Great Ideas in Computer Science

1.  The Great Ideas of Computer Science So Far

2.  Insight II:  Can do anything that a computer can
                    do, using only 5 actions:
                    *    either Karel's 5 basic instructions
                         or the 5 instructions of a Turing
                         machine (to be discussed later)

3.  Insight III:  Can express all complex actions, using
                      only 3 rules of grammar:
                      *    sequence (s1;s2)
                      *    selection (choice):  (if-then-else)
                      *    repetition (while-do)

4.  Insight IIIA:  Can name new instructions defined
                        using insights II & III.

5.  The notion of an "algorithm":
    *    a procedure for solving a problem, such that
         it is unambiguous and effective,
          where "effective" means:  it is correct
                                                & it halts.

6.  Algorithms can be implemented in computer
     programs:
    *    Input (including data) is given to the
          computer running the program that
          implements the algorithm,
         then the program processes the data,
         and the computer provides output

    *    I/P  -->  algorithm (program) --> O/P

7.  Decision Trees:
    *    How to get a computer to help you solve a
        problem

    *    Note that the programmer must know
        (& give to the computer) all the information!
 

2.  Great Idea #8:

e.g.)    A word processor (such as MS Word) or a text
          editor (such as Pico)

a)   Think of text as a single, very long string of
    alphabetical letters, numerals (0, ..., 9), the blank
    space, symbols, <return>, <tab>, etc.

b)    Some word-processing operations:

    insert new text:
        s1 s2 --> s1 s3 s2
        e.g.)    'abde' --> 'abcde'

    delete text:
        s1 s2 s3 --> s1 s3
        e.g.)    'abxcd' --> 'abcd'

    move text (= delete from one place
                        & insert in another)
        s1...s2...s3...s4 --> s1...s3...s2...s4
        e.g.)    'acbd' --> 'abcd'

    copy text (=insert)
        s1...s2...s3 -->    s1...s2...s2...s3
        e.g.)    'abc' --> 'abbc'

    replace text (=delete old string & insert new one)
        s1 --> s2
        e.g.)    'axc' --> 'abc'

    concatenate text (=join, or insert):
        s1, s2 --> s1s2
        e.g.)    'ab', 'cd' --> 'abcd'

    etc.
 

3.  The Post Correspondence Problem