Computer Science Backbone of the Liberal Arts

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Computer ScienceBackbone of the Liberal Arts

• Where is the Science in Computer Science

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Science?

• A natural science?
• Experimentation?
• Empirical Approach?
• Labs?

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Oxford Dictionary Definition

• Sometimes the term science is used to denote a
  department of practical work which depends on the
  knowledge and conscious application of
  principles an art, on the other hand being
  understood to require merely knowledge of
  traditional rules and skill acquired by habit.

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What is Computer Science?

• Don Knuth an algorithmic approach to problem
  solving
• Algorithms encompass the whole range of concepts
  dealing with well-defined processes, including
  the structure of data that is being acted upon as
  well as the structure of the sequence of
  operations being performed.

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What is a Liberal Arts Education?

• Not about facts, but relationships
• Not about squelching curiosity, but fostering it
• About learning to learn
• About analytic thinking
• About making choices that lead to an enjoyment
  and appreciation of life
• About ideas and their representation

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The Seven Liberal Arts

• The Trivium grammar, rhetoric, logic (traced to
  5th century)
• The Quadrivium arithmetic, music, geometry, and
  astronomy (Interpretation of the universe, begun
  by Greeks)

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A Bit of History

• Euclid set the tone for trying to describe the
  world. (modeling)
• The Elements a best seller for centuries
• Erastosthenes algorithm for finding primes
• 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
• How many primes? Twin primes? Prime forms?
  (contributions to other disciplines)

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Mersenne numbers 2p 1 1952 Computers found
that these are prime for p 521, 607, 1279,
2203, and 2281. K Largest Mersenne prime found is
2206091 1. 14 pages to exhibit at 75
characters per line and 60 lines per page.
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So What?

• Significance of Notation
• Expressiveness for ideas
• 0 Mayas and Arabs about the same time
• 1577 Robert Recorde
• Leibnitz dream general method in which all
  truths of reason would be reduced to a kind of
  calculation All I have contributed is
  notation.

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Logic for Analytical Thinking

• George Boole algebraic basis for logic
• Augustus DeMorgan
• David Hilbert Formalize all of mathematics as
  an axiomatic system in which theorems would be
  proved purely by symbol manipulation (automated
  process)

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20th Century CS Ideas

• Bertrand Russell Principia Mathematica small
  number of axioms, 3 volumes
• Alan Turing set out to achieve Hilberts goal by
  designing a theoretic machine for determining
  whether a given statement is true or false.
• Concluded that decidability is out of the question

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Greatest single piece of work in the whole
history of mathematical logic

• Kurt Godel proof that Hilberts proposal was
  impossible. Any formal system that included
  arithmetic was either incomplete or inconsistent.
• Proof took 128 pages (1929)
• Current CS concepts can do this in one page.

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Special Challenges

• Represent infinite ideas with finitely many
  symbols real numbers, integers
• Clever ways to carry out fast computations
  space travel
• Providing models for testing without danger
  computer surgery, generations of drug trials

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Classification of Problems

• Solvable
• Tractable
• Intractable
• Unsolvable
• P NP?

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Curriculum What its not

• How to use software packages Theyre out of
  date quickly. Students teach faculty how to use
  them.
• Programming Languages Clever ways to use
  bizarre syntax

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Curriculum What it is

• Criteria for designing good software
• Criteria for choosing good ways to implement
  designs
• Methods for checking efficiency
• Methods and tools for representing abstraction
  advantageously

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More Curriculum

• Aritificial Intelligence biological,
  psychological, philosophical
• Ethical Considerations What can we do? Should
  we do it?

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Example iteration

• Function Fibonacci(n integer) integer
• If(n1 or n2) then Fibonacci 1
• else
• oldfib1 1
• oldfib2 1
• For I 3 to n do
• begin
• Fibonacci oldfi1 oldfib2
• oldfib1 oldfib2
• oldfib 2 Fibonacci
• end

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Example recursion

• Recursive function fib(n integer) integer
• begin
• if (n 0 or n 1) then
• fib 1
• else
• fib fib(n-1) fib(n-2)
• end

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Efficiency Analysis

• Iteration linear (loop is repeated n times
  where n is the number whose fibonacci value is
  required
• Recursion 2n (lifetime of the universe for
  large n). T(n) cT(n-1) T(n-2)
• For n 10, 2n 1024
• For n 1000

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Edsger Dijkstra

• Computers are extremely flexible and powerful
  tools, and many feel that their application is
  changing the face of the earth. I would venture
  the opinion that as long as we regard them
  primarily as tools, we might grossly
  underestimate their significance. Their
  influence as tools might turn out to be but a
  ripple on the surface of our culture, whereas I
  expect them to have a much more profound
  influence in their capacity of intellectual
  challenge.

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The Scaling up Challenge

• Given a large problem to solve
• Split it into smaller problems
• Solve each small problem efficiently
• Compose the small solutions to address the large
  problem

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Top Down Design for a Poem

• Long enough for critics, short enough for public
• Repetition of interesting sound
• Said by some animal not a pig, not a dog, not a
  cow, how about a bird? A black bird?
• Subject poignant and serious death
• Who? Lovely young woman

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Contributions to Life

• Environment (modeling processes)
• Storing and retrieving data (the web every
  aspect of civilization)
• Health (drug testing, record keeping)
• Education (on-line resources)
• Communication (instant)
• Government (voting)

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Churchs Thesis The Intuitive Notion of
Computability

• Algorithms
• Grammars
• Turing Machines
• Primitive Recursive Functions
• Finitely Aximatizable Theories
• Computable Functions

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Summary What is CS?

• A branch of mathematics that addresses
• What problems are solvable?
• How can we express them precisely?
• Which problems are tractable?
• How can we reason about our solutions?
• Do we do our computing the way we do because our
  methods are sound or because of technical
  limitations?

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The CS Hope

• Grant me the courage to solve the problems I can.
• Grant me the insight to recognize those I cannot.
• Grant me the capability to know the difference.

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The Happy CS Major

• Philosophers approach each day with uncertainty,
  hesitancy, and the pessimistic assumption that
  pondering lifes great mysteries may lead us
  nowhere.
• Computer Scientists approach each day with
  optimism, enthusiasm, and a sense of anticipation
  for what problems will be posed and solved.