CSC151.01 2006S, Class 06: Numeric Values

Admin:
* Absent: LaRue
* Tomorrow we meet in 2435
* Two readings for tomorrow: Characters and Strings
* HW2 returned.  Things are looking up on grading.  Perhaps you'll get
  most of your assignments graded.
* Groups for the week assigned.  
  * An and Cloninger
  * Berg and Mertes
  * Bonnin Cadogan and LaRue
  * Brooks and Pan
  * Brown and Harrington
  * Cartegena and Potthoff
  * Howard and Rider
  * McArdle and McFarlin
  * Rich and Zamora
  * McDonald and Miller
  * Thompson and Wood
* Strategy for assigning groups
  * Same sex (We'll do mixed groups next week).
  * Attempt to group first-years and upper-level students.
  * Other strategies in other weeks (often "random")
* Extra credit:
  * Con Brio concert was a myth.
  * Limit to two of any one category (Con Brio concerts, Football 
    games, etc.)
  * Tomorrow: Department Extra (12:45-2:00 p.m. in Science 2424)
  * Thursday: Convo (11:00-noon, Herrick)
* Reminder: I expect you to try to do the reading in advance of 
  each class.
* Apologies: Today is definitely a "lab techniques" day.

Overview:
* Types.
* Review of Reading
* Lab.
* Reflection.

Types of Numbers:
* Categorization: Precise and Imprecise
  * Precise: Represented exactly
  * Imprecise: Approximated
* Approximation may
  * Save memory
  * Some numbers cannot be represented exactly (e.g., pi)
  * The user requests it.  
  * Might be easier to work with
  * More accurately represents situation
  * Permit decimal representation
* Different types of number:
  * Integers 
    * "whole numbers"
    * Numbers with no fractional component
  * Rational
    * Ratio of integers
  * Real
    * Traditionally a bigger category, includes both rational and
      irrational numbers
    * In Scheme, every real is rational
  * Complex
    * Include imaginary parts (the square root of -1)
    * Can be thought of as points on a plane

Aligning Windows
* Some find it useful to resize to have lab and DrScheme side-by-side

Strategies for Answering Questions

* 1. Type the expressions in the bottom window and look at results.
    > (real? 3/4)
    #t
    > (rational? 3/4)
    #t
* 2. Type the expressions in the top window, click "Run", and look at results.
    (real? 3/4)
    (rational? 3/4)
    RUN
    #t
    #t
* 3. Name the expressions in the top window, click "Run", and query results
    (define ex1a (real? 3/4))
    (define ex1b (rational? 3/4))
    RUN
    > ex1a
    #t
    > ex1b
    #t
* Intersperse symbols that indicate what you're computing
    'is-three-forths-real?
    (real? 3/4)
    'is-three-forths-rational?
    (rational? 3/4)
    RUN
    is-three-forths-real?
    #t
    is-three-forths-rational?
    #t

Exploring procedures should normally involve more than one check.

* Positive and negative
* Integer, rational, and complex 
* Exact and inexact
* ...