Math 215 Introduction to Advanced Mathematics
Fall 2006
- Week 1 mathematical statements, logical connectives,
truth tables, negation, implications
Read Chapters 1 and 2
- Week 2 Proofs, direct proofs, proofs by cases,
Read Chapter 3
- Week 3 contrapositives, converses, proofs by contradiction,
proof of irrationality of the square root of two
Read Chapter 4
- Week 4 proof that there are infinitely many prime
numbers, proofs by induction, strong induction
Read Chapter 5
- Week 5 Fibonacci Numbers, Sets,
equality of sets, operations on sets, Venn Diagrams
Read Chapter 6
- Week 6
difference of sets, power sets, complements,
Midterm I Friday October 6, covering Chapters 1-6.
- Week 7
cartesian products, universal and existential quantifiers,
methods of proof,
alternation of quantifiers,
Read Chapter 7
- Week 8
Convergence of sequences, functions
Read handout on sequences and Chapter 8.
- Week 9
graphs of functions, injective, surjective and bijective
functions, inverse functions
Read Chapter 9
- Week 10
image and preimage functions, counting, cardinalitiy of finite
sets, addition and the inclusion-exclusion principle
Read Chapter 10
- Week 11
the multiplication principle, counting the number of functions f:X -> Y,
counting the power set of a finite set, counting the number of
injections f:X->Y
Read Chapter 12.1-12.2
- Week 12
binomial coefficients
Midterm II Friday November 17, Chapters 6-10, 12
Read Chapter 12
- Week 13 pigeon hole principle,
subsets of finite sets are finite
Thanksgiving
Read Chapter 11
- Week 14 cardinalities of infinite sets,
denumerable sets, Dedekind's characterization
of infinite, examples of denumberable sets
Read Chapter 14
- Week 15 Cantor's Theorem,
possible additional topics if time permits: Binomial theorem
(Chapter 12.3) or equivalence relations (Chapter 22)
Last revised: 11/8/06