Day 1: MAT385, Fall, 2002

1. Name
2. Year (Senior, etc.)
3. Major
4. Preferred email address (if different from NKU address)
5. Where are you from?
6. Working? If so, where and how much?
7. Why are you taking this course?
8. What is your math background/experience?
9. Something special about yourself.

We will always spend one hour covering the material of a section in class, and a second hour doing related problems. Your job (if you should choose to accept it): to do the reading, to do the assignments - ahead of time! (That is to say, on time.)

We will be covering portions of the following chapters:

• Chapter 1: Logic
  • strip away meaning in order to concentrate on form
  • translate English into the symbolism of logic (formalize what is often left imprecise)
  • logical reasoning cannot help but stand you in good stead
• Chapter 2: Proofs, Recursion, and Analysis of Algorithms
  • Direct versus indirect proofs, especially for proving logical arguments (from chapter 1).
  • Mathematical induction, leading to recursion
  • Determining the quality of algorithms, by recursion.
• Chapter 3: Sets
  • Elementary aspects of set theory
  • Counting elements of sets: why some infinities are bigger than others.
  • The similarity between logic and set theory will be more apparent later
• Chapter 5: Graphs and Trees
  • Graphs and Trees capture information in many different contexts (e.g. a family tree, a unix file system)
  • How can we manipulate information stored in a graph?
• Chapter 6: Graph algorithms
  • shortest path, minimal spanning tree, etc.
  • Constructing optimal graphs
• Chapter 7: Boolean Algebras and Computer Logic
  • Operations in logic and set theory are specific cases of Boolean Algebras
  • There is a nice correspondence between boolean expressions, truth functions (or tables), and logic networks (which carry out logical functions for technological applications)
  • We simplify, or optimize, logic networks
  • Binary arithmetic is a particular special application of this section
• Chapter 8: Finite State Machines
  • Regular expressions
  • We build machines that recognize expressions (strings of characters), and optimize the machines.