Math 215 Introduction to Advanced Mathematics

Spring 2007

The schedule is subject to revision.

• 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 Tuesday February 20, covering Chapters 1-5.

Feb 27 to March 13 revised to account for snow. The remainder still needs to be revised. (Feb. 24 announcement)

• Week 7 (Feb 27)
  cartesian products, universal and existential quantifiers, methods of proof, alternation of quantifiers, Introduction to functions

Read Chapter 7 and begin chapter 8. The discussion of chapter 8 will continue the next week.

• Week 8 (March 6)
  functions graphs of functions, injective, surjective and bijective functions, inverse functions
  Read Chapter 9
• Week 10 (March 13)
  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,
  Midterm II Tuesday Mar 20, Chapters 6-10
• Spring Break May 26-30
• Week 12
  counting the power set of a finite set, counting the number of injections f:X->Y, binomial coefficients
  Read Chapter 12
  
  
• Week 13 Rational and Real Numbers
  Read Chapter 13
• Week 14 cardinalities of infinite sets, denumerable and countable sets, uncountability of the real numbers
  Read Chapter 14
• Week 15 Cantor's Theorem, equivalence relations
  Read Chapter
  Final Exam: Tuesday May 8- usual time and place
  
  Last revised: 1/10/07