Annotated Web Links

CHAPTER 1 –  The Integers

Return to Annotated Web Links Home

 

 

1.1  Numbers and Sequences

 

Page 8

 

You can find an excellent discussion of diophantine approximation by Jörn Steuding in his course notes on diophantine analysis at http://www.math.uni-frankfurt.de/~steuding/steuding/dioph.pdf

 

Page 11

You can use Neil Sloane's On-Line Encyclopedia of Integer Sequences Web site to determine the possible identity of an integer sequence from its first few terms. You can also check out some "hot sequences" and puzzle sequences that are quite challenging.
http://www.research.att.com/~njas/sequences/index.html (Sloane's On-Line Encyclopedia of Integer Sequences)

 

 

Page 15

 

 

You can find more about the Ulam numbers at http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=002858

Biographical information about Stanislaw Ulam can be found at the MacTutor History of Mathematics Archive at
http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Ulam.html (Ulam)

 

 

1.2   Sums and Products

Page 19

To learn more about figurate number consult
http://mathworld.wolfram.com/FigurateNumber.html (Figurate Number)

 

To find out more about triangular numbers and their properties, go to http://www.shyamsundergupta.com/triangle.htm (Fascinating Triangular Numbers)

 

 

 

1.3  Mathematical Induction

 

 

Page 23

 

There are a lot of websites about mathematical induction.   For a list see http://www.eduseek.com/static/navigate8166.html

 

 

Page 24

A brief biography of Francesco Maurolico, the first person to have published a proof using mathematical induction, can be found at the MacTutor History of Mathematics archive at
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Maurolico.html (Maurolico)

 

Page 28

A picture of the 19th century original box cover for the Tower of Hanoi puzzle and the text of the original instructions in French, and translated into English, can be seen at the site of Paul K. Stockmeyer, a computer science professor at William and Mary College at http://www.cs.wm.edu/~pkstoc/toh.html (Tower of Hanoi)

Several interesting papers about the Tower of Hanoi problem and its generalizations written by Paul K. Stockmeyer can be downloaded from
http://www.cs.wm.edu/~pkstoc/h_papers.html (Tower of Hanoi Papers)

 

An overview of web resources on the Tower of Hanoi can be found at http://hanoitower.mkolar.org/HTonWebE.html (Tower of Hanoi (TH) on the Web)

 

Page 29

 

An excellent site for exploring Egyptian fractions can be found at http://www.ics.uci.edu/~eppstein/numth/egypt/  (Egyptian fractions)

 

 

 

 

 

1.3  The Fibonacci Numbers

Page 30

Biographical information about Fibonacci can be found at the MacTutor History of Mathematics Archive at
http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Fibonacci.html (Fibonacci)

 

 

A compendium of information about the Fibonacci numbers can be found at http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/

 

 

Page 31

A variety of ways that Fibonacci number 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 (The Fibonacci Numbers and Golden Section in Nature).

 

Information about applications of Fibonacci numbers to art, architecture, and music can be found at http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html (Fibonacci Numbers and The Golden Section in Art, Architecture and Music)

 

 

Page 33

 

The website for the Fibonacci Quaterly can be found at http://www.engineering.sdstate.edu/~fib/  (Fibonacci Quarterly Home Page)

 

 

Page 34

 

You can find more information about the Lucas numbers at http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/lucasNbs.html

 

 

1.5   Divisibility

Page 41

You can find the excellent expository article by Jeff Lagarias on the Collatz conjecture, which goes by many different names, including the "3x+1 problem" at
http://www.cecm.sfu.ca/organics/papers/lagarias/index.html (The 3x+1 problem and its generalizations)

 

An extensive exploration of the 3x+1 problem and numerical results can be found at http://personal.computrain.nl/eric/wondrous/index.html (On the 3x+1 problem).   You can join the search for new records relating to this problem at this site.