3 Conjectures and Counterexamples, 2.4 If-Thens Revisited, 2.5 Proof by Contrapositive, 2.6 Proof by Contradiction, 2.7 Proof by Cases, 2.8 Existence Proofs, 2.9 Proofs and Tautologies   (13 Pages)

Chapter Three:   Mathematical Induction     Sections: 3.1 Another Method of Proof, 3.2 Two Examples, 3.3 Strong vs. Weak Induction, 3.4 Two More Examples, 3.5 The Well-Ordering Principle, 3.6 Recursively-Defined Functions   (12 Pages)

Chapter Four:   Counting     Sections 4.1 Tweo Classics, 4.2 Basic Counting Principles, 4.3 Permutations and Combinations, 4.4 Poker Hands, 4.5 The Binomial Theorem, 4.6 The Multinomial Theorem   (9 Pages)

Chapter Five:   Number Theory     Sections 5.1 Prime Numbers, 5.2 Least Common Multiple, 5.3 Congruences, 5.4 Divisibility Rules   (9 Pages)

Chapter Six:   Sets and Infinity     Sections 6.1 Russell's Paradox, 6.2 Another Paradox, 6.3 Infinity, 6.4 The Real Numbers are Uncountable, 6.5 The Power Set, 6.6 Yet Another Paradox, 6.7 The Continuum Hypothesis   (12 Pages)



Homework Assignments

Homework One   Assigned: January 22, 2004   Due: January 29, 2004

Homework Two   Assigned: January 27, 2004   Due: February 3, 2004

Homework Three   Assigned: February 3, 2004   Due: February 10, 2004

Homework Four   Assigned: March 4, 2004   Due: March 16, 2004

Homework Five   Assigned: March 23, 2004   Due: March 25, 2004

TAKE-HOME EXAMINATION   Assigned: March 25, 2004   Due: April 1, 2004
Please note that the typo on problem three has been corrected. You may wish to print out a new version of the exam.

FINAL EXAMINATION   Assigned: April 29, 2004   Due: May 6, 2004