By Varun Kanade: A) This is about John von Neumann, one of the founders of Computer Science John von Neumann was a child prodigy. Though his primary interest was Mathematics, he ended up doing diploma in Chemical Engineering from Technische Hochschule in Zürich in 192. In Zurich he used to interact with eminent mathematicians such as Pol ya and Weyl. In 1928 he obtained a doctoral degree in Mathematics. In 1930 he was invited to join Princeton University. He was one of the six professors at the Institute of Advanced Studies, at Princeton, a position he retained till the end of his life. Post world war II, von Neumann concentrated on the development of the Institute for Advanced Studies (IAS) computer and its copies around the world. His work with the Los Alamos group continued and he continued to develop the synergism between computers capabilities and the needs for computational solutions to nuclear problems related to the hydrogen bomb. In 1950 he was employed by IBM as a consultant. von Neumann's contributions to the field of computing are the application of his concepts of mathematics to computing, and the application of computing to his other interests such as mathematical physics and economics. He was unimpressed by the FORTRAN project, and did not feel the necessity for anything other than machine language. This is a famous quoute by John von Neumann. "If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is. Anyone who considers arithmetical methods of producing random numbers is, of course, in a state of sin." Ref: 1. http://ei.cs.vt.edu/~history/VonNeumann.html 2. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Von_Neumann.html B) Some pretty userful(?) sites http://www.afm.sbu.ac.uk/ http://www.cs.pdx.edu/~schubert/cs510fv/ http://www.cs.rhul.ac.uk/home/helen/epsrc_bcsp/info.html http://drona.csa.iisc.ernet.in/~deepakd/verification-03/verification.html http://www.cs.unh.edu/~charpov/Teaching/CS-745/title.html By Harsh Jain: a)Alonzo Church,Father of Lambda Calculus. Alonso Church was a student at Princeton receiving his first degree in 1924, then his doctorate three years later. he was awarded his doctorate for his dissertation entitled Alternatives to Zermelo's Assumption. His work is of major importance in mathematical logic, recursion theory and in theoretical computer science. He created the *lambda-calculus* in the 1930s which today is an invaluable tool for computer scientists. He is best remembered for Church's Theorem (1936), which says that there is no decision procedure for the full predicate calculus. It appears in An unsolvable problem in elementary number theory published in the American Journal of Mathematics 58 (1936), 345-363. His work extended that of Gödel. Church founded the Journal of Symbolic Logic in 1936 and remained an editor until 1979. He wrote the book Introduction to Mathematical Logic in 1956. Reference Links :-> http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Church.html http://en.wikipedia.org/wiki/Lambda_calculus b)Some cool links http://vl.fmnet.info/ The World Library for Formal Methods http://www.math.tau.ac.il/~guy/pa/pltheory.html Collection of Links to Online Books/Courses/Others http://www.cs.cornell.edu/Courses/cs686/2003SP/ Course Page at Cornell http://www.iist.unu.edu/home/Unuiist/newrh/II/1/3/1/page.html seems relevant (lbntl)http://www.cse.iitb.ac.in/harsh/links.html Under Section Theorictical CS,growing section of links By Pranav Kumar: A. Donald Knuth Born:1938,Wisconsin US He is a Professor Emiritus at Stanford,and is best known for his series of books under the head "Art of Computer Programming".Donald Knuth is one of the most prominent theoritical computer scientists.Basically a mathematician at heart,Knuth invented Tex for typesetting mathematical papers.It would interest you to know that he wrote 2 papers in Mathematics in his graduation year and the second one was co-authered by two indians :) Knuth-Bendix Algo(covered in cs206)is another fundamental algo for computing with groups and semi-groups.(Bendix was his student) www-gap.dcs.st-and.ac.uk/~history/Mathematicians/knuth.html www-cs-faculty.stanford.edu/~knuth/ B.Course Links GNU-Prolog http://pauillac.inria.fr/~diaz/gnu-prolog Google Dir http://directory.google.com/Top/Computers/Programming/Languages/Prolog/ By Anish Chandak: A)Augustus De Morgan - A mathematician who loved teaching :) Augustus De Morgan was born in Mandura, India, on June 27, 1806. His father was a colonel in the Indian Army.He entered Trinity College, Cambridge, in 1823 and graduated four years later. Augustus De Morgan was an important innovator in the field of logic. In addition, he had many contributions to the field of mathematics and the chronicling of the history of mathematics("Arithmetical Books", in which he describes the work of over fifteen hundred mathematicians and discusses subjects such as the history of the length of a foot). His most important work, Formal Logic, included the concept of the quantification of the predicate, an idea that solved problems that were impossible under the classic Aristotelian logic. For example, the following is only workable using De Morgan's method: * In a particular group of people, o most people have shirts o most people have shoes o therefore, some people have both shirts and shoes. De Morgan's other works include a system of notations for symbolic logic that could denote converses and contradictions and the famous De Morgan laws i) the complement of the intersection of any number of sets equals the union of their complements. ii)the complement of the union of any number of sets equals the intersection of their complements. If you want to know more about Morgon do visit the following site.It has large and some great links :) 2) Some links where you can get books/compiled material on logic :- a)http://www.cis.upenn.edu/~jean/gbooks/home.html b)http://euclid.trentu.ca/math/sb/pcml/ A link to Trent University,where this course is tought. Somelinks that might be useful for our course :- i)http://www.cs.waikato.ac.nz/~marku/formalmethods.html ii)http://logic.philosophy.ox.ac.uk/ iii)http://plato.stanford.edu/entries/ (A great collection at Stanford) By Kartik Desikan: (A) Gottlob Frege ------------- He is considered the 'father of predicate logic'. His works are greatly applied in mathematical logic as well as analytic philosophy. In his early papers,he presented for the first time what we would recognise today as a logical system with negation, implication, universal quantification, essentially the idea of truth tables etc. Furthermore he was the first person to fully develop the main thesis of logicism,that mathematics is reducible to logic. In his later papers he went on to work on this thesis and set his own definitions of the basic concepts of arithmetic(in the form of axioms), and deduced from them, the basic laws of arithmetic. Unfortunately his genius was not acknowledged by other contemporary mathematicians, and one of his axioms was found to be inconsistent, and under depression he led himself to believe that his work was utter waste. Mathematicians and philosophers now believe the otherwise ... Ref: 1. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Frege.html Biography... 2. http://plato.stanford.edu/entries/frege/ His works are detailed here... 3. http://www.ac-nancy-metz.fr/enseign/philo/textesph/Frege.pdf If you can understand German, his paper 'Die Grundlagen der Arithmetik' (The foundations of arithmetic) is at the above link (B) Lynx -------- 1. This is the homepage site of the book "Logic in Computer Science:modelling and reasoning about systems" http://www.cs.bham.ac.uk/research/lics/ The link 'WWW Tutor' contains Multiple Choice Qs on Logic especially 2. The world of logic... http://www.uni-bonn.de/logic/world.html A site with a plethora of links on logic 3. Material on logic and computation... http://www.andrew.cmu.edu/~avigad/Teaching/landc_notes.ps No specific course based on this particular notes on the site... 4. CSG 274 http://www.ccs.neu.edu/home/attie/FMSA-csg274/ Few articles in 'Reading' looks relevant, and the 'Project' links are also interesting ... By Kumar Gaurav Bijay (2005013): A) This report is an account of Brunn born Austrian(now in Czech Republic) Kurt Godel (1906-78) - one of the pioneers in the field of algorithm verification .Though he is also remembered by physicists(for his famous cosmological model where time-like lines close back on themselves indicating that distant past and distant future are identuical), two of his major achievements in mathematics and logic need mention here:- 1>Incompleteness Principle : Godel inherited a new point of view to artificial intelligence(AI) and human mind concept by his increadible theorem. For many years, people also held the belief that if any problem could be precisely stated, then with enough effort a solution could eventually be found (or else a proof that no solution exists could be provided).One of the great supporters of the above belief was one of the greatest mathematicians of all times, David Hilbert.However the hopes of Hilbert and his followers were dashed when, in 1931, the brillant 25-year-old Austrian mathematical logician Kurt Godel produced a startling theorem which effectively destroyed the Hilbert Programme The source of the theorem depends on the Russell Paradox. In 1902, the British logician and philosopher Bertrand Russell produced his famous paradox. Russell paradox says that; ``R is the set of all sets which are not members of themselves''. So,now is R a member of itself or not?? What Godel showed was that any such precise ('formal') mathematical system of axioms and rules of procedure whatever, provided that it is broad enough to contain descriptions of simple arithmetical propositions and provided that it is free from contradiction, must contain some statements which are neither provable nor disprovable by the means allowed within the system. The truth of such statements is thus 'undecidable' by the approved procedures. Some links: i>http://www.cse.iitd.ernet.in/~suban/cs120/history.html ii>http://www.history.mcs.standrews.ac.uk/history/Mathematicians/Godel.html 2> Modal logic and the proof of "Existence of God" : Gödel has sketched a revised version of Anselm's traditional ontological argument for the existence of God. However, a deeper reason for Gödel's contribution to the ontological argument is that the most sophisticated versions of the ontological argument are nowadays written in terms of modal logic, a branch of logic that was familiar to the medieval scholastics, and axiomatized by C. I. Lewis . It turns out that modal logic is not only a useful language in which to discuss God, it is also a useful language for "proof theory", the study of what can and cannot be proved in mathematical systems of deduction. Consider the following "proof" for the existence of God. Let us call it the argument from omniscience. 1>God is understood to be an individual or being who knows everything, i.e., is omniscient. If something is true, God (real or fictitious) would know it. Similarly, if something is false, God (real or fictitious) would know that as well.Also,God encompasses all rationality. 2>All rational individuals believe in their own existence. Even if they don't exist, this is presumed to be the case. Existing individuals believe correctly in their own existence, while fictitious individuals are sadly mistaken on this point. 3>If God did not exist, then by our first point, above, God would know that he or she did not exist. But this contradicts our second point. So God must exist. Ok,so no-one is convinced by this argument.The basic idea of this argument is that it is modally naive. What have we managed to prove by the argument above, if not the existence of God? The argument defines God to be an omniscient and rational individual. Now mathematicians tend to broadly accept the idea that you can define terms as you like.We would all accept, I think, that whether this being should be called God or not, a proof of the existence of an omniscient rational being is no small accomplishment. So that is not the problem with the argument. The real problem is that the argument makes an assumption that is not brought out explicitly. It assumes that it is possible for an omniscient rational individual to exist, where omniscience includes knowledge about one's own existence. So what the argument really seems to show is that (for God as defined): "If it is possible for a rational omniscient being to exist THEN necessarily a rational omniscient being exists." Link :i>http://www.stats.uwaterloo.ca/~cgsmall/ontology.html B>Course-related stuff: 1>Links: a>http://www.mcs.vuw.ac.nz/courses/COMP202/2003T2/lectures b>http://facstaff.pepperdine.edu/lrogers/ma220/ma220schf3.html 2>Books: a>FM 99 - formal methods : world congress on formal methods in the development of computing systems : proceedings, Toulouse, France, Sept. 20-24, 1999 / edited by Jeannette M. Wing, Jim Woodcock and Jim Davies - 681.3.06:51 b>Formal methods in artificial intelligence / translated by J. Howlett - 681.342 By Lakshmi Narayanaswamy: A) GERHARD GENTZEN Gerhard Gentzen was one of the major figures in the development of modern logic during its stormy period in the 1930s. Born in Greifswald on the Baltic Sea in 1909 he finally was called as a lecturer to the Mathematics Department of the German University in Prague. Immediately after the war, in May 1945, he was imprisoned by the Czechs and died of starvation