CHAPTER 1 WEB LINKS
Chapter 1 - Section 1.1 page
2: Aristotle -- Overview [Internet Encyclopedia of Philosophy]
Information on the life and works of Aristotle can be found at the
Internet Encyclopedia of Philosophy. Pay particular attention to the section on
logic to learn how propositional logic and calculus were first developed.
http://www.utm.edu/research/iep/a/aristotl.htm
Chapter 1 - Section
1.1 page 2: Aristotle
You can find biographical information on the life and works of Aristotle,
with some interesting links, at the MacTutor History of Mathematics Archive at
the University of St. Andrews, Scotland.
http://www-groups.dcs.st-andrews.ac.uk/~history/Biographies/Aristotle.html
Chapter 1 - Section
1.1 page 3: Applied Logic for Computer Science
Check out the course notes for the course Applied Logic for Computer Science given at the University of Western Ontario. These notes cover propositional calculus, predicate calculus, automated theorem proving, resolution, Boolean algebra, DNA computing, and many other topics. If you cannot get the PDF versions of the course notes, you can
access PostScript versions and use a PostScript previewer such as Ghostscript or Ghostview (available for free download) or Adobe Acrobat Distiller (available commercially).
https://web.archive.org/web/20110109052605/http://www.csd.uwo.ca/~lila/209.html
Chapter 1 - Section
1.1 page 3: CS381 Web Course Materials
A website for an Internet based Discrete Structures course from Old Dominion University with lots of useful material on logic can be found here. The online exercises provided are good tests of your understanding of topics in logic.
http://www.cs.odu.edu/~toida/nerzic/content/web_course.html
Chapter 1 - Section 1.1 page 3: Logic and Mathematics
An overview of logic and the philosophy of mathematics can be found at this website. There are sections on propositional and predicate calculus, as well as additional topics on the foundations of mathematics.
http://www.personal.psu.edu/t20/papers/philmath/
Chapter 1 - Section
1.1 page 3: Logic and Mathematics
The Wikipedia article on Mathematic Logic is a useful resource.
https://en.wikipedia.org/wiki/Mathematical_logic
Chapter 1 - Section
1.1 page 3: Mathematical Atlas: Mathematical logic and foundations
A good introduction to mathematical logic can be found on the archive of the Mathematical Atlas site.
Chapter 1 - Section
1.1 page 3: Logic Introduction
An excellent introduction to logic, including propositional logic, predicate logic, and rules of inference, can be found at the Introduction to Logic site by Stefan Waner and Steven R. Costenoble.
https://www.zweigmedia.com/RealWorld/logic/logicintro.html
Chapter 1 - Section
1.1 page 3: Truth Values
You can use the javascript truth
table tool to find the truth table of a compound proposition at
http://web.stanford.edu/class/cs103/tools/truth-table-tool/.
If your system supports Java, you can use the applet at
https://www.maa.org/press/periodicals/loci/resources/truth-table-applet or
https://web.archive.org/web/20100729101825/http://www.uiowa.edu/~linguist/classes/lfr-fall98/software/truth_tables.html for the same purpose.
Chapter 1 - Section
1.1 page 5: Roger Parsons world of George Boole
You can find an extensive biography of George Boole, including a portrait, at the Roger P@rsons_world of Lincolnshire site.
Chapter 1 - Section 1.1
page 5: George Boole
You can find a biography of George Boole on the Britannica site
https://www.britannica.com/biography/George-Boole
Chapter 1 - Section
1.1 page 5: 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/Biographies/Boole.html
Chapter 1 - Section 1.1 page 5: "The Calculus of Logic" by 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/
Chapter 1 - Section
1.1 page 12: Bitwise Operations
Information on bitwise operations can be found on this Wikipedia page.
http://en.wikipedia.org/wiki/Bitwise_operation
Chapter 1 - Section
1.5 page 12: John Wilder Tukey
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/Biographies/Tukey.html
Chapter 1 - Section
1.2 page 17: CMU Computer Science Department
A description of fuzzy logic can be found at the Carnegie Mellon School of Computer Science website.
