A first course in the techniques of proving theorems and abstract mathematical results. Includes an introduction to set theory and the propositional calculus

Table of Contents

Pre-Requisites

FTCAP

Content

Topics will include: Propositions and Connectives, Conditionals and Biconditionals, Quantifiers, Basic Proof Methods I, Basic Proof Methods II, Proofs Involving Quantifiers, Additional Examples of Proofs, Basic Notions of Set Theory, Set Operations, Extended Set Operations and Indexed Families of Sets, Induction, Equivalent Forms of Induction, Principles of Counting, Cartesian Products and Relations, Equivalence Relations, Partitions, Ordering Relations, Graphs of Relations, Functions as Relations, Constructions of Functions, Functions that are Onto; One-to-one Functions, Equivalent Sets; Finite Sets, Infinite Sets, Countable Sets, Ordering of the Cardinal Numbers, Comparability of Cardinal Numbers and the Axiom of Choice, Algebraic Structures, Groups, Examples of Groups, Subgroups, Cosets and Lagrange's Theorem, Quotients Groups, Isomorphism; The Fundamental Theorem of Group Homomorphisms

Goals

None

Assessment

1. Each question you want to get regraded should be on a separate page or pages. Multipart questions can go on the same page.
2. Show all your work for the question.
3. Attach all the regrade pages together using either staples or a paper-clip and slip the regrade into the exam.
4. You must include your original exam. No original, no regrade.

Schedule

Whatever

Syllabi

Spring 2005

Resources

None available, anywhere ever.