after two months. He introduced the notion of 'logical consequence' which provided a logic closer to mathematical reasoning than the systems proposed by Frege, Russell and Hilbert. In a paper published in Mathematische Zeitschrift in 1935 Gentzen introduced two new versions of predicate logic no w called the N-system and the L-system. In the following year he gave a consistency proof in terms of an N-type logic for the system S of arithmetic with induction. He joined the University of Gottingen as Hilbert's assistant in 1934. In fact, Gentzen's was the most outstanding contribution to Hilbert's programme of axiomatising mathematics! Sadly, the Second World War and his untimely death came in the way of his dream to research further to establish the foundations of mathematics. References: http://www.menzler-trott.de/d_genz_d.html (translated from German) http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Gentzen.html II) URLs to look up : http://www.earlham.edu/~peters/courses/log/loghome.htm This is a philosophy course called "Symbolic Logic"! :o) Will junta who have Philosophy probably learn about this too? This particular site has notes on Propositional as well as Predicate logic. http://www.math.auckland.ac.nz/~class315/handouts.html This is a math course alright! - complete with tutorials, assignments and solutions! :o) Book to refer: Logic for Mathematicians by A G Hamilton (517.1 Ham) By Sridhar E: A) Biography Born: 10 Sept 1839 in Cambridge, Massachusetts, USA Died: 19 April 1914 in Milford, Pennsylvania, USA Charles Peirce's contributions to logical theory are numerous.He worked on relations building on ideas of De Morgan influenced Schroder, and through Schroder, Peano, Russell, Lowenheim and much of contemporary logical theory.Although Frege anticipated much of Peirce's work on relations and quantification theory, and to some extent developed it to a greater extent, Frege's work remained out of the mainstream until the twentieth century.In contrast to Frege's highly systematic and thoroughly developed work in logic, Peirce's work remains fragmentary and extensive, rich with profound ideas but most of them left in a rough and incomplete form. Pierce's major contribution to logic are: (i) Quantification theory (ii) Propositional logic (iii)Boolean Algebra (iv) "Pierce's remarkable theorem" He has also worked on Three-valued logic,Calculus of relations and Existential graphs. Reference: http://plato.stanford.edu/entries/peirce-logic/#Oth Pierce's Logic.. http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Peirce_Charles.html B) Links with useful material : http://www.cfdvs.iitb.ac.in/resources/Docs/verification/course/fsvp.html An annotated bibliography on the History of Logic.. http://www.formalontology.it/history_of_logic.htm http://www.rpi.edu/~heuveb/courses/Logic/Intro/Summer2003/logic_notes.html By NItin Gupta: (A) Wilhelm Ackermann Ackermann received his doctoral degree in 1925 with a thesis Begründung des "tertium non datur" mittels der Hilbertschen Theorie der Widerspruchsfreiheit written under Hilbert and was a proof of the consistency of arithmetic without induction. It was intended to be a consistency proof for elemenary analysis although this proof contained significant errors. Ackermann was also the main contributor to the development of the logical system known as the epsilon calculus, originally due to Hilbert. This formalism formed the basis of Bourbaki's logic and set theory. Among Ackermann's later work there are consistency proofs for set theory (1937), full arithmetic (1940), type free logic (1952), further there was a new axiomatization of set theory (1956), and a book Solvable cases of the decision problem (North Holland, 1954). Ref: http://www-gap.dcs.st-and.ac.uk/%7Ehistory/Mathematicians/Ackermann.html (B) Course Links http://fmt.cs.utwente.nl/Docs/publications/index.php?project_id=4&project_name=SPACE World Congress on Formal Methods (FM) http://www.informatik.uni-trier.de/~ley/db/conf/fm/ By SUDEEP JUVEKAR: A) Biography ----------- George Boole ------------- Born: 2 Nov 1815 in Lincoln, Lincolnshire, England Died: 8 Dec 1864 in Ballintemple, County Cork, Ireland George Boole is considered to be one of the most influential logician of the world (Pretty famous one.) His early insrtuctions in Maths came from his father. By the time he was 12, he gained proficiency in Maths as well as Latin. At 16, he was appointed a school teacher in Lincoln.He began publishing in the Cambridge Mathematical Journal. and his interests were also influenced by Duncan Gregory as he began to study algebra. An application of algebraic methods to the solution of differential equations was published by Boole in the Transactions of the Royal Society and for this work he received the Society's Royal Medal. Boole was appointed to the chair of mathematics at Queens College, Cork in 1849. He taught there for the rest of his life, gaining a reputation as an outstanding and dedicated teacher. In 1854 he published An investigation into the Laws of Thought, on Which are founded the Mathematical Theories of Logic and Probabilities. Boole approached logic in a new way reducing it to a simple algebra, incorporating logic into mathematics. He pointed out the analogy between algebraic symbols and those that represent logical forms. It began the algebra of logic called Boolean algebra which now finds application in computer construction, switching circuits etc. Boole also worked on differential equations, the influential Treatise on Differential Equations appeared in 1859, the calculus of finite differences, Treatise on the Calculus of Finite Differences (1860), and general methods in probability. He published around 50 papers and was one of the first to investigate the basic properties of numbers, such as the distributive property, that underlie the subject of algebra. Article by: J J O'Connor and E F Robertson Source : http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Boole.html B) Some links:- ----------- http://www.informatik.uni-stuttgart.de/zd/buecherei/NCSTRL_listings/FMI/index.html.en E0 222 Course Homepage :- Contains some useful assignment problems.. http://drona.csa.iisc.ernet.in/~deepakd/toc/toc.html course material:- www.city.academic.gr/special/research/ xcityng/papers/Sot-Kef-00.pdf By Shishir K Agarwal: PART A ALAN TURING --------------------------------------------------------------------- Born: 23 June 1912 in London, England Died: 7 June 1954 in Wilmslow, Cheshire, England --------------------------------------------------------------------- Alan Mathison Turing (June 23, 1912 - June 7, 1954) was a British mathematician and is considered to be one of the fathers of modern computer science. He provided an influential formalisation of the concept of algorithm and computation: the Turing machine. He formulated the now widely accepted Church-Turing thesis, namely that every other practical computing model had either the equivalent or a subset of the capabilities of a Turing machine. During World War II he headed a successful effort of breaking the German secret code. After the war, he worked with one of the earliest digital computers, and later he provided a provocative contribution to the discussion "Can machines think?" In his monumental paper "On Computable Numbers, with an Application to the Entscheidungsproblem" (1936), he reformulated Kurt Goedel's 1931 results on the limits of proof and computation, substituting Goedel's universal artihmetics-based formal language by Turing machines, formal devices capable of performing any conceivable mathematical problem once it was represented as an algorithm. Turing machines are to this day the central object of study in computational theory. He went on to prove that there was no solution to the Entscheidungsproblem by first showing that the halting problem for Turing machines is unsolvable: it is not possible to algorithmically decide whether a given Turing machine will ever halt. Turing tackled the problem of artificial intelligence, and proposed an experiment now known as the Turing test, an attempt to define a standard for a machine to be called "sentient". Refrences: http://en.wikipedia.org/wiki/Alan_Turing http://www-gap.dcs.st-and.ac.uk/%7Ehistory/Mathematicians/Turing.html -------------------------------------------------------------------------- PART B Course Related Links http://www.afm.lsbu.ac.uk/logic-prog/ http://www.cas.mcmaster.ca/~lawford/CS734/outline.html http://www.cs.umass.edu/~immerman/cs691/cs691.html http://www.imit.kth.se/courses/2G1516/ By Nitin Sagar: A) Famous Logician: Stephen Cole Kleene ------------------- Stephen Cole Kleene (January 5, 1909 - January 25, 1994) was an American mathematician whose work at the University of Wisconsin - Madison helped lay the foundations for theoretical computer science. Kleene was best known for founding the branch of mathematical logic known as recursion theory together with Alonzo Church, Kurt Gödel, Alan Turing and others; and for inventing regular expressions. By providing methods of determining which problems are soluble, Kleene's work led to the study of which functions are computable. The Kleene star, Kleene's recursion theorem and the Ascending Kleene Chain are named after him.He also contributed to mathematical intuitionism as founded by Luitzen Egbertus Jan Brouwer. Important Publications 1) Introduction to Metamathematics (1952) 2) Mathematical Logic (1967). 3) Representation of Events in Nerve Nets and Finite Automata in Automata Studies (1956) eds. C. Shannon and J. McCarthy. Also a branch os algebra was named after him, namely Kleene algebra. Extract taken from: http://en.wikipedia.org/wiki/Stephen_Cole_Kleene B) Course Related Webpages: http://www.cas.mcmaster.ca/~lawford/2F04/ A course offered in the McMaster University, Canada SE2F04 : Applications of Mathematical Logic in Software Engineering http://www.cs.queensu.ca/~cisc422/readings.html Webpage for the course CISC422: Formal Methods in Software Engineering Books related to Logic/Formal Methods in Software Enginnering: M. Huth and M. Ryan 'Logic in Computer Science : Modeling and reasoning about systems' D. Peled 'Software Realiability Methods' By Rajat Jain: A. Dr. John Rushby : John Rushby is a program director at the Computer Science Laboratory of SRI International in Menlo Park California, where he leads a research program in formal methods and dependable systems. His group develops mechanized formal verification systems (the most recent is called PVS), and applies them to problems in hardware design, and to fault-tolerant and safety-critical systems. PVS is in use at several hundred sites worldwide; descriptions of some applications and the group's publications are available online at http://www.csl.sri.com/programs/formalmethods/ Dr. Rushby joined SRI in 1983 and served as Director of its Computer Science Laboratory from 1986 to 1990. Prior to that, he held academic positions at the Universities of Manchester and Newcastle upon Tyne in England. He received BSc and PhD degrees in Computing Science from the University of Newcastle upon Tyne in 1971 and 1977, respectively. He is an associate editor for the Formal Aspects of Computing (FACS) Journal; he also served as associate editor for Communications of the ACM 1986-96, and for IEEE Transactions on Software Engineering 1996-2000. He is author of the section on formal methods in the FAA Digital Systems Validation Handbook (the guide for aircraft certifiers). Links: http://www.cs.ncl.ac.uk/old/events/intl.seminars/2001/speakers.html http://www.csl.sri.com/users/rushby/abstracts/ress02 http://www.csl.sri.com/programs/formalmethods/ ------------- B. Useful Links for the course: http://www.engin.umd.umich.edu/CIS/course.des/cis376/lectures http://www.soften.ktu.lt/li/jep-06032/city/courses/IFPR617/IFPR619.lnot.html By Kuntal Loya: A) Biography BERTRAND RUSSELL Bertrand Arthur William Russell was born in 1872 in an aristocrat English family. Hestudied philosophy and logic at Cambridge University, starting in 1890. He became a fellow of Trinity College in 1908. In 1920, Russell travelled to Russia and subsequently lectured in Peking on philosophy for one year. In 1939 he joined the University of California, Los Angeles but soon (1944) returned to Britain and rejoined the faculty of Trinity College. Russell's contributions to logic and the foundations of mathematics include his discovery of Russell's paradox, his defense of logicism (the view that mathematics is, in some significant sense, reducible to formal logic), his development of the theory of types, and his refining of the first-order predicate calculus. Rusell's paradox uses classical logic, all sentences are entailed by a contradiction. His basic idea behind the paradox was that reference to sets such as the set of all sets that are not members of themselves could be avoided by arranging all sentences into a hierarchy, beginning with sentences about individuals at the lowest level, sentences about sets of individuals at thenext lowest level, sentences about sets of sets of individuals at the next lowest level, and so on. Using a vicious circle principle Russell was able to explain why the unrestricted comprehension axiom fails: propositional functions, such as the function "x is a set," may not be applied to themselves since self-application would involve a vicious circle. Russell's basic idea for defending logicism was that numbers may be identified with classes of classes and that number-theoretic statements