Lecture7 History CS

8/12/2019 Lecture7 History CS

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CT3340/CD5540

Research Methodology for Computer Science and Engineering

History of Computer Science

Gordana Dodig-Crnkovic

Department of Computer Science and EngineeringMlardalen University

2003


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HISTORY OF COMPUTER SCIENCE

LEIBNIZ: LOGICAL CALCULUS

BOOLE: LOGIC AS ALGEBRA

FREGE: MATEMATICS AS LOGIC CANTOR: INFINITY

HILBERT: PROGRAM FOR MATHEMATICS

GDEL: END OF HILBERTS PROGRAM

TURING: UNIVERSAL AUTOMATON VON NEUMAN: COMPUTER


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SCIENCE

21

Natural Sciences

(Physics,

Chemistry,

Biology, )

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Social Sciences(Economics, Sociology, Anthropology, )

3

The Humanities(Philosophy, History, Linguistics )

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Logic

&

Mathematics1

Culture(Religion, Art, )

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The whole is more than the sum of its parts. Aristotle, Metaphysica


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SCIENCE, RESEARCH, DEVELOPMENT AND TECHNOLOGY

Science

Research

Development

Technology


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LEIBNIZ: LOGICAL CALCULUS

Gottfried Wilhelm von Leibniz

Born: 1 July 1646 in Leipzig, Saxony (now Germany)Died: 14 Nov 1716 in Hannover, Hanover (now Germany)


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LEIBNIZS CALCULATING

MACHINE

For it is unworthy of excellent men to lose hours like slaves inthe labor of calculation which could safely be relegated to

anyone else if the machine were used.


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LEIBNIZS LOGICAL CALCULUS

DEFINITION 3. A is in L, or L contains A, is the same as to say that L can bemade to coincide with a plurality of terms taken together of which A is one. BN = L signifies that B is in L and that B and N together compose orconstitute L. The same thing holds for larger number of terms.

AXIOM 1. B N = N B.POSTULATE. Any plurality of terms, as A and B, can be added to compose

A B.

AXIOM 2. A A = A.PROPOSITION 5. If A is in B and A = C, then C is in B.

PROPOSITION 6. If C is in B and A = B, then C is in A.

PROPOSITION 7. A is in A.

(For A is in A A (by Definition 3). Therefore (by Proposition 6) A is in A.)

.

PROPOSITION 20. If A is in M and B is in N, then A B is in M N.


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BOOLE: LOGIC AS ALGEBRA

George Boole

Born: 2 Nov 1815 in Lincoln, Lincolnshire, EnglandDied: 8 Dec 1864 in Ballintemple, County Cork, Ireland


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George Boole is famous because he showed that rules used inthe algebra of numbers could also be applied to logic.

This logic algebra, called Boolean algebra, has manyproperties which are similar to "regular" algebra.

These rules can help us to reduce an expression to anequivalent expression that has fewer operators.


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Properties of Boolean Operations

A ANDB A B

A OR B A + B


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A B A|B

0 0 0

0 1 1

1 0 1

1 1 1

OR (|)


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A B Q

0 0 0

0 1 11 0 1

1 1 1

OR Gate


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AND Operator

dairy products AND export AND europe

All terms are present


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AND (&)

A B A&B

0 0 0

0 1 0

1 0 0

1 1 1


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A B Q

0 0 0

0 1 0

1 0 0

1 1 1

AND Gate


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XOR Operator (Exclusive OR)

sheep XOR goatsOne or other term is present, but not both.


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A B A^B

0 0 00 1 1

1 0 1

1 1 0

XOR (^)


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A B Q

0 0 0

0 1 1

1 0 1

1 1 0

XOR Gate


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A ~A

0 1

1 0

NOT (~)


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A Q

0 1

1 0

NOT Gate


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NAND

A B NAND

0 0 10 1 1

1 0 1

1 1 0

All inputs on = off, else on.


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A B Q

0 0 1

0 1 1

1 0 1

1 1 0

NAND Gate


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A B Q

0 0 10 1 0

1 0 0

1 1 0

NOR Gate


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XNOR

A B NOR

0 0 10 1 0

1 0 0

1 1 1


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A B Q

0 0 1

0 1 0

1 0 0

1 1 1

XNOR Gate


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FREGE: MATEMATICS AS LOGIC

Friedrich Ludwig Gottlob Frege

Born: 8 Nov 1848 in Wismar, Mecklenburg-Schwerin (now Germany)Died: 26 July 1925 in Bad Kleinen, Germany


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The Predicate Calculus (1)

In an attempt to realize Leibnizs ideas for a language of

thought and a rational calculus, Frege developed a formalnotation (Begriffsschrift).

He has developed the first predicate calculus: a formal systemwith two components: a formal language and a logic.


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The Predicate Calculus (2)

The formal language Frege designed was capable of:expressing

predicational statements of the form xfallsunder the conceptF and xbears relationRtoy, etc.,

complex statements such as it is not the case that ...

and if ... then ..., and

quantified statements of the form Somexis such that...x... and Everyxis such that ...x....


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The Analysis of Atomic Sentences andQuantifier Phrases

Fred loves Annie. Therefore, some xis such that xloves

Annie.

Fred loves Annie. Therefore, some xis such that Fred loves x.

