Math 8

Announcements
June 25, 2007: This website will be updated regularly for the rest of the class.

July 3, 2007: The movie The Proof has been rescheduled for Friday July 6 in lecture.

July 13, 2007: The deadline for homework 3 has been moved to Wednesday July 18.

July 20, 2007: The deadline for homework 4 has been moved to Wednesday July 25.



Syllabus
Lecture: MWF 2:00 - 2:50 in 2120 Girvetz
Instructor: Peterson Trethewey
Office: 6432-P South Hall
Office Hours: MWF 12-1
email: peterson@math.ucsb.edu

TA: Ellie Grano
Discussions:
TR 2:00-2:50 in 1236 HSSB
TR 3:00-3:50 in 1224 HSSB
email: ellie@math.ucsb.edu

Website: The lecture schedule, homework assignments, and announcements will be posted on the course website

http://math.ucsb.edu/~peterson/teaching/math8/index.html

Textbook: Larry J. Gerstein: Introduction to Mathematical Structures and Proofs (Springer-Verlag).

Prerequisites: Math 3B or equivalent.

Description: The first half of the class covers subjects which are widely regarded as fundamental to all mathematics. Topics include: symbolic logic, set theory, fuctions, cardinality and general techniques of mathematical proof. The second half of the course focuses on number theory and combinatorics. We will cover divisibility, prime numbers, GCD/LCM, Euclid's algorithm, congruence, groups of permutations and other topics if time permits.

Homework: Homework is assigned every monday, and due the following monday. Students are encouraged to collaborate on solving homework problems, but the work you turn in must be your own. Some problems on each homework assignment will be graded. Late homework will not be accepted.

Exams: There will be one midterm exam, and a final exam, see the online schedule for the dates.

Quizzes: There will be a short quiz every week in discussion.

Grading: HW: 40%, Quizzes: 10%, Midterm: 20%, Final: 30%

DSP: Students with disabilities can get assistance from the Disabled Students Program Office (893-2668). I am happy to work with them and with you.




Schedule

(subject to change)
Date Lecture Topic Relevant Websites Homework
6/25 Introduction and Symbolic Logic HW1 (due Monday 7/2)
6/27 More Symbolic Logic If and Only If
6/29 Circuits with Logic Gates Java Circuit Simulator
7/2 The Method of Mathematical Induction Induction vs Infinite Descent HW2 (due 7/9)
7/4 (Holiday) Proof by Contradiction
7/6 Movie: The Proof Biography: Sophie Germain
7/9 Sets, Unions, Intersections, Power sets Set Theory Symbol Reference Homework 3 (due 7/18)
7/11 Quantifiers, Pairs, Cartesian Product
7/13 Equivalence Relations, Partitions Equivalence Relations
7/16 Equivalence Relations Continued Homework 4 (Due 7/25)
7/18 Functions, Injections, Surjections, Bijections An Introduction to Functions and A Picture
7/20 Cardinality, Countable and Uncountable Infinities, Cantor's Diagonalization Pigeonhole Principle (java)
7/23 TBA Homework 5 (Due 7/30)
7/25 Review
7/27 Midterm on Logic and Set Theory
7/30 Prime Numbers, Divides Operator Mersenne Primes Homework 6 (Due 8/6)
8/1 Divisibility, GCD, Euclid's Algorithm RSA Factoring Challenge
8/3 More on Euclid's Algorithm and the Fundamental Theorem of Arithmetic
8/6 Congruence (mod n) A Game Homework 7 (Due 8/13)
8/8 The Euler Totient Function Modular Arithmetic
8/10 Fermat's Little Theorem Revisited
8/13 Intro to Groups A different look at Groups Homework 8 (Due 8/20)
8/15 The Choice Function, Pascal's Triangle, Binomial Coefficients A picture, The Fibonacci Numbers in Pascal's Triangle
8/17 Permutations and The Symmetric Group
8/20 Cycle Notation, Cycle Decomposition Rubik's Cube Site including a Java Cube Simulator Homework 9 (Due Wednesday 8/29)
8/22 Odd and Even Permutations
8/24 Another Look at Group Theory
8/27 TBA Practice Final
8/29 Review
8/31 Cumulative Final