may be explained in terms of quantifiers and identity. He used logic to clarify issues in Philosophy and made significant contributions in fields like metaphysics, epistemology, ethics and political theory. Russell's most important writings relating to these topics include Principles of Mathematics (1903), "Mathematical Logic as Based on the Theory of Types" (1908), Principia Mathematica (1910, 1912, 1913), An Essay on the Foundations of Geometry (1897), and Introduction to Mathematical Philosophy (1919). In 1950, Russell was made Nobel Laureate in Literature "in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought". References: http://plato.stanford.edu/entries/russell/ http://www.knowledgerush.com/kr/jsp/db/author.jsp?authorId=671&authorName=Bertr$ B) URLs http://www.kddresearch.org/Courses/Fall-2001/CIS730/Lectures/Lecture-11-20010927.pdf http://www.cs.bham.ac.uk/resources/modules/2001/syls/syl-08764.html By HARSHIT CHOPRA: A) A biography of Howard Hathaway Aiken Howard Aiken studied at the University of Wisconsin, Madison obtaining a doctorate from Harvard in 1939. While he was a graduate student and an instructor in the Department of Physics at Harvard Aiken began to make plans to build a large computer. These plans were made for a very specific purpose, for Aiken's research had led to a system of differential equations which had no exact solution and which could only be solved using numerical techniques. However, the amount of hand calculation involved would have been almost prohibitive, so Aiken's idea was to use an adaptation of the punched card machines which had been developed by Hollerith. Aiken wrote a report on how he envisaged the machine, and in particular how such a machine designed to be used in scientific research would differ from a punched card machine. He listed four main points [2]:- ... whereas accounting machines handle only positive numbers, scientific machines must be able to handle negative ones as well; that scientific machines must be able to handle such functions as logarithms, sines, cosines and a whole lot of other functions; the computer would be most useful for scientists if, once it was set in motion, it would work through the problem frequently for numerous numerical values without intervention until the calculation was finished; and that the machine should compute lines instead of columns, which is more in keeping with the sequence of mathematical events. The report was sufficient to prompt senior staff at Harvard to contact IBM and an agreement was made that Aiken would build his computer at the IBM laboratories at Endicott, helped by IBM engineers. Working with three engineers, Aiken developed the ASCC computer (Automatic Sequence Controlled Calculator) which could carry out five operations, addition, subtraction, multiplication, division and reference to previous results. Aiken was much influenced in his ideas by Babbage's writings and he saw the project to build the ASCC computer as completing the task which Babbage had set out on but failed to complete. The ASCC had more in common with Babbage's analytical engine that one might imagine. Although it was powered by electricity, the major components were electromechanical in the form of magnetically operated switches. It weighed 35 tons, had 500 miles of wire and could compute to 23 significant figures. There were 72 storage registers and central units to perform multiplication and division. The gain an idea of the performance of the machine, a single addition to about 6 seconds while a division took about 12 seconds. ASCC was controlled by a sequence of instructions on punched paper tapes. Punched cards were used to enter data and the output from the machine was either on punched cards or by an electric typewriter. Having completed construction of ASCC in 1943 it was decided to move the computer to Harvard University where it began to be used from May 1944. Grace Hopper worked with Aiken from 1944 on the ASCC computer which had been renamed the Harvard Mark I and given by IBM to Harvard University. The computer figured highly in the Bureau of Ordnance's Computation Project at Harvard University, to which Hopper had been assigned, being used by the US navy for gunnery and ballistics calculations. Aiken completed the Harvard Mark II, a completely electronic computer, in 1947. He continued to work at Harvard on this series of machines, working next on the Mark III and finally the Mark IV up to 1952. He not only worked on computer construction, but he also published on electronics and switching theory. In 1964 Aiken received the Harry M Goode Memorial Award, a medal and $2,000 awarded by the Computer Society links:- 1) www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Aiken.html 2) www.sis.pitt.edu/~mbsclass/hall_of_fame/aiken.htm 3) www.britannica.com/eb/article?eu=4231 and more on google..... B) links of Formal Methods (just googled, so may match with others):- 1) www.cs.indiana.edu/formal-methods-education/ 2) theory.doc.ic.ac.uk/ a few top universities in the US offering the course :- 1) Stanford University 2) Carnegie Mellon University 3) University of Texas 4) MIT By Pradeep Kanade: Part A : JOHN VENN Born: 4 Aug 1834 in Hull, England Died: 4 April 1923 in Cambridge, England Venn's family background led him to be ordained as a deacon at Ely in 1858, and as a priest in 1859. After that, he held offices at Cheshunt, Hertfordshire, and Mortlake, Surrey until 1862, when he returned to the Cambridge as a college lecturer in moral sciences. For the next thirty years, Venn became interested in logic. He published three standard texts based upon this topic. He wrote The Logic of Chance in 1866, Symbolic Logic in 1881, and The Principles of Empirical Logic in 1889. John Venn is remembered chiefly for his logical diagrams.Venn became critical of the methods used in diagrams in the nineteenth century, especially those of George Boole and Augustus de Morgan.Venn wrote the book Symbolic Logic mostly to interpret and make his own personal corrections on Boole's work, but this was not the reason Venn became so famous. Venn wrote a paper entitled On the Diagrammatic and Mechanical Representation of Prepositions and Reasonings introducing diagrams known today as Venn diagrams. More about Venn Diagrams at http://www.venndiagram.com Reference Links - http://www.andrews.edu/~calkins/math/biograph/biovenn.htm http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Venn.html Part B : Links which may be useful for the Course - 1) Lectures notes on Formal Methods at Monash University Australia : http://www.csse.monash.edu.au/courseware/cse2303/lectures/lecture.html 2) The World Wide Web Virtual Library:Formal Methods : http://vl.fmnet.info 3) VIS and Formal Verification : http://www-cad.eecs.berkeley.edu/Respep/Research/vis/doc/VisUser/vis_user/node1.html By Ajay Singh: A)Biography C.A.R. Hoare Sir Charles Antony Richard Hoare, also known less formally as Tony Hoare, is a British computer scientist, probably best known for the development of Quicksort, the world's most widely used sorting algorithm, and perhaps even the world's most widely used algorithm of any kind, in 1960. He also developed Hoare logic, and the formal language Communicating Sequential Processes (CSP) used to specify the interactions of concurrent processes. Born in Colombo (Sri Lanka) to British parents, he received his Bachelor's degree in Classics from the University of Oxford in 1946. He remained an extra year at Oxford studying graduate-level statistics, and then studied computer translation of human languages at Moscow State University in Russia. In 1960, he started working at Elliot Brothers, Ltd, a small computer manufacturing firm, where he implemented Algol 60 and began developing algorithms in earnest. He became a Professor of Computing Science at Queen's University, Belfast in 1968, and in 1977 moved back to Oxford as a Professor of Computing. He is now an Emeritus Professor there, and is also a senior researcher at Microsoft Research in Cambridge, England. He received the 1980 ACM Turing Award for "his fundamental contributions to the definition and design of programming languages". The award was presented to him at the ACM Annual Conference in Nashville, Tennessee, on October 27, 1980, by Walter Carlson, Chairman of the Awards committee. In his speech[1], Hoare made the following oft-quoted humorous claim:- "I conclude that there are two ways of constructing a software design: One way is to make it so simple that there are obviously no deficiencies and the other way is to make it so complicated that there are no obvious deficiencies." Ref 1)http://www.ezresult.com/article/C._A._R._Hoare 2)http://www.braithwaite-lee.com/opinions/p75-hoare.pdf B) Course related Links1)www.cs.pitt.edu/~utp/cs1502/lectures 1)www.cs.pitt.edu/~utp/cs1502/lectures 2)http://logic.philosophy.ox.ac.uk/ 3)http://facstaff.pepperdine.edu/lrogers/ma220/ma220schf3.html By GAURAV KUMAR (02D05010): (A): "Friedrich Wilhelm Karl Ernst Schröder" Born: 25 Nov 1841 in Mannheim, Germany Died: 16 June 1902 in Karlsruhe, Germany Ernst Schröder's important work is in the area of algebra, set theory and logic. His work on ordered sets and ordinal numbers is fundamental to the subject. In 1877 in 'Der Operations-kreis des Logikkalkuls' Schröder, influenced by Boole and Grassmann, emphasised the duality of conjunction (intersection) and disjunction (union) showing how dual theorems could be found. He seems to be the first to use the term mathematical logic and he compares algebra and Boole's logic saying: "There is certainly a contrast of the objects of the two operations. They are totally different. In arithmetic, letters are numbers, but here, they are arbitrary concepts." In 'Vorlesungen über die Algebra der Logik', a large work published between 1890 and 1905 (it was completed by E. Müller after his death), Schröder gave a detailed account of algebraic logic, provided a source for Tarski to develop the modern algebraic theory and gave an extensive bibliography of the history of logic. Lattice theory also grew out of this work. In addition to his work on logic he wrote an important article Über iterirte Functionen (1871) often cited as a basis of modern dynamical systems theory. ******************************** # (B): Tutorials on Formal methods : http://hissa.nist.gov/~black/formaltut.html Applied logic and formal methods: www.lingard.co.uk/men/is.html - 2k By nishant mishra: A) JOSE LUIZ FIADEIRO BIOGRAPHY --------- Jose Luiz Fiadeiro was born in 1961 in Lisbon, Portugal. He graduated in Mathematics from the University of Lisbon (Faculty of Sciences) in 1985, and obtained his PhD in Mathematics from the Technical University of Lisbon (Faculty of Engineering) in 1989, where he became Assistant Professor and, in April 1992, Associate Professor. He held a grant for post-doctoral studies at Imperial College, London, from October 1988 to March 1991, where he contributed to the FOREST project (Formal Requirements Specification Techniques, funded by the UK Department of Trade and Industry) and the IS-CORE Working Group (Information Systems: Correctness and Reusability, BRA 3023). He was again on leave at Imperial College from March 1994 to September 1994 where he contributed to the ESF-ATP project (Eureka Software Factory - Advanced Technology Programme), funded by the UK Department of Trade and Industry. Until December 1993 he was also a researcher at INESC (Instituto de Engenharia de Sistemas e Computadores), where he was leader of the Logic Engineering Group. He is currently Associate Professor at the Department of Informatics, Faculty of Sciences, University of Lisbon, which he joined in June 1993, and member of the Lisbon Center for Complexity Sciences. He has been principal investigator of various international research projects, namely IS-CORE II (Information Systems: Correctness and Reusability, BRA 6071), MODELAGE (A Common Formal Model of Cooperating Intelligent Agents, BRA 8319), and MEDICIS (HCM Scientific Network CHRX-CT92-0054). He was the coordinator of a national project on Interoperability of Deductive Databases (JNICT PBIC/C/TIT/1227/92). He is currently the coordinator of a national project on Agent Modelling in Organisations (MAGO: PCSH/OGE/1038/95) and also researcher of the ESCOLA project (Executable Specifications of Concurrent Systems: Languages and Applications, JNICT PBIC/P/MAT/1629/93). His research interests include software specification formalisms and methods, especially as applied to component-based, reactive systems, and their integration in the wider area of General Systems Theory. His main contributions have been in the formalisation of specification and program design techniques, namely within the object-oriented paradigm, using modal logics (temporal and dynamic) and of their underlying modularisation principles using Category Theory. He is the organiser of the forthcoming Third International Workshop on Deontic Logic in Computer Science and of the first instance of the new European Spring Conferences on Theory and Practice of Software Science. B) LINKS 1)http://www.braithwaite-lee.com/opinions/p75-hoare.pdf 2)www.city.academic.gr/special/research/ By Vijay Agrawal (02D05008): (A): Herbert Alexander Simon Herbert Alexander Simon was born in Milwaukee, Wisconsin, on June 15, 1916, is a social scientist and computer theorist who made pioneering contributions in the fields of mathematical economics, organization theory, cognitive psychology and artificial