Both inferences are instances of a single valid inference rule.


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Proof

As part of his predicate calculus, Frege developed a strictdefinition of a proof. In essence, he defined a proof to be

any finite sequence of well-formed statements such thateach statement in the sequence either is an axiomorfollows from previous members by a valid rule ofinference.


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CANTOR: INFINITY

Georg Ferdinand Ludwig Philipp Cantor

Born: 3 March 1845 in St Petersburg, RussiaDied: 6 Jan 1918 in Halle, Germany


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Infinities

Set of integers has an equal number of members as the set ofeven numbers, squares, cubes, and roots to equations!

The number of points in a line segment is equal to thenumber of points in an infinite line, a plane and allmathematical space!

The number of transcendental numbers, values such as and ethat can never be the solution to any algebraicequation, were much larger than the number of integers.


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Hilbert described Cantor's work as:- ...the finest product ofmathematical genius and one of the supreme achievementsof purely intellectual human activity.


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HILBERT: PROGRAM FORMATHEMATICS

David Hilbert

Born: 23 Jan 1862 in Knigsberg, Prussia (now Kaliningrad, Russia)Died: 14 Feb 1943 in Gttingen, Germany


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Hilbert's program

Provide a single formal system of computation capable ofgenerating all of the true assertions of mathematics fromfirst principles (first order logic and elementary set

theory).

Prove mathematically that this system is consistent, that is,that it contains no contradiction. This is essentially a proofof correctness.

If successful, all mathematical questions could be establishedby mechanical computation!


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GDEL: END OF HILBERTS PROGRAM

Kurt Gdel

Born: 28 April 1906 in Brnn, Austria-Hungary (now Brno, Czech Republic)Died: 14 Jan 1978 in Princeton, New Jersey, USA


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Incompleteness Theorems

1931 ber formal unentscheidbare Stze der PrincipiaMathematica und verwandter Systeme.

In any axiomatic mathematical system there arepropositions that cannot be proved or disproved within theaxioms of the system.

In particular the consistency of the axioms cannot beproved.


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TURING: UNIVERSAL AUTOMATON

Alan Mathison Turing

Born: 23 June 1912 in London, EnglandDied: 7 June 1954 in Wilmslow, Cheshire, England


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When war was declared in 1939 Turing moved to work full-time at the Government Code and Cypher School atBletchley Park.

Together with another mathematician W G Welchman,Turing developed the Bombe, a machine based on earlierwork by Polish mathematicians, which from late 1940 was

decoding all messages sent by the Enigma machines of theLuftwaffe.


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At the end of the war Turing was invited by the NationalPhysical Laboratory in London to design a computer.

His report proposing the Automatic Computing Engine(ACE) was submitted in March 1946.

Turing returned to Cambridge for the academic year 1947-48 where his interests ranged over topics far removed fromcomputers or mathematics, in particular he studiedneurologyandphysiology.


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1948 Newman (professor of mathematics at the University ofManchester) offered Turing a readership there.

Work was beginning on the construction of a computingmachine by F C Williams and T Kilburn. The expectationwas that Turing would lead the mathematical side of thework, and for a few years he continued to work, first on thedesign of the subroutines out of which the larger programs

for such a machine are built, and then, as this kind of workbecame standardised, on more general problems ofnumerical analysis.


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VON NEUMAN: COMPUTER

John von Neumann

Born: 28 Dec 1903 in Budapest, HungaryDied: 8 Feb 1957 in Washington D.C., USA


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In the middle 30's, Neumann was fascinated by the problemof hydrodynamical turbulence.

The phenomena described by non-linear differential equations

are baffling analytically and defy even qualitative insightby present methods.

Numerical work seemed to him the most promising way toobtain a feeling for the behaviour of such systems. This

impelled him to study new possibilities of computation onelectronic machines ...


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Von Neumann was one of the pioneers of computer sciencemaking significant contributions to the development oflogical design. Working in automata theory was a

synthesis of his early interest in logic and proof theory andhis later work, during World War II and after, on largescale electronic computers.

Involving a mixture of pure and applied mathematics as wellas other sciences, automata theory was an ideal field for

von Neumann's wide-ranging intellect. He brought to itmany new insights and opened up at least two newdirections of research.


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He advanced the theory of cellular automata,advocated the adoption of the bit as a measurement ofcomputer memory, and

solved problems in obtaining reliable answers fromunreliable computer components.


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Computer Science Hall of Fame

Richard Karp Donald Knuth Manuel Blum

Stephen Cook Sheila Greibach Leonid Levin


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COMPUTING

Overall structure of the CC2001 report


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Technological advancement

over the past decade The World Wide Web and its applications

Networking technologies, particularly those based on TCP/IP

Graphics and multimedia

Embedded systems

Relational databases

Interoperability

Object-oriented programming

The use of sophisticated application programmer interfaces (APIs)

Human-computer interaction Software safety

Security and cryptography

Application domains


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Overview of the CS Body of Knowledge

Discrete Structures Programming Fundamentals Algorithms and Complexity Programming Languages

Architecture and Organization Operating Systems Net-Centric Computing Human-Computer Interaction Graphics and Visual Computing Intelligent Systems

Information Management Software Engineering Social and Professional Issues Computational Science and Numerical Methods

Documents

Lecture7 History CS