Web Links for Chapter 1
Section 1.1 Logic
Page 2
Information on logic and its applications can be found at
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An extensive biography of George Boole, including a portrait, can be found at the Roger P@rsons_world
of Lincolnshire site.
http://homepages.enterprise.net/rogerp/george/boole.html (Roger P@rsons_world of George Boole)
A biography and a portrait of George Boole can be found at the MacTutor History of Mathematics Archive at the University of St Andrews, Scotland.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Boole.html (Boole)
A copy of George Boole's pioneering article "The Calculus of Logic," published in 1848, can be seen at the History of Mathematics Archive at the School of Mathematics, Trinity College, Dublin, Ireland.
http://www.maths.tcd.ie/pub/HistMath/People/Boole/CalcLogic/
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Information on Boolean searching can found at
The particular way to carry out Boolean searches and other types of searches for a particular search engine is usually described somewhere on the site of that search engine. For example, check out the following pages:
http://www.excite.com/Info/advanced.html (Excite)
http://www.gmu.edu:8765/help/boolean.html (Infoseek)
http://www.hotbot.com/help/tips/search_features.asp (Hotbot)
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A biography and photograph of John Tukey can be found at the MacTutor History of Mathematics Archive at the University of St Andrews, Scotland.
http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Tukey.html (Tukey)
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A list of paradoxes can be found at
Section 1.2 Propositional Equivalences
Page 16
Biographical information about Augustus De Morgan can be found at the MacTutor History of Mathematics Archive at the University of St Andrews, Scotland.
http://www-history.mcs.st-and.ac.uk/history/Mathematicians/De_Morgan.html (De Morgan)
Page 19
Biographical information and portraits of Ada Lovelace can be found at
and the MacTutor History of Mathematics Archive at the University of St Andrews, Scotland.
http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Lovelace.html (Lovelace)
More biographical information about Ada Lovelace can be found at the site for the book Ada: The Enchantress of Numbers by Betty Toole.
Ada Lovelace's notes about Charles Babbage's Analytical Engine can be found at
http://www.cs.yale.edu/HTML/YALE/CS/HyPlans/tap/Files/ada-lovelace-notes.html
A good starting place to find more out about Ada Lovelace is
Section 1.3 Predicates and Quantifiers
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Biographical information about Charles Peirce, as well as information about his work and the numerous activities devoted to the study of his philosophy and writings can be found at several Web sites, including
http://www.iupui.edu/~peirce/web/desc/desc.htm (The Peirce Edition Project)
A biography of Peirce can also be found at the MacTutor History of Mathematics Archive at the University of St Andrews, Scotland.
http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Peirce_Charles.html (Peirce).
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A home page for Lewis Carroll provides information about his life, his writings, his puzzles, on-line texts, related academic studies and societies, objects to buy, and so on.
http://www.lewiscarroll.org/carroll.html (Lewis Carroll Home Page)
Lewis Carroll puzzles and games are also accessible at
http://home.earthlink.net/~lfdean/carroll/puzzles/index.html
Explore Lewis Carroll's Game of Logic and play with some interactive applets at
More information about the history of set theory can be found at the MacTutor History of Mathematics Archive at the University of St Andrews, Scotland
http://www-history.mcs.st-and.ac.uk/history/HistTopics/Beginnings_of_set_theory.html#61
(The Beginning of Set Theory)
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Some people claim that every actor from a movie made during the last 15 years can be connected to Kevin Bacon in 6 steps or less. You can learn more about this, and finding additional links about this, at the following site
http://www.cs.virginia.edu/cgi-bin/cgiwrap/webman/oracle/link_bacon
(Six Degrees of Kevin Bacon)
Section 1.4 Sets
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Material on set theory can be found at the Department of Mathematics of the University of California at San Bernardino Math Notes Web site at
http://www.math.csusb.edu/notes/sets/sets.html (Notes on Set Theory)
A biography and a photograph of Georg Cantor can be found at the MacTutor history of Mathematics Archive at the University of St Andrews, Scotland.
http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Cantor.html (Cantor)
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A biography and a photograph of Betrand Russell can be found at the MacTutor History of Mathematics Archive at the University of St Andrews, Scotland.
http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Russell.html (Russell)
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Biographical information about John Venn can be found at the MacTutor History of Mathematics Archive at the University of St Andrews, Scotland.
http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Venn.html (Venn)
Information about Venn diagrams, especially there combinatorial properties) can be found at
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Biographical information and a portrait of René Descartes can be found at the MacTutor History of Mathematics Archive at the University of St Andrews, Scotland.
http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Descartes.html (Descartes)
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The on-line Stanford Encyclopedia of Philosophy contains an excellent discussion of Russell's paradox.
http://plato.stanford.edu/archives/win1997/entries/russell-paradox/
You can also read more about Russell's paradox at the Cut-the-Knot site
http://www.cut-the-knot.com/selfreference/russell.html (Russell's Paradox)
Section 1.5 Set Operations
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Material on set operations can be found at the Math Notes site of the Department of Mathematics at the University of California at San Bernardino
http://www.math.csusb.edu/notes/sets/node2.html#SECTION00020000000000000000 (More on Set Operations)
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A description of fuzzy logic can be found at
http://www.cs.cmu.edu/afs/cs.cmu.edu/project/ai-repository/ai/html/faqs/ai/fuzzy/part1/faq-doc-2.html (Carnegie Mellon Unversity, Computer Science Department)
A brief course in fuzzy logic and control, which can be downloaded via ftp, can accessed using the Web page
http://www.flll.uni-linz.ac.at/aboutFLLL/index.html (About the FLLL)
Section 1.6 Functions
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Consult the following pages by Peter Williams to see how to show functions are one-to-one and/or onto.
http://www.math.csusb.edu/notes/proofs/bpf/node4.html (Proving Functions One-to-One)
http://www.math.csusb.edu/notes/proofs/bpf/node5.html (Proving Functions Onto)
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How the floor and ceiling functions can be used to model telephone rates can be found at a site developed by Evan Glazer, a high school teacher at Glenbrook South High School in Glenview, Illinois.
http://www.glenbrook.k12.il.us/gbsmat/phone/phone.html (Unsure about which telephone plan to use?)
Section 1.7 Sequences and Summations
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Neil Sloane's On-Line Encyclopedia of Integer Sequences Web site can be used to determine the possible identity of an integer sequence from its first few terms. To use the site for this purpose, enter the first few terms of a sequence and click to get feedback on which sequence or sequences may be the sequence of interest. This site also offers the opportunity to check out some "hot sequences" and offers some puzzle sequences that are quite challenging.
http://www.research.att.com/~njas/sequences/index.html (Sloane's On-Line Encyclopedia of Integer Sequences)
For more information about Neil Sloane and his many activities and interests consult his home page at
Section 1.8 The Growth of Functions
Page 82
Biographical information about Paul Bachmann can be found at the MacTutor History of Mathematics Archive at the University of St Andrews, Scotland.
http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Bachmann.html (Bachmann)
Biographical information and a portrait of Edmund Landau can be found at the site of the Edmund Landau Center for Research in Mathematical Analsyis at the Hebrew University in Israel
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Donald Knuth's home page, containing a wealth of information about his activities, books, and interests can be found at
http://www-cs-faculty.Stanford.EDU/~knuth/ (Donald Knuth's home page)
An interesting interview with Donald Knuth (by Dan Doernberg on December 7th, 1993) which includes Knuth's musing on many different topics can be found at the Computer Literacy site:
http://www.cbooks.com/interviews/knuth_interview.html (Computer Literacy Interview with Donald Knuth)
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