intelligence. Through all of his research work, Simon has been interest in decision-making and problem-solving processes, and the implications of these processes for social institutions. In the past 25 years, he has made extensive use of the computer as a tool for both stimulating human thinking and augmenting it with artificial intelligence. Simon earned a B. A. in political science from the University of Chicago in 1936, then worked there as director of public administration studies before gaining a doctorate in 1943. His undergraduate term paper about decision-making in organizations led to a research assistantship for him at University of California, Berkeley in 1942.In 1978, for his pioneering research into the decision-making process within economic organizations, Herbert Simon received the Alfred Nobel Memorial Prize. Herbert Alexander gives great contributions to the Artificial Intelligence field. He claims there are two main goals of Artificial Intelligence. One is to use the power of computer to augment human thinking. The other is to use a computer's artificial intelligence to understand how humans think in a human way. Simon also believes "AI is an Empirical Science", which means empirical knowledge must guide computer-system design. He thinks in the long run, we should design many computer-systems though experiences and the only way computer-systems could be perform better by practicing. References: 1. http://cil.andrew.cmu.edu/projects/old/herbert_simon.html 2. http://www.nobel.se/laureates/economy1978-1-bio.html 3. http://www.nobel.se/laureates/economy1978-1-press.html 4. http://artsci.wustl.edu/~philos/MindDict/simon.html 5. http://dream.dai.ed.ac.uk/papers/donald/subsectionstar4_3.html 6. The article from Herbert A. Simon, "AI is an empirical science" (B): Some useful links: 1.http://www.cs.umass.edu/~immerman/cs691/cs691.html 2.http://www.cs.bham.ac.uk/resources/modules/2001/syls/syl-08764.html By Kautilya Jain: # David Duetsch : Physicist, computer scientist. Inventor of the mathematical model for the quantum computer. # DAVID DEUTSCH'S research in quantum physics has been influential and highly acclaimed. His papers on quantum computation laid the foundations for that field, breaking new ground in the theory of computation as well as physics, and have triggered an explosion of research efforts worldwide. His work has revealed the importance of quantum effects in the physics of time travel, and he is an authority on the theory of parallel universes. Born in Haifa, Israel, David Deutsch was educated at Cambridge and Oxford universities. After several years at the University of Texas at Austin, he returned to Oxford, where he now lives and works. He is a member of the Centre for Quantum Computation at the Clarendon Laboratory, Oxford University. # Links About David Duetsch : http://www.qubit.org/people/david/David.html http://xxx.lanl.gov/abs/math.HO/9911150 # Links For The "Formal Methods In CS" : http://dir.yahoo.com/Science/Computer_Science/Formal_Methods/ http://www.eecs.umich.edu/gasm/ http://www.cse.iitb.ac.in/~siva/cs206 By Abhay Kumar Jha: A: Biography Giuseppe Peano was one of the pioneers in mathematical logic and axiomatization of mathematics.He also had many important discoveries in the field of analysis and was one of the leading authorities on auxillary languages. He was born to a poor farming family in Spinetta ,Italy on August 27,1858.In 1876 ,he enrolled at the University of Turin to study engineering but later decided on mathematics.The university would be his home for the rest of his life.After graduating ,he became a University Asssistant in 1880,professor at the Royal Military Academy in 1886,extraordianry professor in 1890 and ordinary professor in 1895. For the first part of his life, mathematics dominated Peano's life. During this period, almost all of his mathematical discoveries were made. He proved that y' = f(x,y) on the sole condition that f is continuous and set the minimum conditions for second order partials of an equation to be equal. He was the first person to develop a space-filling curve, a one-dimensional curve that fills all the points in a two-dimensional space. He also developed independently a method of successive approximations for the solution of differential equations and developed the idea of the cluster point of a function. He was also an early supporter of the use of recursive functions and vectors. Peano's greatest contributions, however, were in the fields of axiomatization of mathematics and mathematical logic . Axiomatization of mathematics is the development of the postulates (axioms) and definitions that are the basis of the mathematical system. His most famous set, known as Peano's postulates, put forth the axioms of natural numbers. In addition, he also developed a related set for geometry. Mathematical logic quickly became the focus of his work. In 1889, Peano published his first version of a system of mathematical logic in his work Arithmetics principia, which included his famous axioms of natural numbers. Two years later, he established a journal, the Rivista, in which he proposed the symbolizing of all mathematical propositions into his system. The project, which became known as the Formulario, became his focus for the next fifteen years. When it was finished in 1908, the book contained over 4200 symbolized formulas and theorems with proofs in only 516 pages. His work did not go unnoticed. He was elected to the Academy of Sciences in Turin in 1891 and was a speaker at several International Congress of Mathematics. In addition, he was honored by the Italian government with several knighthoods, including the Order of the Crown of Italy. ref: http://www.shu.edu/projects/reals/history/peano.html http://www.swif.uniba.it/lei/foldop/foldoc.cgi?logicization+of+arithmetic B:Useful Links http://www.cs.swan.ac.uk/~csetzer/logic-server/ http://poincare.mathematik.uni-tuebingen.de/~logik/logiclinks.html http://www.math.niu.edu/~rusin/known-math/index/03-XX.html http://www.ed.ac.uk/~pmilne/ml/home.html http://www.degruyter.de/rs/167_MA_D_SR_DEU_h.cfm?rc=16225&fg=MA By Chinmay Karande: Paul Isaac Bernays: Axiomatic Set Theory Born: 17 Oct 1888 in London, England Died: 18 Sept 1977 in Zurich, Switzerland Bernays is perhaps best known for his joint two volume work Grundlagen der Mathematik (1934-39) with Hilbert. This attempted to build mathematics from symbolic logic. In 1899 Hilbert had written Grundlagen der Geometrie and, in 1956, Bernays revised this work on the foundations of geometry. Bernays, influenced by Hilbert's thinking, believed that the whole structure of mathematics could be unified as a single coherent entity. In order to start this process it was necessary to devise a set of axioms on which such a complete theory could be based. He therefore attempted to put set theory on an axiomatic basis to avoid the paradoxes. Between 1937 and 1954 Bernays wrote a whole series of articles in the Journal of Symbolic Logic which attempted to achieve this goal. He attempted to modify von Neumann's axiom system to include features from Zermelo's. He formulated the principle of dependent choices, a form of the axiom of choice independently studied by Tarski later. He used number theoretic models similar to those used by Ackermann to show the independence of his axioms. In 1958 Bernays published Axiomatic Set Theory in which he combined together his work on the axiomatisation of set theory. Bernays's work on an axiomatic basis for mathematics was taken further by Gödel. http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Bernays.html * The links www.cs.queensu.ca/~cisc422 www.site.uottawa.ca/~afelty/courses/csi5110/index.html www.plu.edu/~phil/233SYL98.html www.cs.umass.edu/~immerman/cs691/cs691.html By Suyash S Shringarpure.: A]Tarski, Alfred (1902-1983): He was a Polish/US mathematician and logician whose contributions to logic and metamathematics had lasting influence on the field in the 20th century. He is perhaps best known for the Banach-Tarski Paradox which proves that a sphere can be cut into a finite number of pieces and then reassembled into a sphere of larger size, or alternatively it can be reassembled into two spheres of equal size to the one original. In 1933 Tarski published The concept of truth in formalized languages which is his now famous paper on the concept of truth. Tarski is recognised as one of the four greatest logicians of all time, the other three being Aristotle, Frege, and Gödel. Of these Tarski was the most prolific as a logician and his collected works, excluding his books, runs to 2500 pages. Tarski made important contributions in many areas of mathematics: set theory, measure theory, topology, geometry, classical and universal algebra, algebraic logic, various branches of formal logic and metamathematics. He produced axioms for 'logical consequence', worked on deductive systems, the algebra of logic and the theory of definability. He can be considered a mathematical logician with exceptionally broad mathematical interests. For more information about Alfred Tarski check out the foll. urls: http://www-gap.dcs.st-and.ac.uk/%7Ehistory/Mathematicians/Tarski.html His papers on logic can be seen at: 1)The truth theorem- http://www.ditext.com/tarski/tarski.html 2)System of geometry- http://www.math.ucla.edu/~asl/bsl/0502-toc.htm B] Notes on logic: http://www.thoralf.uwaterloo.ca/htdocs/lmcs.html http://www.ltn.lv/~podnieks/mlog/ml.htm By Raja Agrawal: a)Maurice Vincent Wilkes Born 26 June 1913 Dudley, Staffordshire, England; Director of the Cambridge Computer Laboratory throughout the whole development of stored program computers starting with EDSAC; inventor of labels, macros and microprogramming; with David Wheeler and Stanley Gill, the inventor of a programming system based on subroutines. English mathematician who led the team at Cambridge University that built the EDSAC (electronic delay storage automatic calculator) 1949, one of the earliest of the British electronic computers. Wilkes was born in Dudley and studied at Cambridge. During World War II he became involved with the development of radar. He was director of the Cambridge Mathematical Laboratory 1946-80. In the late 1940s Wilkes and his team began to build the EDSAC. At the time, electronic computers were in their infancy. Wilkes chose the serial mode, in which the information in the computer is processed in sequence (and not several parts at once, as in the parallel type). This design incorporated mercury delay lines (developed at the Massachusetts Institute of Technology, USA) as the elements of the memory. In May 1949 the EDSAC ran its first program and became the first delay-line computer in the world. From early 1950 it offered a regular computing facility to the members of Cambridge University, the first general-purpose computer service. Much time was spent by the research group on programming and on the compilation of a library of programs. The EDSAC was in operation until 1958. EDSAC II came into service 1957. This was a parallel-processing machine and the delay line was abandoned in favour of magnetic storage methods. References:: http://ei.cs.vt.edu/~history/Wilkes.html www.inamori-f.or.jp/KyotoPrizes/contents_e/laureates/profile/co_08infmaurice.html http://www.cartage.org.lb/en/themes/Biographies/MainBiographies/W/Wilkes/1.html b)some useful course links:: www.csl.sri.com/papers/csl-93-7 www.csa.iisc.ernet.in/academics/ curriculum/soi2000/node4.html www.cs.rhul.ac.uk/research/formal/ www.informatik.uni-stuttgart.de/zd/buecherei/NCSTRL_listings/FMI/index.html.en drona.csa.iisc.ernet.in/~deepakd/toc/toc.html By Behjat Siddiquie: A) DAVID HILBERT David Hilbert (January 23, 1862 - February 14, 1943) was a German mathematician born in Königsberg, Prussia (now Kaliningrad, Russia) who is known for several contributions to mathematics: * Solving several important problems in the theory of invariants.Hilbert's basis theorem solved the principal problem in the 1800s invariant theory by showing that any form of a given number of variables and of a given degree has a finite, yet complete system of independent rational integral invariants and covariants. * Unifying the field of algebraic number theory with his 1897 treatise Zahlbericht (literally "report on numbers"). * Providing the first correct and complete axiomatization of Euclidean geometry to replace Euclid's axiomatization of geometry, in his 1899 book Grundlagen der Geometrie ("Foundations of Geometry"). * His suggestion in 1920 that mathematics be formulated on a solid and complete logical foundation (by showing that all of mathematics follows from a finite system of axioms, and that that axiom system is consistent). This is still the most popular philosophy of mathematics usually called formalism. However, Gödel's Incompleteness Theorem showed in 1931 that his grand plan was impossible. * Hilbert's paradox of the Grand Hotel, a musing about strange properties of the infinite. * Laying the foundations of functional analysis by studying integral equations and Hilbert spaces. * Putting forth an influential list of 23 unsolved problems in the Paris conference of the International Congress of Mathematicians in 1900. * Hilbert helped provide the basis for the theory of automata which was later built upon by computer scientist Alan Turing. Additionally, Hilbert is responsible for assisting several advances in the mathematics of quantum mechanics. These include his integral calculations of hilbert spaces and proving the