# Math 109 Winter 2007

### Instructors

#### Professor:

Name Office E-mail Phone Office Hours Lecture Time Lecture Place
Prof. Daniel Rogalski AP&M 5131 drogalsk@math.ucsd.edu 534-4421 M11am-12pm, W 3-4pm MWF 2-2:50pm WLH 2207

#### Teaching Assistant:

Name Office E-mail Office Hours Section Times Section Place
Larissa Horn 6452 AP&M ldhorn@math.ucsd.edu W1-2pm, F10-11am Tue 7-7:50pm, 8-8:50pm HSS 2152

### General Course Information

Textbook: An introduction to Mathematical Reasoning, by Peter J. Eccles.

This course is intended to prepare you for the upper-division math courses required of math majors. In it, you will learn basic concepts including properties of integers, set theory, functions, and counting. You will also learn techniques and conventions for writing proofs in higher mathematics.

There will be 2 in-class midterms on Wed. 1/31/07 and Wed. 2/28/07, and a final exam on Mon 3/19/07 from 3pm-6pm. No makeup exams will be given.

Homework assignments will be due weekly on Fridays in class. Late homework cannot be accepted. Here is my specific Homework policy for this class.

The final grade will be determined as follows: Homework 25%, Midterms 25%, Final Exam 50%.

More detailed descriptions, including a tentative syllabus, may be found in the first day course handout here: Course syllabus
Check below for more up-to-date information about the schedule of homework and lectures.

### Schedule of Lectures:

1/8/07. Propositions. Introduction to arithmetic (even and odd).
1/10/07 Connectives (and, or, not, implies). Order properties of the real numbers. Direct proofs.
1/12/07 Proofs by contradiction and by contrapositive. Proof that sqrt(2) is irrational.
1/15/07 NO CLASS
1/17/07 Proofs by induction I. (chap 5)
1/19/07 Proofs by induction II (strong induction). Proof that any positive integer > 1 can be written as a product of primes. Fibonacci numbers.
1/22/07 Set Theory I: sets, defining sets, union, intersection, difference. Proving two sets are equal. (chap 6)
1/24/07 Set Theory II: complements and the power set. Introduction to quantifiers (chap 7).
1/26/07 Finish quantifiers. The division theorem and proof. (chap 15).
1/29/07 Applications of the division theorem. The Euclidean Algorithm. (chap 16)
1/31/07 EXAM I
2/2/07 The Euclidean Algorithm.
2/5/07 Application of the Euclidean Algorithm and diophantine equations.
2/7/07 Proof of the theorem on the solutions to ax + by = c. Introduction to functions (chap 8-9).
2/9/07 More on functions. Injections and surjections.
2/12/07 Bijections. Composition of functions. Inverse functions.
2/14/07 Images and inverse images of subsets under functions. Congruence of integers (chap 19)
2/16/07 Congruence, continued. Congruence classes (chap 21).
2/19/07 NO CLASS
2/21/07 Z_m: Addition and multiplication of congruence classes. (chap 21)
2/23/07 Equivalence relations I. (chap 22)
2/26/07 Equivalence relations and Partitions. (chap 22)
2/28/07 EXAM II
3/2/07 Definition of finite sets. The pigeonhole principle. (Chap 10-11).
3/5/07 Elementary counting. Inclusion/exclusion. (Chap 10, 12).
3/7/07 Permutations/Combinations/Binomial Theorem. (Chapter 12)
3/9/07 Countability I (Chapter 14)
3/12/07 Countability II (Chapter 14)
3/14/07 Preview of courses after Math 109
3/16/07 Review.
3/19/07 Final Exam, 3-6pm.

### Homework Assignments and other handouts:

Homework #1, due 1/12/07

Homework #2, due 1/19/07

Homework #3, due 1/26/07

Homework #4, due 2/02/07

Homework #5, due 2/09/07

Exam I plus solutions

Homework #6, due 2/16/07

Homework #7, due 2/23/07

Homework #8, due 3/9/07

Exam II plus solutions

Homework #9, due 3/16/07