Exploring Mathematics

Allen Klinger, © 12/17/2004

This enables accessing material relating to two things: school mathematics and items that can help sustain or initiate interest in the many things that build ability in reasoning about quantity and shape. The items vary in level, but at least the beginning of each should be easy to understand. (Italic links signify expository items I've written.)

Starting

Read

Night Sky

Words

Sizes

Questions

Culture

Associate

Ten

Puzzling

Sounds*

Listen

Probability

Multiply

Numerals

Sequences [8]

Numbers

Recent

Math Sources

Algorithms [3]

World [2]

Curves [6]

Solid & Knotted [11]

Sphere's Insides

Computer Sources

GAP [6]

Binary+

Area^ [4]

Games

Seeds

Mancala

Laskers

Cards

People/Problems

Sonia

Easy?

C [2]

L [5]

Math Reference

Sum Integers' Powers [7]

Counting

 sticksTally

China's

References

[1] Devlin, Keith, The Millennium Problems, NY: Basic Books, 2002, p. ix.

[2] Weisstein, Eric W., World of Mathematics http://mathworld.wolfram.com/, published as CRC Concise Encyclopedia of Mathematics, Second Edition; also see Previato, Emma (Editor), Weisstein, Eric W., Dictionary of Applied Math for Engineers and Scientists (Comprehensive Dictionary of Mathematics); http://mathworld.wolfram.com/CollatzProblem.html

[3] Black, Paul E., Dictionary of Algorithms and Data Structures, http://www.nist.gov/dads/ .

[4] Joyce, David E., (Dept. of Mathematics and Computer Science , Clark University, Worcester, MA), Euclid's Books, Guide, http://aleph0.clarku.edu/~djoyce/java/elements, e.g., http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI47.html

[5] Lagarias, Jeff, "The 3x+1 problem and its generalizations," American Mathematical Monthly, 92, 3-23, 1985.

[6] http://www.gap-system.org/~gap/ and http://www-gap.dcs.st-and.ac.uk/~history/Curves/Curves.html, University of St. Andrews, Scotland.

[7] Weisstein, Eric W., "Faulhaber's Formula," MathWorld--A Wolfram Web Resource, http://mathworld.wolfram.com/FaulhabersFormula.html.

[8] "The On-Line Encyclopedia of Integer Sequences," maintained by N. J. A. Sloane njas@research.att.com, AT&T Research.

[9] Nelsen, Roger B., Proofs Without Words, The Mathematical Association of America, 1993.

[10] Conway, John H. and Guy, Richard K., The Book of Numbers , Springer-Verlag, 1996.

[11] http://www.scientek.com/macsyma/plotsurf.htm, Macsyma (2.4) notebook illustrating Three Dimensional Surfaces.

Acknowledgement

*The voice in the following three files and some successor links is Jennifer (Jen, Hsu-hua) Chen; the animations were by Yu-Chian Tseng. + and ^ include work by Navid Aghdaie and Dorene Lau whose projects are Binary and Women In Math Careers, the latter consisting of these four parts:
Right Triangle Triangles in Space Round - Ellipse Repeat - Recursion
A visual excerpt from Right Triangles motivates the Pythagorean theorem (for the same material translated into Spanish see Pita'goras).
Nelsen [9] has collected proofs (not motivations, but rigorous demonstrations) of facts. Two different ways to see equation (3) of [7] follow. Many people know that result as the product of n, (n + 1), and (2n + 1) divided by 6.

Visually

Sum Squares

Sum Squares By Three
The recent book [10] shows this and many more interesting items by an exposition both mathematical in style, and through visual means.
Mathematics evolved from dealing with practical problems. It is the basic knowledge that is essential to working with technology. Periodicals' articles about modern technical issues and achievements, can start one in grasping the wonders of both. Some recognized sources are found from links at News.
12/17/2004 Version http://www.cs.ucla.edu/~klinger/newmath/index2.html
©2004 Allen Klinger