Intro to Abstract Math

There is no textbook for this course. All lecture notes will be scanned and posted right here.

Office Hours: Mon 1-2pm, Thurs 2-3pm, and by appointment.
Item Date Information
Homework 1
Solutions
Wed Sept 9 Course Notes
What is a Theorem?
The Pythagorean Theorem
Euclid's Elements
Euclid Handout
Euclid's Proof of Prop I.47
Definition of "Euclidean Space"
Homework 2
Solutions
Wed Sept 23 Course Notes
Square Root of 2, 3, 5
Proof by Contradiction
Boolean Functions
Truth Tables
Contrapositive, De Morgan's Law
Definition of "Limit"
Exam1 Solutions
Fri Sept 23 Total: 24 points
A = 21-23 (7 students)
B = 16-20 (7 students)
C = 11-15 (7 students)
[Note: These ranges are very rough.]
Homework 3
Solutions
Mon Oct 12 Course Notes
The Definition of Z
Axioms of Addition
Axioms of Multiplication
Axioms of Order
The Well-Ordering Axiom
Definition of "Induction"
Homework 4
Solutions
Wed Oct 28 Course Notes
The Division Theorem
Greatest Common Divisor
The (Extended) Euclidean Algorithm
Bézout's Identity
Euclid's Lemma
Fundamental Theorem of Arithmetic
Exam2 Solutions
Fri Oct 30 Total: 24 points
A = 20-22 (8 students)
B = 16-19 (6 students)
C = 11-15 (6 students)
[Note: These ranges are very rough.]
Homework 5
Solutions
Wed Nov 18 Course Notes
Applications of the FTA
Euclid's Proof of Infinite Primes
Equivalence Relations
Modular Arithmetic
Fermat's little Theorem
Homework 6
Solutions
Fri Dec 4 Course Notes
The Binomial Theorem
The Freshman's Dream
Euler's Proof of FlT
RSA Cryptosystem
Exam3 Mon Dec 7