mathematical equivalency of Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave equation. This informaton was obtained from the site http://en.wikipedia.org/wiki/David_Hilbert More information about him and his works can be obtained from the following sites http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Hilbert.html http://mathematicsbooks.org/search_David_Hilbert/searchBy_Author.html 2) Some useful links on formal methods are a) http://www.rspa.com/spi/formal.html b) http://www.ics.uci.edu/~redmiles/ics121-FQ99/lecture/ten/ c) http://vl.fmnet.info/ d) http://www.dcs.gla.ac.uk/~jon/facs/ By Dhammachintak Neel: Jan Lukasiewicz (21 December 1878 - 13 February 1956) was a mathematician born in Lvov. His major mathematical work centred on mathematical logic. He thought innovatively about traditional propositional logic, the principle of non-contradiction and the LAW OF EXCLUDED MIDDLE. Lukasiewicz worked on multi-valued logics, including his own three-valued PROPOSITONAL CALCULUS, the first non-classical LOGICAL CALCULUS . He is responsible for one of the most elegant axiomatizations of classical propositional logic; it has just three axioms and is one of the most used axiomatizations today. Lukasiewicz's Polish Notation of 1920 was at the root of the idea of the recursive stack a last-in, first-out computer memory store invented by Charles Hamblin of the New South Wales University of Technology (NSWUT), and first implemented in 1957. This design led to the English Electric multi-programmed KDF9 computer system of 1963, which had two such hardware register stacks. A similar concept underlies the Reverse Polish Notation (or postfix notation) of Hewlett Packard calculators. http://en.wikipedia.org/wiki/Jan_Lukasiewicz LINKS :-> http://www.cs.rice.edu/CS/Verification/Courses/courses.html http://gruffle.comlab.ox.ac.uk/archive/formal-methods.html http://www.cs.man.ac.uk/~voronkov/teaching/lics.html#reading By ravi vijay (02005006): 1) biogarphy: Emmy Amalie Noether Born: 23 March 1882 in Erlangen, Bavaria, Germany Died: 14 April 1935 in Bryn Mawr, Pennsylvania, USA Emmy Noether is considered one of the leading mathematicians and logicians of her times. Emmy Noether's father Max Noether was a distinguished mathematician and a professor at Erlangen. Her mother was Ida Kaufmann, from a wealthy Cologne family. Both Emmy's parents were of Jewish origin and Emmy was the eldest of their four children some of her important contributions to the fields of physics , algebra and logic are : a) Proved that a physical system described by a Lagrangian invariant with respect to the symmetry transformations of a Lie group has, in the case of a group with a finite (or countably infinite) number of independent, infinitesimal generators, a conservation law for each such generator, and certain `dependencies' in the case of a larger infinite number of generators. The latter case applies, for example, to the general theory of relativity and gives the Bianchi identities. These `dependencies' lead to understanding of energy-momentum conservation in the general theory. Her paper proves both the theorems described above and their converses. These are collectively referred to by physicists as Noether's Theorem. b)The main body of her work was in the creation of modern abstract algebra.It was she who taught us to think in terms of simple and general algebraic concepts - homomorphic mappings, groups and rings with operators, ideals ...theorems such as the `homomorphism and isomorphism theorems', concepts such as the ascending and descending chain conditions for subgroups and ideals, or the notion of groups with operators were first introduced by Emmy Noether and have entered into the daily practice of a wide range of mathematical disciplines.This influence is also keenly felt in H. Weyl's book Gruppentheories und Quantenmechanik. c)The theory of non-commutative algebras and their representations was built up by Emmy Noether in a new unified, purely conceptual manner by making use of all the results that has been accumulated by the ingenious labors of decades by Frobenius, Dickson, Wedderburn and others. n 1933 her mathematical achievements counted for nothing when the Nazis caused her dismissal from the University of Göttingen because she was Jewish. She accepted a visiting professorship at Bryn Mawr College in the USA and also lectured at the Institute for Advanced Study, Princeton in the USA. here are some of the links highlighting the works of emmy noether : a) http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Noether_Emmy.h tml b)http://www.emmynoether.com/ c)http://www.agnesscott.edu/lriddle/women/noether.htm 2) some of the links providing useful course material : a)www.comp.nus.edu.sg/~hugh/TeachingStuff/cs415.pdf b)http://formalmethods.syr.edu/ c)http://www.rbjones.com/rbjpub/methods/fm/fm010.htm By Parijat (02d05002): Godfrey Harold Hardy (1877-1947) Hardy was a British mathematician who produced over 300 research papers and some famous books including 'A Mathematician's Apology'. Hardy was a prodigiously clever student and he knew it. He always topped his class but he was too shy to go in front of the school and receive prizes. Hardy himself says that he did not recall having any passion for mathematics when he was young. The only way he thought of mathematics was in terms of exams and scholarships. Later however, he became a firm believer of rigorous mathematical proof and an avid cricket player and fan. Hardy once wrote his New Year resolutions to his friend: 1. To prove the Riemann hypothesis, 2. To make a brilliant play in a crucial cricket match, 3. To prove the nonexistence of God, 4. To be the first man atop Mount Everest, 5. To be proclaimed the first president of the U.S.S.R., Great Britain, and Germany, and 6. To murder Mussolini. Though may not have been successful in most of his other endeavours, he was atleast partially successful in proving the Riemann hypothesis though maybe not in the same year. One may recall that Hardy is the same person to whom Ramanujam had written before Hardy called him to London to work with him. World War I had been painful had been painful for Hardy and so had World War II. In 1939 (the year the war began), at the age of 62, he had a heart attack. His remarkable mental powers began leaving him soon after. It was at this stage that he wrote 'A Mathematicians Apology' which is one of the most vivid descriptions of how a mathematician thinks and the pleasure of mathematics. Hardy received many honours for his work. He was elected a Fellow of the Royal Society in 1910, he received the Royal Medal of the Society in 1920 and Sylvester Medoal of the Society in 1940. He also received the Copley Medal of the Royal Society in 1947 for his distinguished part in the development of mathematical analysis during the previous 30 years. For a more detailed biography, visit http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Hardy.html Another good resource for mathematics (and other sciences too) is: http://mathworld.wolfram.com By kumar digvijay singh (02d05012): A) LEON CHWISTEK Born: 6/13/1884 in Zakopane Died: 8/20/1944 in Moscow. Avant-garde painter, theoretician of modern art, along with Witkiewicz the main theorist of the Formism; literary critic, logician, philosopher,member of the avant-garde group known as THE FORMISTS; creator of the aesthetic theories of "plurality of realities" and Zonism. Leon Chwistek was a renowned mathematician and philosopher. In 1906 he obtained a doctorate in philosophy from Jagiellonian University and began teaching math at J. Sobieski Middle School the same year. He taught for twenty years with some interruptions. In 1908-1909 he resumed his studies in philosophy in Gattingen. Between 1914 and 1916 he served in the ranks of the Polish Legions and in 1922 became a lecturer in mathematics at Jagiellonian University. In 1930 he took over as head of the faculty of mathematical logic at John Casimir University in Lviv. He abandoned the city with the withdrawing Red Army in 1941. He settled in Tbilisi, where he resumed teaching, this time focusing on mathematical analysis. In 1943 he moved to Moscow where he became an activist in the Association of Polish Patriots. In the 1920s-30s many philosophers in Europe attempted to reform traditional philosophy by means of mathematical logic.Leon Chwistek did not believe that such a reform could succeed. He thought that reality could not be described in one homogenous system, which would be based on the principles of formal logic, because there is not one reality but many. Chwistek developed his theory of the multiplicity of realities first with regard to the arts. He distinguished four basic types of realities and then matched them with four basic types of painting. Here are the four types of realities: 1)The popular reality (common-sense realism); 2)The physical reality (constructed by physics); 3)The phenomenal reality (sensual impressions); 4)The visionary/intuitive reality (dreams, hallucinations, subconscious states). Chwistek never intended his views to constitute a new metaphysical theory. He was a defender of "sound reason", against metaphysics and the irrationalistic feelings. His theory of plural reality was merely an attempt to specify the various ways in which the term ?"real" is used.In 1917 he was a co-founder of the Krakow-based group known as the POLISH EXPRESSIONISTS (renamed the FORMISTS in 1919) and went on to become its leading theoretician. Chwistek's attitude as a Formist was shaped in a fundamental way by the aesthetics of French Cubism and Italian Futurism,from which he drew his concept of autonomous artistic form as freed of the responsibility to imitate nature. In 1935 the Lodz-based periodical "Forma" / "Form" published a debate between Chwistek and Wladyslaw Strzeminski, which amounted to a confrontation between Zonism and Unism, between Chwistek's program of spirited art informed by concepts of biological vitality and Strzeminski's Constructivist program and the idea of intellectualized and socially beneficial art. In proposing what amounted to anti-Unism, Chwistek propagated creative spontaneity, conceived as a reaction against the ballast of traditional concepts and the emptiness of speculative Abstraction. Chwistek was also a portrait artist, painting images of approximately one hundred personages from Krakow's scientific and intellectual community between 1926 and 1930. Leon Chwistek first define the term "Architecture of curved shapes" in his theoritical design based on the Krywan? mountain in the Tatras. Chiwistek thoughts on logic and mathematics : ------------------------------------------------ "The reduction of arithmetic and geometry to the principles of formal logic, which was attained by Wittgenstein and Russell at the beginnings of the century, was the crucial moment in the attempt to fix the boundary of the exact sciences.If the attempt to construct a great system of logic from which all the apriori sciences could be derived were successuful,completely new perspectives would be opened up to science and an adeguate base for a critical and a rationalistic method would be attained. A system of logic which permits mathematical theorems to be proved without the aid of the intuition of the creative individual by mechanical operations,which can be performed by one who can understand ordinary arythmetic was sought. The attainment of this ideal would have been so a great triumph for science that in comparison with it the attempt of the irrationalists would seem like child's play. It was to be expected that the representative of radical criticism would have accepted the work of Whitehead and Russell with enthusiasm." REFRENCES :: http://www.culture.pl/en/culture/artykuly/os_chwistek_leon http://eber.kul.lublin.pl/~polhome/PolPhil/Chwi/Chwistek.html ============================================ B) USEFULL LINKS: ============================================ http://hissa.nist.gov/~black/formaltut.html http://www.afm.sbu.ac.uk/ http://www.csci.csusb.edu/dick/samples/prolog.html http://www.kddresearch.org/Courses/Fall-2001/CIS730/ http://www.cs.uiowa.edu/~fleck/181.html By Nakul Aggarwal: A) Luitzen Egbertus Jan Brouwer Born: 27 Feb 1881 in Overschie (now a suburb of Rotterdam), Netherlands Died: 2 Dec 1966 in Blaricum, Netherlands He attended high school in Hoorn, a town on the Zuiderzee north of Amsterdam. His performance there was outstanding and he completed his studies by the age of fourteen. He had not studied Greek or Latin at high school but both were required for entry into university, so Brouwer spent the next two years studying these topics. While still an undergraduate Brouwer proved original results on continuous motions in four dimensional space Other topics which interested Brouwer were topology and the foundations of mathematics. In his 1908 paper The Unreliability of the Logical Principles Brouwer rejected in mathematical proofs the Principle of the Excluded Middle, which states that any mathematical statement is either true or false. In 1918 he published a set theory developed without using the Principle of the Excluded Middle Founding Set Theory Independently of the Principle of the Excluded Middle. Part One, General Set Theory. His 1920 lecture Does Every Real Number Have a Decimal Expansion? was published in the following year. The answer to the question of the title which Brouwer gives is "no". Also in 1920 he published Intuitionistic Set Theory, then in 1927 he developed