Chapter 1 -
Section 1.2 page 17: About the Fuzzy
Logic Laboratorium Linz
Information about fuzzy logic can be found at
https://www.scientificamerican.com/article/what-is-fuzzy-logic-are-t/
and at
Chapter 1 - Section 1
page 17: Paradoxes (Logic)
You can find a list of paradoxes at
https://web.archive.org/web/20060907194629/http://www.eecs.berkeley.edu/~fmang/paradox.html
Chapter 1 - Section 2
page 19: Boolean Searching on the Internet
Information on Boolean searching can found at
https://library.uaf.edu/ls101-boolean
and at
https://web.archive.org/web/20070717161044/http://www.internettutorials.net/boolean.html
Chapter 1 - Section 2
page 19: Boolean Searches
How 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, see
https://support.google.com/websearch/answer/2466433?hl=en
Chapter 1 - Section 2
page 19: Boolean Searching on the Internet
This primer about Boolean logic and how it can be used to search for information on the Internet can be found at
https://www.lifewire.com/what-does-boolean-search-3481475
Chapter 1 - Section 2
page 19: Boolean Searching
This site provides useful information and a demonstration of Boolean searching.
http://booleanblackbelt.com/tag/boolean-search-string-examples/
Chapter 1 - Section 2
page 20: Logic Puzzles
You can find some interesting logic puzzles at
https://web.archive.org/web/20040726235538/http://dfcurran.com:80/logic/logicpuz.html
Chapter 1 - Section 2 page 20: Brain Food
You can find many logic puzzles, as well as other types of puzzles, at http://rinkworks.com/brainfood/
Chapter 1 - Section 2 page 20: EncycloZine
Logic Puzzles
A large collection of logic puzzles and paradoxes can be found at
http://brainden.com/logic-puzzles.htm and at
https://web.archive.org/web/20010509194424/http://encyclozine.com:80/Puzzles/Logic/
Chapter 1 - Section 2
page 20: Index of Logic Puzzles
A large collection of logic puzzles, complete with clues, answers and solutions, can be found here.
https://www.brainzilla.com/logic/zebra/
and at
https://web.archive.org/web/20040405235605/http://brownbuffalo.sourceforge.net:80/puzzle_index.html
Chapter 1 - Section 2
page 20: Logic Problems Page
Useful web sites on complicated logic puzzles can be found at
https://web.archive.org/web/20040401170550/http://www.geocities.com/Heartland/Plains/4484/logic.htm
Chapter 1 - Section 2
page 20: Logic Puzzles
A very large collection of various logic puzzles and their solutions can be found at the rec.puzzles archive at
http://mathforum.org/rec_puzzles_archive/logic/
Chapter 1 - Section 2
page 20: Mike's Logic and Math Problems
A collection of various logic puzzles and their solutions can be found at
http://www.puzzlersparadise.com/page1034.html
and at
https://web.archive.org/web/20040807000426/http://mathproblems.info:80/group7.html
Chapter 1 - Section 2
page 20: Borborygmus' Logic Problems
You can find a growing list of logic puzzles at
https://www.riddles.com/logic-puzzles
and at
https://web.archive.org/web/20050306160522/http://www.nzorgan.com/borborygmus/logic_puzzles.htm
Chapter 1 - Section 2
page 21: Raymond Smullyan
Biographical information about Raymond Smullyan can be found at
http://www-history.mcs.st-and.ac.uk/Biographies/Smullyan.html
Chapter 1 -
Section 2 page 25: Solution of the Zebra
Puzzle
A solution to the Zebra Puzzle can be found at
http://mathforum.org/dr.math/problems/joseph8.5.97.html
Chapter 1 - Section 3
page 26: CS381 Web Course Materials
A website for an Internet based Discrete Structures course from Old Dominion University with lots of useful material on propositional logic can be found at
http://www.cs.odu.edu/~toida/nerzic/content/web_course.html
Chapter 1 - Section 3 page 31: Augustus de Morgan
Information about Augustus De Morgan can be found at
http://www-history.mcs.st-and.ac.uk/history/Biographies/De_Morgan.html
Chapter 1 - Section 3 page 32: Agnes Scott College
Biographical information and portraits of Ada Lovelace can be found at
http://www.agnesscott.edu/lriddle/WOMEN/love.htm
Chapter 1 - Section 3
page 32: Ada Augusta
You can find biographical information on Ada Lovelace at
http://www-groups.dcs.st-andrews.ac.uk/~history/Biographies/Lovelace.html
Chapter 1 - Section 3 page 32: Ada: The Enchantress of
Numbers
you can find more biographical information about Ada Lovelace at the site for the book Ada: The Enchantress of Numbers by Betty Toole at
http://www.well.com/user/adatoole/bio.htm
Chapter 1 - Section 3
page 32: TAP: Ada Lovelace - Notes
You can find Ada Lovelace's notes about Charles Babbage's Analytical Engine at
http://www.cs.yale.edu/homes/tap/Files/ada-lovelace-notes.html
Chapter 1 - Section 3
page 32: Ada Byron King
A good place to find more out about Ada Lovelace is
https://www.agnesscott.edu/lriddle/women/love.htm
Chapter 1 – Section 3 page 35:
To learn about the history of Sudoku, consult
http://www.sudokudragon.com/sudokuhistory.htm
Chapter 1 - Section
1.3 page 37:
You can learn how to use Mathematica to solve Soduku boards by representing them as satisfiability problems at
https://syntacticsalt.com/blog/2016-03-07-solving-sudoku-via-sat.html
Chapter 1 - Section 3
page 37:
Biographical information on Sheffer can be found at
https://www.revolvy.com/page/Henry-M.-Sheffer
Chapter 1 - 4 page
40: CS381 Web Course Materials
A site for an Internet based Discrete Structures course from Old Dominion University with lots of useful material on predicate logic can be found here. The online exercises provided are good tests of your understanding of topics in logic.
