Web Links for Chapter 3
Section 3.1. Methods of Proof
Page 168
A discussion of proof methods can be found at the site of the Mathematics Department of the University of California at San Bernardino.
An interesting variety of proofs in mathematics can be found at the Cut-the-Knot site (select item 17 on the list)
Common fallacies to avoid in arguments can be found at
Several different types of fallacies that arise in incorrect proofs can be found at the University of Toronto Mathematics Network Site
Page 181
An interesting discussion of the halting problem by Martin Cohn and Harry Mairson of the Computer Science Department at Brandeis University can be found at
Page 182
The latest information about Goldbach’s conjecture and related conjectures can be found at
http://www.utm.edu/research/primes/notes/conjectures/ (Conjectures and Open Questions)
A biography of Christian Goldbach is available from the MacTutor History of Mathematics archive.
Section 3.2. Mathematical Induction
Page 188
A brief biography of Francesco Maurolico is available from the MacTutor History of Mathematics archive.
Page 189
Some examples of proofs using mathematical induction similar to those in the text, with hints provided along the way, can be found at
Page 196
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.
Section 3.3. Recursive Definitions
Page 205
A wealth of information about the Fibonacci numbers and the golden mean can be found at the Department of Computing, University of Surrey, site:
An biography of Fibonacci and a description of his mathematical work can be found at
A biography and portrait of Fibonacci can be found at
Another brief biography and an excellent photograph of a statue of Fibonacci in Pisa can be found at
Page 207
A brief biography and a photograph of Gabriel Lamé can be found at the MacTutor History of Mathematics Archive, University of St Andrews, Scotland.
An article written by Erric Gosset describing Sierpinski curves, a family of curves defined recursively, can be found at
Page 211
A biography of Wilhelm Ackermann can be found at
Page 212
A biography and a photograph of G.H. Hardy can be found at
Section 3.4. Recursive Algorithms
Page 214
A brief introduction to recursive procedures can be found at
http://unics.rrzn.uni-hannover.de/zzzzwg1/HPF-Kurs/HTMLHPFCourseNotesnode131.html
Section 3.5. Program Correctness
Page 220
You can find the home page of C.A.R.(Tony) Hoare, including a brief biography and information about his work and research interests at
Page 223
You can see a proof of correctness involving loop invariants at
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