a theory of functions On the Domains of Definition of Functions without the use of the Principle of the Excluded Middle. B) links :: http://archive.comlab.ox.ac.uk/formal-methods.html http://goanna.cs.rmit.edu.au/~winikoff/links/research.html http://theory.stanford.edu/people/uribe/research.html Avinash Radhakrishnan A. Biography of a Logician : He was a mathematician, logician, photographer, poet, clergyman, professor and the author of Alice's Adventures in Wonderland. Yes ! i am talking about Lewis Carrol. Born Charles Lutwidge Dodgson at Daresbury, Cheshire, England, in 1832, he was educated at Rugby and Oxford, took orders in 1861, and was a lecturer in mathematics at Christ Church College, Oxford, from 1855-81when he resigned to devote his life to writing under his pseudonym, Lewis Carroll. As a boy he was fascinated by the craft of conjuring and this, together with ideas for games, puzzles, anagrams, riddles, chess problems, mathematical recreation and logic, occupied his mind for all of his life. He was responsible for many original puzzles and new innovations, including Doublets invented in 1879 and The Game of Logic in 1886. One can appreciate the extent of his obsession with puzzles when considering that almost all seventy-two of his Pillow-Problems, many of which had complicated mathematical solutions, were compiled by him while lying awake at night. He would commit nothing to paper until the morning, when he would first of all write down the answer, followed by the question and then the detailed solution. Apart from pamphlets and small textbooks for students, Dodgson's other important mathematical works were the two series of Curiosa Mathematica (1888 and 1802). Though he printed several logical puzzles, his only books in this area were intended for children, though logicians consider Symbolic Logic (1896) important. Dodgson is also remembered for his pamphlets and letters on "Proportional Representation," conveniently collected and assessed by Duncan Black in The Theory of Committees and Elections (1958). Carroll's Paradox : In 1895, in the journal Mind, Carroll, published a playful dialogue between Achilles and the Tortoise which brought to light a central problem in logic as it was understood at the time. Specifically, he showed that merely having axioms even the best and most perfect axioms is not sufficient for determining truth in a system of logic; for one also must be very careful about one's choice of rules of inference. In other words, one's assumptions must be explicitly augmented by the exact mechanisms by which one is to deduce consequences from those assumptions. In his dialogue (link is given below), Carroll tackles the single most important rule of first-order logic, modus ponens, which says that if a statement P is assumed, and if the conditional statement P implies Q is also assumed (or previously proved), then the statement Q itself is a logical consequence and may therefore be considered proved. What Achilles learns, to his lasting regret, is that modus ponens must be first granted as a rule of inference, for otherwise no conclusion can ever be reached. What the Tortoise Said to Achilles (by Lewis Carroll) http://www.mathacademy.com/pr/prime/articles/carroll/index.asp Some links to Carroll and his puzzles : http://www.cut-the-knot.org/LewisCarroll/soriteses.shtml http://www.cut-the-knot.org/LewisCarroll/soriteses.shtml http://www.uz.ac.zw/science/maths/zimaths/catrat.htm A sort of detail biography of Carroll : http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Dodgson.html Books on Logic by Carroll : Symbolic Logic and The Game Of Logic, Lewis Carroll, Dover books, 1958. B. Some Useful links on Formal Methods : Prof. Bowen's site : http://www.jpbowen.com/ http://www.cafm.lsbu.ac.uk/ http://www.eecs.umich.edu/gasm/ http://shemesh.larc.nasa.gov/fm/ http://lal.cs.byu.edu/ Site with lots of links and tools: http://www.afm.sbu.ac.uk/ Ritesh Arora A) John McCarthy -- Originator of LISP programming Language & one of the founders of Artificial Intelligence. John McCarthy, Hoover Institution Senior Fellow, was born in Boston in 1927 and grew up there and in Los Angeles. He received a B. S. in mathematics in 1948 from the California Institute of Technology and a Ph.D. in mathematics in 1951 from Princeton University. He taught at Princeton University, Dartmouth College, Massachusetts Institute of Technology, and Stanford University. He has been a Professor of Computer Science at Stanford University since 1962 and was Director of the Artificial Intelligence Laboratory at Stanford from 1965 to 1980. He is also Charles M. Pigott Professor in the School of Engineering. McCarthy is one of the founders of artificial intelligence research, his interest starting in 1948. Since 1958, he work has emphasized epistemological problems, i.e., the problems of what information and what modes of reasoning are required for intelligent behavior. He originated the LISP programming language for computing with symbolic expressions, was one of the first to propose and design time-sharing computer systems, and pioneered in using mathematical logic to prove the correctness of computer programs. He has also written papers on the social implications of computer and other technology. He received the A.M. Turing Award of the Association for Computing Machinery in 1971 for his contributions to computer science. He received the first Research Excellence Award of the International Conference on Artificial Intelligence in 1985. He received the Kyoto Prize in 1988 and the National Medal of Science in 1990. He is a member of the American Academy of Arts and Sciences, the National Academy of Engineering, and the National Academy of Sciences. His recent work includes formalization of non-monotonic reasoning whereby people and computers draw conjectural conclusions by assuming that complications are absent from a situation. His current work involves the formalization of context in mathematical logic. Recent : JUNE 18, 2003 John McCarthy, professor emeritus of computer science and pioneer in artificial intelligence (AI), received the "Benjamin Franklin Medal" in Computer and Cognitive Science on April 24. The Franklin Institute in Philadelphia bestowed the award, lauding McCarthy for "multiple contributions to the foundations of artificial intelligence and computer science including the development of the LISP language, the invention of time-sharing interactive programming, and key developments in the application of formal logic to commonsense reasoning." Ref: 1) http://news-service.stanford.edu/news/2003/june18/mccarthy-618.html 2) http://www-hoover.stanford.edu/BIOS/mccarthy.html B) Usefull Links: 1)http://dir.yahoo.com/Science/Computer_Science/Formal_Methods/ 2)http://dir.yahoo.com/Science/Computer_Science/Logic_Programming/ 3)http://www.ai.univie.ac.at/~juffi/Ilp-Vu/ilp-vu-program.html By Naveen Sharma: Prof. Albert R.Meyer Biography Prof. Meyer has been at MIT since 1969. He is best known for his contributions to computational complexity theory, including the formulation of the POLYNOMIAL-TIME HIERARCHY and the first proofs of the exponential complexity of known decision problems. He has contributed extensively to Type Theory and Semantics of programming languages and concurrent processes. As an outgrowth of his recent responsibility for several large introductory courses, he has become interested in educational technology. Prof. Meyer has supervised twenty-six Ph.D students, many now prominent researchers on the faculty of leading departments throughout the country. He is a member of numerous professional societies and editorial boards, is a member of the American Academy of Arts and Science, and is Editor-in-Chief of the journal Information and Computation. Recent and/or Significant Publications Jim, T. and A.R. Meyer, "Full Abstraction and the Context Lemma," SIAM J. Computation 25, 3 (1996), 663--696. Bruce, K.B., A.R. Meyer and J.C. Mitchell, "The Semantics of Second-Order Lambda Calculus," Information and Computation, 85 (1990), 76--134. Reprinted in: Gerard Huet, editor. LOGICAL FOUNDATIONS OF FUNCTIONAL PROGRAMMING, chapter 10, pp213--272. University of Texas at Austin Year of Programming Series. Addison-Wesley Publishing Company, 1990. Mayr, E. and A.R. Meyer, " The Complexity of the Word Problems for Commutative Semigroups and Polynomial Ideals," Advances in Mathematics, 46,3 (1982), 305--329. Stockmeyer, L. and A.R. Meyer, "Word Problems Requiring Exponential Time," 5th ACM Symp. on Theory of Computing, (May, 1973), 1--10. Awards * ACM - Fellow * American Academy of Arts and Sciences - Fellow 1987 ref--http://www.lcs.mit.edu/people/bioprint.php3?PeopleID=295 Useful urls 1.http://www.ee.princeton.edu/research/ 2.http://www.lcs.mit.edu By PC: BIOGRAPHY:- CHARLES BABBAGE Born December 26, 1791 in Teignmouth, Devonshire UK, Died 1871, London; Known to some as the "Father of Computing" for his contributions to the basic design of the computer through his Analytical machine. His previous Difference Engine was a special purpose device intended for the production of tables. While he did produce prototypes of portions of the Difference Engine, it was left to Georg and Edvard Schuetz to construct the first working devices to the same design which were successful in limited applications. Significant Events in His Life: 1791: Born; 1810: Entered Trinity College, Cambridge; 1814: graduated Peterhouse; 1817 received MA from Cambridge; 1820: founded the Analytical Society with Herschel and Peacock; 1823: started work on the Difference Engine through funding from the British Government; 1827: published a table of logarithms from 1 to 108000; 1828: appointed to the Lucasian Chair of Mathematics at Cambridge (never presented a lecture); 1831: founded the British Association for the Advancement of Science; 1832: published "Economy of Manufactures and Machinery"; 1833: began work on the Analytical Engine; 1834: founded the Statistical Society of London; 1864: published Passages from the Life of a Philosopher; 1871: Died. Other inventions: The cowcatcher, dynamometer, standard railroad gauge, uniform postal rates, occulting lights for lighthouses, Greenwich time signals, heliograph opthalmoscope. He also had an interest in cyphers and lock-picking, but abhorred street musicians. HIS OTHER CONTRIBUTIONS: Many of the molecular machines proposed for nanotechnology implement on the nanoscale designs that would seem more familiar at the macroscopic scale. One type of molecular machine that has attracted particular attention has been the molecular mechanical computer. While such computers are unlikely to be as fast as future electronic computers they are conceptually simple and relatively easy to design and analyze, making them attractive targets for theoretical analysis and strong evidence that molecular computation is feasible. Perhaps the most famous mechanical computer was Charles Babbage's Analytical Engine, first proposed in the 1830's. Babbage gave the idea of a type of mechanical rod LOGIC, a proposal of particular interest in light of more recent proposals by Drexler (see chapter 12 of Nanosystems) for nanomechanical computation which implement binary logic operations using molecular "rods." LINKS-> eels.lub.lu.se/ei/721.1.html dmoz.org/Science/Math/Logic_and_Foundations citeseer.nj.nec.com/18562.html By Puneet Maheshwari: part A: Cantor, Georg (1845-1918) Georg Cantor put forth the modern theory on infinite sets that revolutionized almost every mathematics field. However, his new ideas also created many dissenters and made him one of the most assailed mathematicians in history. Georg Ferdinand Ludwig Philipp Cantor was born in St. Petersburg, Russia, on March 3, 1845. His father was a Danish Jewish merchant while his mother was a Danish Roman Catholic. The family stayed in Russia for eleven years until the father's ailing health forced them to move to the more acceptable environment of Frankfurt, Germany, the country Georg would call home for the rest of his life. In 1862, Georg Cantor entered the University of Zurich only to transfer the next year to the University of Berlin after his father's death. After receiving his doctorate in 1867, he was unable to find good employment and was forced to accept a position as an unpaid lecturer and later as an assistant professor at the backwater University of Halle. It was in 1874 that Cantor published his first paper on the theory of sets In a series of papers from 1874 to 1897, he was able to prove among other things that the set of integers had an equal number of members as the set of even numbers, squares, cubes, and roots to equations; that the number of points in a line segment is equal to the number of points in an infinite line, a plane and all mathematical space; and that the number of transcendental numbers, values such as pi and e that can never be the solution to any algebraic equation, were much larger than the number of integers. In 1904, he was awarded a medal by the Royal Society of London and was made a member of both the London Mathematical Society and the Society of Sciences in Gottingen. He died in a mental institution on January 6, 1918. Today, Cantor's work is widely accepted by the mathematical community. His theory on infinite sets reset the foundation of nearly every mathematical field and brought mathematics to its modern form. part B: www.cs.umass.edu/~immerman/cs691/cs691.html hissa.nist.gov/~black/formaltut.html By Deepali Singla: 1) PART A Stanislaw Lesniewski