http://www.cs.odu.edu/~toida/nerzic/content/web_course.html
Chapter 1 - Section 4 page 40: Logic and Mathematics
An overview of logic and the philosophy of mathematics can be found at the following website. There are sections on propositional and predicate calculus, as well as additional topics on the foundations of mathematics.
http://www.math.psu.edu/simpson/papers/philmath/
Chapter 1 - Section 4 page 42: Charles S. Pierce Studies
Further information about Charles Peirce, his work and his numerous activities devoted to the study of his philosophy and writings, can be found at
and at
Chapter 1 - Section 4
page 42: Charles Sanders Peirce
A biography of Peirce 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/Biographies/Peirce_Charles.html
Chapter 1 - 4 page
54: Lewis Carroll Home Page
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 can be found at
http://www.lewiscarroll.org/carroll.html
Chapter 1 - Section 4 page 54: Lewis Carroll Puzzles and
Games
Lewis Carroll puzzles and games are accessible at.
Chapter 1 - Section 4 page 54: Lewis Carroll's Logic Game
Explore Lewis Carroll's Game of Logic and play with some interactive at
https://www.cut-the-knot.org/LewisCarroll/
Chapter 1 - Section 4
page 55: Resolution, Prolog
A description of Prolog and resolution by Lee Spector at Hampshire College can be found at
http://hampshire.edu/lspector/courses/resolution-prolog/resolution-prolog.html
Chapter 1 - Section 4
page 55: Math 156 Prolog Page (F99)
Information on the Prolog language can be found at the Math 156 Prolog Page, which includes the Toy Prolog interpreter can be found at
http://www.calvin.edu/~rpruim/courses/m156/F99/prolog/intro.shtml
More information about the Toy Prolog interpreter can be found here.
http://www.csse.monash.edu.au/~lloyd/tildeLogic/Prolog.toy/
Chapter 1 - Section 4
page 55: Prolog
Another large collection of Prolog Examples with interactive applets can be found at
https://web.archive.org/web/20040404192100/http://www.probp.com:80/examples.htm
Chapter 1 - Section 4
page 55: Logic Programming
Information on logic programming, including Prolog, can be found at
https://store.fmi.uni-sofia.bg/fmi/logic/skordev/ln/lp/logic-prog.htm
Chapter 1 - Section 5
page 72: The Oracle of Bacon at Virginia
Some people claim that every actor from a movie made during
the last 25 years can be connected to Kevin Bacon in six or fewer steps. You
can learn more about this, and find additional links relating to this
phenomenon, at The Oracle of Bacon, which can be found at
http://www.cs.virginia.edu/oracle/
and at
https://oracleofbacon.org/
Chapter 1 - Section 6
page 78: Resolution
You can learn more about resolution in logic at the Wikipedia page at
http://en.wikipedia.org/wiki/First-order_resolution
Chapter 1 - Section 6
page 79: Classic Fallacies
You can find some incorrect proofs based on fallacious reasoning at
http://www.math.toronto.edu/mathnet/falseProofs/fallacies.html
Chapter 1 - Section 6 page 79: Informal Fallacies
A useful source for information about fallacies can be found at
https://web.archive.org/web/20040117193034/http://www.drury.edu:80/ess/Logic/Informal/Overview.html
Chapter 1 - Section 6
page 79: Fallacies
A long list of fallacies can be found at
http://www.nizkor.org/features/fallacies/ and at
http://www.csun.edu/~dgw61315/fallacies.html
Chapter 1 - Section 7
page 85: How to Write Proofs
Guidance on how to write proofs as well as an introduction to proof strategies, can be found at Larry W. Cusick's website.
