MAT 511: Fundamental Concepts of Mathematics
Fall 2016

## Syllabus and Homeworks

Homeworks
Homework sets will be typically assigned weekly on Thursday and due next Th in class. They will be posted on this web site (NOT on blackboard site!). Late homework will not be accepted. However, grades for homework assignments may be dropped in cases of documented medical problems or similar difficulties.

Below is the tentative syllabus, subject to change.

Week Dates Notes Topics HW Due date
1 8/29 - 9/2 Introduction.
1.1 Logic and connectives
1.2 Conditionals and biconditionals
HW1 9/8
2 9/5 - 9/9 9/5, 9/6: No classes - Labor day 1.3 Quantified Statements Section 1.3: 1 a - g, 9 c- f, 10 f-h. Also, write symbolically the statement "for any positive real number, there exists a smaller positive real number". You are allowed to use variables taking value in the universe of all real numbers. 9/15
3 9/12-9/16 1.4 Basic Proof Methods I
1.5 Basic Proof Methods II
HW3 9/22
4 9/19 - 9/23 Handout 1 1.6 Proofs Involving Quantifiers
1.7 Strategies for Constructing Proofs
HW4 9/29
5 9/26 - 9/30 2.1 Basic Concepts of Set Theory
2.2 Set Operations
HW5 10/6
6 10/3 - 10/7 2.4 Mathematical Induction
2.5 Equivalent Forms of Induction
HW6 10/13
7 10/10 - 10/14 10/13: midterm Review and midterm
8 10/17 - 10/21 3.1 Relations
3.2 Equivalence Relations
HW7 10/27
9 10/24 - 10/28 3.3 Partitions
4.1, 4.2: Functions. 4.5: Set images
HW8 11/3
10 10/31 - 11/4 4.3 Injective and Surjective Functions
4.4 Bijections; Inverse functions
11 11/7 - 11/11 5.1 Equivalent Sets; Finite Sets; pigeonhole principle
2.6 Principles of Counting
HW9 (updated on 11/10) 11/15
12 11/14 - 11/18 2.6 Principles of Counting continued 5.2 Infinite sets HW10 (updated on 11/10) 11/22
13 11/21 - 11/25 No classes on Nov 23-25: Thanksgiving break 5.3 Countable sets
14 11/28 - 12/2 Uncountable sets HW11 12/6
15 12/5 - 12/9