Birth : March 30, 1886, Serpukhov, Russia. Life: He did his preliminary schooling in Russia and the Gymnasium in Siberia.He attended several universaties in continental Europe,finally taking his doctoral degree in 1912 at the Polish Universaty of Lw0(ukraine).His doctoral dissertation of 1911 dealt with the analysis of existential propositions. Lesniewski,after teaching for two years at a Warsaw Gymnasium and spending the war years in Moscow,joined the University of Warsow in 1919,as professor of the philosophy of mathematics. Beginning with the publication, in 1927, of his first mature work on the foundations of mathematics and extending until his death, he published a series of Twelve papers expounding the main lines of his theories of logic and mathematics. Death : May 13, 1939, Warsaw, Poland. Work -- # Lesniewski's efforts to solve antinomies in logic and mathematics led to some great discoveries for which he is known. # Leshniewski's contributions to logic concentrate on the structure of a sentence which according to him consists of subject,an object and a copula # The three major logical systems which Leshniewski developed were: Protothetic, a theory of propositions and propositional functors, Ontology, which is an axiomatised theory of common names based on protothetic and Mereology, which is an axiomatic extension of ontology for a theory of classes quite different from set theory providing a formal theory of part and whole similar to the calculus of individuals. # Stanislaw Leshniewski was one of the co-founders of the Polish School of Logic and an author of a new and wholly original system of the foundations of logic and mathematics. http://www.cs.ualberta.ca/~piotr/Mizar/mirror/http/sum/lesniewski.html http://www-history.mcs.st-and.ac.uk/Mathematicians/Leshniewski.html 2) PART B -- http://www.informatik.uni-trier.de/~ley/db/conf/fm/ http://www.cs.bham.ac.uk/resources/modules/2001/syls/syl-08764.html By Pravin Joshi: 1) PART A :- Personalites in Computer Science ---------------------------------------------- Name - Claude Elwood Shannon Birth - April 30, 1916 Gaylord, Michigan USA Died - 24 Feb 2001, Medford, Massachusetts, USA Biography ---------- A Midwesterner, Claude Shannon was born in Gaylord, Michigan in 1916. From an early age, he showed an affinity for both engineering and mathematics, and graduated from Michigan University with degrees in both disciplines. For his advanced degrees, he chose to attend the Massachusetts Institute of Technology. There he wrote a thesis on the use of Boole's algebra to analyse and optimise relay switching circuits. He joined Bell Telephones in 1941 as a research mathematician and remained there until 1972. At the time, MIT was one of a number of prestigious institutions conducting research that would eventually formulate the basis for what is now known as the information sciences. Its faculty included mathematician Norbert Wiener, who would later coin the term cybernetics to describe the work in information theories that he, Shannon and other leading American mathematicians were conducting; and Vannevar Bush, MIT’s dean of engineering, who in the early 1930s had built an analog computer called the Differential Analyzer The Differential Analyzer was developed to calculate complex equations that tabulators and calculators of the day were unable to address. It was a mechanical computer, using a series of gears and shafts to engage cogs until the equation was solved. Once it completed its cycle, the answer to the equation was obtained by measuring the changes in position of its various machine parts. Its only electrical parts were the motors used to drive the gears. With its crude rods, gears and axles, the analyzer looked like a child’s erector set. Setting it up to work one equation could take two to three days; solving the same equation could take equally as long, if not longer. In order to work a new problem, the entire machine, which took up several hundred feet of floor space, had to be torn apart and reset to a new mechanical configuration. While at MIT, Shannon studied with both Wiener and Bush. Noted as a ‘tinkerer,’ he was ideally suited to working on the Differential Analyzer, and would set it up to run equations for other scientists. At Bush’s suggestion, Shannon also studied the operation of the analyzer’s relay circuits for his master’s thesis. This analysis formed the basis for Shannon’s influential 1938 paper "A Symbolic Analysis of Relay and Switching Circuits," in which he put forth his developing theories on the relationship of symbolic logic to relay circuits. This paper, and the theories it contained, would have a seminal impact on the development of information processing machines and systems in the years to come. Shannon’s paper provided a glimpse into the future of information processing. While studying the relay switches on the Differential Equalizer as they went about formulating an equation, Shannon noted that the switches were always either open or closed, or on and off. This led him to think about a mathematical way to describe the open and closed states, and he recalled the logical theories of mathematician George Boole, who in the middle 1800s advanced what he called the logic of thought, in which all equations were reduced to a binary system consisting of zeros and ones. Boole’s theory, which formulated the basis for Boolean algebra, stated that a statement of logic carried a one if true and a zero if false. Shannon theorized that a switch in the on position would equate to a Boolean one. In the off position, it was a zero. By reducing information to a series of ones and zeros, Shannon wrote, information could be processed by using on-off switches. He also suggested that these switches could be connected in such a way to allow them to perform more complex equations that would go beyond simple ‘yes’ and ‘no’ statements to ‘and’, ‘or’ or ‘not’ operations. Shannon graduated from MIT in 1940 with both a master’s degree and doctorate in mathematics. After graduation, he spent a year as a National Research Fellow at the Institute for Advanced Study at Princeton University, where he worked with mathematician and physicist Hermann Weyl. In 1941, Shannon joined the Bell Telephone Laboratories, where he became a member of a group of scientists charged with the tasks of developing more efficient information transmitting methods and improving the reliability of long-distance telephone and telegraph lines. Shannon believed that information was no different than any other quantity and therefore could be manipulated by a machine. He applied his earlier research to the problem at hand, again using Boolean logic to develop a model that reduced information to its most simple form--a binary system of yes/no choices, which could be presented by a 1/0 binary code. By applying set codes to information as it was transmitted, the noise it picked up during transmission could be minimized, thereby improving the quality of information transmission. In the late 1940s, Shannon’s research was presented in The Mathematical Theory of Communications, which he co-authored with mathematician Warren Weaver. It was in this work that Shannon first introduced the word ‘bit,’ comprised of the first two and the last letter of ‘binary digit’ and coined by his colleague John W. Turley, to describe the yes-no decision that lay at the core of his theories. In the 1950s, Shannon turned his efforts to developing what was then called "intelligent machines,"–mechanisms that emulated the operations of the human mind to solve problems. Of his inventions during that time, the best known was a maze-solving mouse called Theseus, which used magnetic relays to learn how to maneuver through a metal maze. Shannon’s information theories eventually saw application in a number of disciplines in which language is a factor, including linguistics, phonetics, psychology and cryptography, which was an early love of Shannon’s. His theories also became a cornerstone of the developing field of artificial intelligence, and in 1956 he was instrumental in convening a conference at Dartmouth College that was the first major effort in organizing artificial intelligence research. Achievement ------------ Noted as a founder of information theory, Claude Shannon combined mathematical theories with engineering principles to set the stage for the development of the digital computer. The term ‘bit,’ today used to describe individual units of information processed by a computer, was coined from Shannon’s research in the 1940s. He published A Mathematical Theory of Communication in in the Bell System Technical Journal (1948). His work founded the subject of information theory and he proposed a linear schematic model of a communications system. He gave a method of analysing a sequence of error terms in a signal to find their inherent variety, matching them to the designed variety of the control system. In 1952 he devised an experiment illustrating the capabilities of telephone relays. Honors and awards ------------------ Shannon was awarded the National Medal of Science in 1966. Excerpted from : http://www.thocp.net/biographies/shannon_claude.htm 2) PART B :- Course Related Links ---------------------------------- http://www.cs.utah.edu/classes/cs6110/ http://hissa.nist.gov/~black/formaltut.html By N.khogendro singh (02d05014): Part-A -------------- Kurt Godel *************************************************************************** Kurt Godel was born in 1906 in Brunn, then part of the Austro-Hungarian Empire and now part of the Czech Republic, to a father who owned a textile factory and had a fondness for logic and reason and a mother who believed in starting her son's education early. By age 10, Godel was studying math, religion and several languages. By 25 he had produced what many consider the most important result of 20th century mathematics: his famous " incompleteness theorem." Godel's astonishing and disorienting discovery, published in 1931, proved that nearly a century of effort by the world's greatest mathematicians was doomed to failure. Godel's 1931 article did something else: it invented the theory of recursive functions, which today is the basis of a powerful theory of computing.Indeed, at the heart of Godel's article lies what can be seen as an elaborate computer program for producing M.P. numbers, and this "program" is written in a formalism that strongly resembles the programming language Lisp, which wasn't invented until nearly 30 years later. He died at age 72 in a Princeton hospital, essentially because he refused to eat. *************************************************************************** ****************** Part-B ---------- URLS (1) http://www.cs.unh.edu/~charpov/Teaching/CS-745/index-noframes.html (2) http://www.dcs.warwick.ac.uk/people/academic/Ranko.Lazic/teach/logic/ (3) www.cs.nott.ac.uk/~txa/g51mcs/notes.pdf *************************************************************************** ***************** By Rishi Gupta: Doug Lenat has set out to build programs to solve the central problems of Artificial Intelligence: to make a machine learn and to instill it with common knowledge and common sense. Born in Philadelphia in 1950, Lenat grew up there and in Wilmington, Delaware. His family owned a soda bottling business. In the school library during sixth grade, Lenat discovered Isaac Asimov's popular books about physics and biology. Science became an outlet for his curiosity about how the world worked. When Lenat was twelve and a half, his father died very suddenly, and young Lenat turned to science as a form of solace. After his father's death, Lenat's family moved frequently and he found himself often starting over in new school districts. Lenat's talents showed. In 1967, he was a finalist in an International Science Fair. He described a closed form definition of the Nth prime number. Along with other winners from the Delaware Valley, Lenat received an all expenses-paid trip to Detroit. At the time, Lenat was disappointed about the location --- the previous year's fair had been held in Tokyo --- but the fair had other benefits. Contestants were to be judged by practicing scientists, researchers and engineers. Before that, the closest thing to a scientist I had met was my high school science teacher. Lenat entered the University of Pennsylvania in 1968. The Vietnam War was at its height and Lenat received a draft number low enough to make him think he might have to go to war. The uncertainty of those times convinced him to speed up his academic training . He decided to study both physics and math. Lenat started college interested in physics and mathematics, but he changed his mind by the end. he says: I got far enough along in mathematics to realize I would not be one of the world's great mathematicians... I got far enough along in physics to realize that in some sense it was all built on sand --- that people were spending their lives doing things like finding mathematical solutions to things like Einstein's astrophysical equations --- whether or not it had any physical significance or reality... People would walk around with ever-growing chest pocket cards of elementary particles which really means resonances that were found but not understood. Things were just happening that divorced themselves from physical reality. A course taught by John W. Carr III in 1971 introduced Lenat to Artificial Intelligence. Computers had created the technology for Artificial Intelligence, but research, Lenat