http://zimmer.csufresno.edu/~larryc/proofs/proofs.html
Chapter 1 - Section 7
page 85: Proving Real Theorems
A website with more information on several different methods of proof can be found at
http://www.math.lsa.umich.edu/~jchw/PrimerOnProof.pdf
Chapter 1 - Section 7
page 85: Notes on Methods of Proofs
A website describing different proof methods, including existence proofs and uniqueness proofs, can found at
http://www-math.ucdenver.edu/~wcherowi/courses/m3000/lecture3a12.pdf
Chapter 1 - Section 7
page 85: Proofs in Mathematics
An interesting variety of proofs and other problems in mathematics can be found at the Cut-the-Knot site at
https://www.cut-the-knot.org/proofs/index.shtml
Chapter 1 - Section 7
page 85: Tom's Combinatorial Geometry Class
A review of methods of proof can be found at
Chapter 1 - Section 7 page 85: Some Mathematical Proofs
A humorous discussion of bogus proof techniques can be found at
https://web.archive.org/web/20070429081037/http://paul.merton.ox.ac.uk/science/maths-proofs.html
and at
http://staffhome.ecm.uwa.edu.au/~00043886/humour/invalid.proofs.html
Chapter 1 - Section 7 page 90: Proofs by Contradiction
A selection of proofs by contradiction can be found at this site. If you are stuck on an exercise, look at a similar example for a hint.
http://zimmer.csufresno.edu/~larryc/proofs/proofs.contradict.html
Chapter 1 – Section 7
page 93: Incorrect Proofs
You can find out more about common errors in incorrect proofs, consult
http://www.math.lsa.umich.edu/~jchw/PrimerOnProof.pdf, and
https://skullsinthestars.com/2008/12/12/spot-the-math-errors/
Chapter 1 - Section 8
page 102: Mathematical mysteries: Chomp
Find out more about the game of Chomp by consulting this article by Helen Joyce in Plus magazine.
http://plus.maths.org/issue14/xfile/
Chapter 1 - Section 8
page 102: The Game of Chomp
You can learn more about the Game
of Chomp at
http://www.win.tue.nl/~aeb/games/chomp.html
or at
https://plus.maths.org/content/mathematical-mysteries-chomp
Chapter 1 - Section 8
page 102: Chomp
There are quite a few Chomp applets available on the Web, including one written in
javascript at
https://www.math.ucla.edu/~tom/Games/chomp.html.
If your system support Java, you might try
https://web.archive.org/web/20050208033636/http://scs.ryerson.ca:80/~ikokkari/Chomp/Chomp.html
Chapter 1 - Section 8
page 102: Godfrey Harold Hardy
A biography and a photograph of G.H. Hardy can be found at the MacTutor History of Mathematics Archive at the University of St. Andrews, Scotland, at
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Hardy.html
Chapter 1 – Section 8
page 104: Srinivasa Aiyangar Ramanujan
Srinivasa Aiyangar Ramanujan -- A biography and a photograph of Srinivasa Ramanujan can be found at the MacTutor History of Mathematics Archive at the University of St. Andrews, Scotland, at
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Ramanujan.html
Chapter 1 - Section 8 page 108: Pentominoes
You can learn more about tiling checkerboards using pentominoes at
https://www.universalclass.com/articles/math/geometry/what-are-pentominoes.htm
and at
https://web.archive.org/web/20010222022924/http://www.ma.utexas.edu/users/smmg/radin.html
Chapter 1 - Section 8
page 108: The Art of Tiling with Rectangles
A variety of interesting results about tiling checkerboards with dominoes and other rectangular tiles are presented by Norman Do in an interesting article at
http://www.austms.org.au/Publ/Gazette/2005/Nov05/mathellaneous.pdf
and at
http://users.monash.edu/~normd/documents/Mathellaneous-07.pdf
Chapter 1 - Section 8 page 111: Power Page
Some interesting information about conjectures and theorems
about sums of powers of integers can be found at the Power Page at
https://web.archive.org/web/20050426065456/http://www.uwgb.edu:80/dutchs/RECMATH/rmpowers.htm/
Chapter 1 - Section 8
page 111: Fermat's Last Theorem
You can learn about the history of Fermat's last theorem at
http://mathworld.wolfram.com/FermatsLastTheorem.html and at
Chapter 1 - Section 8 page 111: 11D41 Higher degree
equations; Fermat's equation
You can obtain information about Fermat's last theorem at
http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Fermat's_last_theorem.html
and at
Chapter 1 - Section Section 8 page 111: Mathematical Problems - Problem Solving
Links to a large number of sites where you can find information about mathematical problems, including famous open problems and questions from mathematical competitions, have been collected by Bruno Kevius, and are available at
http://mathres.kevius.com/problem.html and at
https://web.archive.org/web/20010803170004/https://www.abc.se/~m9847/matre/problem.html/
Chapter 1 - Section 8 page 111: Unsolved Problems
To learn more about unsolved problems, begin with this collection of links from Wolfram’s MathWorld at
http://mathworld.wolfram.com/UnsolvedProblems.html
Chapter 1 - Section 8
page 112: Introduction
More information about the 3x+1 problem can be found in this expository article by Jeff Lagarias.
http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/node1.html#SECTION00010000000000000000