University of Rhode Island MTH307: Introduction to Mathematical Rigor
Spring 2016


Here is a course timetable showing exactly where we are in class. I will attempt to update it at least weekly, to give you an idea of the reading you need to do to prepare for class.

Week beginningSectionNotes
01/251.1 Introduction to Sets
1.2 Cartesian Products
First week of classes
02/011.3 Subsets
1.4 Power Sets
1.5 Union, Intersection and Difference
1.6 Complements
02/081.7 Venn Diagrams
1.8 Indexed Sets
1.9 Sets which are Number Systems
02/152.1 Statements
2.2 And, Or, Not
2.3 Conditional Statements
2.4 Biconditional Statements
02/222.5 Truth Tables for Statements
2.6 Logical equivalence
2.7 Quantifiers
2.8 More on Conditional Statements
2.9 Translating English to Symbolic Logic
02/292.10 Negating Statements
2.11 Logical Inference
4.1 Theorems
4.2 Definitions
03/074.3 Direct Proof
4.4 Using Cases
4.5 Treating Similar Cases
Midterm I in class: 03/10/16
03/145.1 Contrapositive Proof
5.2 Congruence of Integers
03/21Spring BreakHave a good one!
03/286.1 Proof by Contradiction
6.2 Proving Conditional Statements by Contradiction
04/047.1 Proving Biconditional Statements
7.3 Existence and Uniqueness Proofs
7.4 Constructive v Non-Constructive Proofs
8.1 How to Prove a∈A
8.2 How to Prove A⊆B
8.3 How to Prove A=B
04/119 Disproof
10 Mathematical Induction
04/1810 Mathematical InductionMidterm II in class: 04/19/16
04/2511 Relations
12 Functions
13 Cardinality
13 will be touched on very briefly, and will likely not be examined