decided, was still at an early stage. By Yash: Johann Carl Friedrich Gauss 1. Gauss' Biography Born: April 30, 1777, Brunswick, Germany Died: February 23, 1855, Göttingen, Germany Life: From the outside, Gauss' life was very simple. Having brought up in an austere childhood in a poor and uneducated family he showed extraordinary precocity. He received a stipend from the duke of Brunswick starting at the age of 14 which allowed him to devote his time to his studies for 16 years. Before his 25th birthday, he was already famous for his work in mathematics and astronomy. When he became 30 he went to Göttingen to become director of the observatory. He rarely left the city except on scientific business. From there, he worked for 47 years until his death at almost 78. In contrast to his external simplicity, Gauss' personal life was tragic and complicated. Due to the French Revolution, Napoleonic period and the democratic revolutions in Germany, he suffered from political turmoil and financial insecurity. He found no fellow mathematical collaborators and worked alone for most of his life. An unsympathetic father, the early death of his first wife, the poor health of his second wife, and terrible relations with his sons denied him a family sanctuary until late in life. Even with all of these troubles, Gauss kept an amazingly rich scientific activity. An early passion for numbers and calculations extended first to the theory of numbers, to algebra, analysis, geometry, probability, and the theory of errors. At the same time, he carried on intensive empirical and theoretical research in many branches of science, including observational astronomy, celestial mechanics, surveying, geodesy, capillarity, geomagnetism, electromagnetism, mechanism optics, actuarial science. His publications, abundant correspondence, notes, and manuscripts show him to have been one of the greatest scientific virtuosos of all time. Work: Gauss showed his genius early and made many of his important discoveries before he was twenty. His greatest work was done in the area of higher arithmetic and number theory; his Disquisitiones Arithmeticae (completed in 1798 but not published until 1801) is one of the masterpieces of mathematical literature.He discovered the law of quadratic reciprocity.He showed that a regular polygon of n sides can be constructed using only compass and straight edge only if n is of the form 2p(2q+1)(2r+1) . . . , where 2q + 1, 2r + 1, . . . are prime numbers.In 1801, following the discovery of the asteroid Ceres by Piazzi, Gauss calculated its orbit on the basis of very few accurate observations, and it was rediscovered the following year in the precise location he had predicted for it. He tested his method again successfully on the orbits of other asteroids discovered over the next few years and finally presented in his Theoria motus corporum celestium (1809) a complete treatment of the calculation of the orbits of planets and comets from observational data.Important contributions to differential geometry as well as to such practical results as his invention of the heliotrope, a device used to measure distances by means of reflected sunlight. In 1833 he invented the electric telegraph. REFRENCES: http://www.geocities.com/RainForest/Vines/2977/gauss/ http://www.infoplease.com/ce6/people/A0820346.html http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Gauss.html 2.USEFULL LINKS FOR COURSE: http://hissa.nist.gov/~black/formaltut.html http://www.kddresearch.org/Courses/Fall-2001/CIS730/ By Gaurav Magare: #1. Got to do with the significant contributors in logic, etc. here's Alessandro Pedoa Alessandro Padoa attended secondary school in Venice, then studied engineering at the University of Padua. He was awarded a mathematics degree from the University of Turin in 1895. After graduating, Padoa became a secondary school teacher, teaching in Pinerolo, Rome and Cagliari. However, Padoa gave many lectures at universities and lectures at congresses. Beginning in 1898 he gave a series of lectures at the Universities of Brussels, Pavia, Berne, Padua, Cagliari and Genoa. He lectured at congresses in Paris, Cambridge, Livorno, Parma, Padua and Bologna. From 1909 he taught at the Technical Institute in Genoa. Padua belonged to Peano's school of mathematical logic, popularising this type of work. He gave the important lecture Essay of an algebraic theory of whole numbers, preceded by a logical introduction to any deductive theory at the International Congress of Philosophy in Paris in 1900. He had discovered an important method in the theory of definition which became even more important when model theory was developed and Tarski proved Padoa's method in 1924. Padoa was the first to present a method to prove that a primative term of a theory cannot be defined within the system using the remaining primative terms. This result was first made public in his lecture at the Paris Congress referred to above. Padoa believed, correctly, that his result was of major importance and wrote in this paper:- We can now settle completely (and, we believe, for the first time) a question of the greatest logical importance. Immediately following the Congress of Philosophy in Paris, the Second International Congress of Mathematicians took place. Padoa spoke on A new system of definitions for Euclidean geometry but began with a summary of his lecture at the Philosophy Congress. Charlotte Scott found this one of the most interesting talks at the Congress but wrote:- "We can now settle completely (and, we believe, for the first time) a question of the greatest logical importance." Mr Padoa did not get beyond this definition, possibly because he had entered so minutely into the details of the proof of the independance of the seven postulates that he had exhausted his allowance of time. Halsted also attended the Congress and wrote that Padoa was:- .. among the most interesting personalities present. In 1934 Padoa was awarded the mathematics prize of the Accademia dei Lincei. The links to pages relating to him and his work... 1) http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Padoa.html ..and the references at 2) http://www-gap.dcs.st-and.ac.uk/~history/References/Padoa.html ..and a few italian links as well which i left logically et preferably. #2. Got to do with course links for other universities and institutions. 1). http://www.cs.indiana.edu/formal-methods-education/ 2). http://www.cas.mcmaster.ca/~lawford/CS734/outline.html 3). http://www-sop.inria.fr/certilab/Joelle.Despeyroux/courses/sec-soft/ 4). http://www.usp.edu.pe/~cursounu/ 5). http://www.isse.gmu.edu/~duminda/classes/spring01/swse623.html By Nikhil Rao: Part A: Allen Newell ------------ Born: 1927 Died: 1992 Claim to Fame: With Herbert A. Simon and J.C Shaw in 1957, he first articulated a rule-based model of human and computer problem solving. Newell earned an international reputation for his pioneering work in artificial intelligence, the theory of human cognition, and the development of computer software and hardware systems for complex information processing. Newell's career spanned the entire computer era, which began in the early 1950s. In computer science, he worked on areas as diverse as list processing, computer description languages, hypertext systems, and psychologically based models of human-computer interaction. In 1949 Newell received a bachelor's degree in physics from Stanford University. He spend a year at Princeton University doing graduate work in mathematics, and work for the Rand Corporation as a research scientist from 1950 to 1961. Newell earned a doctor's degree in industrial administration from Carnegie Institute of Technology in 1957. The fields of artificial intelligence and cognitive science grew in part from his idea that computers could process symbols as well as numbers and, if programmed properly, would be capable of solving problems in the same way humans do. Throughout his research career, his work touched on architectures to support intelligent action in humans and machines. Works ----- 1. The Logic Theory Machine: A Complex Information Processing System 2. GPS, A Case Study in Generality and Problem Solving 3. Human Problem Solving 4. The Psychology of the Human Computer 5. Unified Theories of Cognition Ref: http://stills.nap.edu/readingroom/books/biomems/anewell.html http://home.sei.pku.edu.cn/~panying/turing/1975-1.htm http://www.sis.pitt.edu/~mbsclass/hall_of_fame/newell.htm Part B: the sites... http://www.afm.lsbu.ac.uk/ http://www.cs.cornell.edu/Courses/cs686/2003SP/ By LekhRaj: A. CHARLES LUTWIDGE DODGSON Born:27 Jan 1832 in Daresbury,England Died:14 Jan 1898 in Guilford,England Although he was a mathematician,he is best known as the author of Alice's adventures in wonderland(1865) and through the looking glass(1872), children's books that are among the most popular of all time. As a mathematician, Dodgson was rather conservative but certainly thorough and careful. He was the author of a fair number of mathematics books including: A syllabus of plane algebraical geometry (1860), Two Books of Euclid (1860), The Formulae of Plane Trigonometry (1861), Condensation of Determinants (1866), Elementary Treatise on Determinants (1867), Examples in Arithmetic (1874), Euclid and his modern rivals (1879), Curiosa Mathematica, Part I: A New Theory of Parallels (1888), and Curiosa Mathematica, Part II: Pillow Problems thought out during Sleepless Nights (1893). None of his mathematics books have proved of enduring importance except for Euclid and his modern rivals (1879) which is of historical interest. As a mathematical logician, he was interested in increasing understanding by treating it as a game. He published The Game of Logic in 1887 and Symbolic Logic Part I in 1896. By 1896 Dodgson had developed a mechanical test of validity for a large part of the logic of terms. As early as 1894 Dodgson used truth tables for the solution of specific logic problems. The application of truth tables and matrices did not come into general use until 1920. By 1896 Dodgson had developed the method of trees for determining some validity, which bears a resemblance to the trees frequently employed by contemporary logicians. B.links: http://www-history.mcs.st-andrews.ac.uk/history/References/Dodgson.html http://www.lewiscarroll.org/carroll.html http://www-groups.dcs.st-and.ac.uk/~history/Quotations/Dodgson.html By Kashyap Paidimarri (02005014): _____________________________________________________________________________ A)Person:: Tom Henzinger Tom Henzinger is a Professor of Electrical Engineering and Computer Sciences at the University of California, Berkeley. He holds a Dipl.-Ing. degree in Computer Science from Kepler University in Linz, Austria, an M.S. degree in Computer and Information Sciences from the University of Delaware, and a Ph.D. degree in Computer Science from Stanford University (1991). He was an Assistant Professor of Computer Science at Cornell University (1992-95), and a Director of the Max-Planck Institute for Computer Science in Saarbruecken, Germany (1999). His research focuses on modern systems theory, especially formalisms and tools for the component-based and hierarchical design, implementation, and verification of embedded, real-time, and hybrid systems. His HyTech tool was the first model checker for mixed discrete-continuous systems. For more information on Tom Henzinger:: 1)http://www-cad.eecs.berkeley.edu/~tah/ _____________________________________________________________________________ B)world wide web links for lecture notes:: 1))http://www.cs.indiana.edu/formal-methods-education/Courses/ 2))http://www.eecs.berkeley.edu/~necula/294softqual/ berkeley 3)http://www.cl.cam.ac.uk/users/mjcg/Teaching/SpecVer1/SpecVer1.html 4)http://www.cl.cam.ac.uk/users/mjcg/Teaching/SpecVer2/SpecVer2.html cambridge 5)http://www-logic.stanford.edu/main.html#courses stanford 6)http://shemesh.larc.nasa.gov/fm/ formal methods at NASA 7)http://www-2.cs.cmu.edu/~svc/ carnegie-mellon By Ritesh: Claude Shannon Noted as a founder of information theory. Claude Shannon was born in Gaylord, Michigan in 1916. From an early age, he showed an affinity for both engineering and mathematics, and graduated from Michigan University with degrees in both disciplines. For his advanced degrees, he chose to attend the Massachusetts Institute of Technology. There he wrote a thesis on the use of Boole's algebra to analyse and optimise relay switching circuits. He joined Bell Telephones in 1941 as a research mathematician and remained there until 1972. Claude Shannon combined mathematical theories with engineering principles to set the stage for the development of the digital computer. The term 'bit, today used to describe individual units of information processed by a computer, was coined from Shannon's research in the 1940s. He published A Mathematical Theory of Communication in in the Bell System Technical Journal (1948). His work founded the subject of information theory and he proposed a linear schematic model of a communications system. He gave a method of analysing a sequence of error terms in a signal to find their inherent variety, matching them to the designed variety of the control system. In 1952 he devised an experiment illustrating the capabilities of telephone relays. LINKS Links for perl http://archive.ncsa.uiuc.edu/General/Training/PerlIntro/ http://www.pageresource.com/cgirec/ptut3.htm http://www.comp.leeds.ac.uk/Perl/start.html http://www.perlmonks.org/index.pl?node=Tutorials