CSC151.01 2006S, Class 54: What is Computer Science, Revisited?

Admin:
* EC: The final Thursday Extra of the semester is Thursday at noon.
  * Topic: Using Scheme to write a ray tracer
  * Pizza
* I anticipate distributing grades tomorrow.

Overview:
* What is CS?
* Subfields of CS.
* Related Disciplines.

/What is CS?/

* Computer Science is the study of Algorithms and Data
  * An algorithm is a set of instructions that do something
  * Data, by example, can be numbers, lists, vectors, files, ...
* How did we study algorithms?
  * Looked at building blocks
  * Reading: Compared different algorithms for the same problem
    * E.g., kernels or not
    * E.g., How do humans think about it
  * Designed algorithms
  * Implemented algorithms in Scheme
  * Wrote algorithms in English
  * Observed in action
    * To better understand
    * To check for correctness
    * For cost/efficiency
  * Found general techniques for writing algorithms

How do computer scientists study algorithms?
* Design algorithms
* Implement those designs
* Analyze for efficiency
  * Experimentally
  * Mathematically: Through proof
* Analyze for correctness
  * Experimentally
  * Mathematically: Through proof
* Find ways to design algorithms
* And domains

What kinds of subfields are there?

* Architecture and organization - The hardware
  * How do I represent data?
  * How do I efficiently provide the basic operations?
Example
  * Most modern computers represent all data as a sequence of 0's
    and 1's.
  * Represent positive integers using binary numbers.
  * Addition: Use things that are easy to build
    * And gates, (and 1 1) = 1 (and anything else) = 0
    * Or gates are 1 when either input is 1
    * Not gates Convert 1 to 0 or 0 to 1.
    * Given a = (a8 a4 a2 a1) and b = (b8 b4 b2 b1), 
      compute the sum of a and b
     * Worry about the 1's position
       (not (or (and a1 b1) (not (and b1 b2))))
  * CSC211

* Operating Systems - Supporting Programs
  * Access to mouse, keyboard, hard drive, etc.
  * Interesting problems that come up
  * Famous OS problem: Dining philosophers
  * CSC213

* Software Design - Building Programs
  * Technical: How do you structure large programs
  * Social: How do you structure teams
  * Process: Waterfall vs. Agile
  * CSC223 - CSC152 is prereq

* Algorithms
  * Design (typical designs)
  * New, general algorithms
  * Prove aspects of algorithms
  * Interesting variants
  * Proof: If your basic operations are comparison and swapping in
    a vector, you can't do better than c*nlogn
  * CSC301
  * A bit in CSC152
  * MAT218, but not really

Programming Languages:
* The design of the languages in which we write algorithms
* Taught in CSC302

Theory
* What does it mean to be computable?
  * Church-Turing Thesis: All sufficiently powerful models 
    are equivalent
* What things are and are not computable?
  * The Halting problem: Given a procedure and an input to that
    procedure, determine whether or not it produces a value
    (alternately, recurses forever)
* What things are difficult to compute?
  * The travelling salesperson problem - Given a set of cities,
    find the shortest path through those cities