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Pages: 1 2 [>>] | - Page 265 - Section 4.1
Francisco Maurolico -- A brief biography of Francesco Maurolico is available from the MacTutor History of Mathematics archive.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Maurolico.html
(Added: Fri Jul 28 2006)
- Page 267 - Section 4.1
Lecture Notes on Algorithm Analysis and Complexity Theory -- Ian Parberry of University of North Texas provides useful useful material on many topics in discrete mathematics with these lecture notes. You will need a PDF viewer to read these notes.
http://www.eng.unt.edu/ian/books/free/lnoa.pdf
(Added: Fri Jul 28 2006)
- Page 267 - Section 4.1
Proof, Induction -- Examples of proof by mathematical induction are provided here.
http://www.maths.ox.ac.uk/current-students/undergraduates/study-guide/p2.2.10.html
(Added: Fri Jul 28 2006)
- Page 267 - Section 4.1
Muddy Children Puzzle -- Muddy Children Puzzle is an interesting mathematical problem, as described here. Try to solve the puzzle using mathematical induction.
http://sierra.nmsu.edu/morandi/CourseMaterials/MuddyChildren.html
(Added: Fri Jul 28 2006)
- Page 277 - Section 4.1
Tiling with Tronimos; An example of proof by induction -- A Java applet illustrating the tiling of square chessboards using L-shaped pieces (which are also called tronimos) can be found at Christopher P. Mawata's site at the University of Tennessee, Chattanooga.
http://www.utc.edu/~cpmawata/trominos/
(Added: Fri Jul 28 2006)
- Page 277 - Section 4.1
Tiling with Right Triominoes -- An applet at developed by Christopher Mawata that uses a recursive algorithm to tile 2n x 2n checkerboards can be found here.
http://www.utc.edu/Faculty/Christopher-Mawata/trominos/
(Added: Fri Jul 28 2006)
- Page 277 - Section 4.1
Triomino Puzzle -- You can manually tile 2n x 2n checkerboards with right triominoes using an applet on the Cut-the-Knot website here.
http://www.cut-the-knot.org/Curriculum/Games/TrominoPuzzle.shtml
(Added: Fri Jul 28 2006)
- Page 288 - Section 4.2
FIST: Fast Industrial-Strength Triangulation of Polygons -- A description of a software package developed by Martin Held for triangulating polygons and information on how to obtain it can be found here.
http://www.cosy.sbg.ac.at/~held/projects/triang/triang.html
(Added: Fri Jul 28 2006)
- Page 288 - Section 4.2
Triangle -- You can learn about and download the Triangle program, developed by Jonathan Shewchuk, at the University of California, Berkeley, for triangulating polygons, here.
http://www.cs.cmu.edu/~quake/triangle.html
(Added: Fri Jul 28 2006)
- Page 288 - Section 4.2
Triangulations -- To learn more about triangulations, check out this page offered by Peter Alfeld at the University of Utah.
http://www.math.utah.edu/~pa/MDS/triangulation.html
(Added: Fri Jul 28 2006)
- Page 288 - Section 4.2
Polygon triangulation -- To learn more about triangulations of polygons, consult the Wikipedia article here.
http://en.wikipedia.org/wiki/Polygon_triangulation
(Added: Fri Jul 28 2006)
- Page 295 - Section 4.3
Sierpinski Curves -- An article written by Erric Gosset describing Sierpinski curves, a family of curves defined recursively, can be found here.
http://www.bethel.edu/college/faculty/projects/gossett/Sierpinski/
(Added: Fri Jul 28 2006)
- Page 297 - Section 4.3
The Fibonacci Numbers and Golden section in Nature - 1 -- A variety of ways that Fibonacci numbers arise in nature, including counting rabbits, can be found on Ron Knott's page at the Department of Computing, University of Surrey site.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html
(Added: Fri Jul 28 2006)
- Page 297 - Section 4.3
The Fibonacci Numbers and the Golden Section -- A wealth of information about the Fibonacci numbers and the golden mean can be found at the Department of Computing, University of Surrey, site.
http://www.ee.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html
(Added: Fri Jul 28 2006)
- Page 298 - Section 4.3
Who was Fibonacci? -- An biography of Fibonacci and a description of his mathematical work can be found here.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibBio.html
(Added: Fri Jul 28 2006)
- Page 298 - Section 4.3
Fibonacci -- A biography and portrait of Fibonacci can be found on the MacTutor History of Mathematics Archive at the University of St. Andrews, Scotland.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Fibonacci.html
(Added: Fri Jul 28 2006)
- Page 299 - Section 4.3
Gabriel Lamé -- A brief biography and a photograph of Gabriel Lamé can be found at the MacTutor History of Mathematics Archive, University of St. Andrews, Scotland.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Lame.html
(Added: Fri Jul 28 2006)
- Page 299 - Section 4.3
Rational Database -- Consult this Wikipedia article to learn more about rational databases.
http://en.wikipedia.org/wiki/Relational_database
(Added: Fri Jul 28 2006)
- Page 304 - Section 4.3
Handout on Structural Induction -- A useful handout on structural induction can be found on the website for CS 205, Introduction to Discrete Structures 1, a course at Rutgers University.
http://www.rci.rutgers.edu/~detlef/data/CS205.Sp01/structInd.pdf
(Added: Fri Jul 28 2006)
- Page 304 - Section 4.3
Example of Structural Induction -- Proofs of three properties of binary trees using structural induction can be found here.
http://sciris.shu.edu/Resources/Cs/c2113/notes11d.htm
(Added: Fri Jul 28 2006)
- Page 304 - Section 4.3
Exercises for the Reader -- Exercises asking for proofs using structural induction concerning binary trees can be found here. Click on the Up button for a list of topics on this website.
http://www-2.cs.cmu.edu/afs/cs/academic/class/15671-f95/www/handouts/induction/node5.html#SECTION00050000000000000000
(Added: Fri Jul 28 2006)
- Page 304 - Section 4.3
Proving a Theorem by Structural Induction -- The method of proving theorem about binary trees by structural induction is illustrated here.
http://www-2.cs.cmu.edu/afs/cs/academic/class/15671-f95/www/handouts/induction/node4.html
(Added: Fri Jul 28 2006)
- Page 304 - Section 4.3
Structural Induction Example - Binary Trees -- An example of proof by structural induction of a result concerning binary trees can be found here.
http://www.cs.sfu.ca/~cameron/Teaching/384/99-3/tree-induction.html
(Added: Fri Jul 28 2006)
- Page 307 - Section 4.3
Generalized Induction -- Some useful notes on generalized induction can be found at the Discrete Mathematics II Project Site developed at North Carolina A&T State University.
http://www.dartmouth.edu/~matc/DiscreteMath/IV.7.pdf
(Added: Fri Jul 28 2006)
- Page 310 - Section 4.3 Exercises
Wilhelm Ackermann -- A biography of Wilhelm Ackermann 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/Ackermann.html
(Added: Fri Jul 28 2006)
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