MATHEMATICAL RESOURCES - The Handy Math Answer Book

The Handy Math Answer Book, Second Edition (2012)

MATHEMATICAL RESOURCES

(Note: The authors have diligently sought and researched the following website addresses, mailing addresses, and phone numbers in order to present this mathematically oriented information. Please realize that some of these sites, addresses, and numbers are eliminated and/or changed over time. We apologize for any closed or modified website listings, mailing addresses, or phone numbers.)

EDUCATIONAL RESOURCES

What types of careers are available to mathematicians?

The number of careers available to mathematicians is much too long to list in this text. Some of the classic jobs include architect, statistician, bookkeeper, systems engineer, research scientist (in many fields, such as geology, physics, astronomy, chemistry, and biology), engineering, and even rocket science; some of the more modern applications include mathematics in materials science, computer animation, neuroscience (in a subfield called biomedical mathematics), and nanotechnology.

To find out more about mathematical careers, check out the following websites:

American Mathematical Society (http://www.ams.org/careers/)—On this site just link to the “archives” to read about mathematicians in various careers.

Society for Industrial and Applied Mathematics (http://www.siam.org/careers/) —This site lists not only careers but also interviews many mathematicians about their work. It also has a list of questions to consider if you are thinking about a career in mathematics.

Mathematical Association of America (http://www.maa.org/students/undergrad/career.html)—This site looks closely at several job specialties in mathematics, provides profiles of many working mathematicians, and lists several books about careers in mathematics.

American Institute of Mathematics (http://www.aimath.org/)—This site has a great deal of information for the mathematical student, including papers on math, careers in mathematics, and research activities.

Association for Women in Mathematics (http://sites.google.com/site/awmmath/)—The offerings at this site are mainly for women in mathematics, including student chapters, announcements for mathematical conferences and lectures, mathematical careers, and travel grants.

Where can I get an undergraduate degree in mathematics?

Finding a college or university offering an undergraduate degree in mathematics is not difficult. Almost every college in the United States offers such a degree, even at liberal-arts-oriented institutions. The major dilemma is easy to see: Which college or university does one choose to obtain a degree?

Although the choice is up to the individual, there are ways to winnow down the vast numbers of schools. One way is to study the curriculum offered by a college’s mathematics department. For example, if the student wishes to go into statistics, explore those colleges with a good reputation in statistics by looking up information about the department and by talking to other mathematicians—or even students—in the field. Several mathematical organizations also offer help with one’s undergraduate choice. For example, the American Mathematical Society offers a web page to help potential undergraduates called “Undergraduate Mathematics Majors,” found at http://www.ams.org/programs/students/undergrad/undergrad. Also check out The Princeton Review, which offers a good website listing undergraduate schools that offer mathematics—and what to expect if you decide to choose a mathematical career. To find out more information, go to: http://www.princetonreview.com/Careers.aspx?cid=94

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A mathematician is just one of many possible careers involving mathematics. There are a number of resources you can explore to learn about math career options.

What are some well-known mathematical institutions around the world?

There are many mathematical institutions around the world, which are often thought of as “think tanks” for mathematics. For example, the Fields Institute for Research in Mathematical Sciences is located at the University of Waterloo in Toronto, Canada (http://www.fields.utoron-to.ca/). This is a center for mathematical research activity that offers, in their own words, “a place where mathematicians from Canada and abroad, from business, industry and financial institutions, can come together to carry out research and formulate problems of mutual interest.”

What month is thought of as “Mathematics Awareness Month”?

Mathematics Awareness Month occurs every April under the auspices of the Joint Policy Board for Mathematics (JPBM). This organization is composed of the Mathematical Association of America, the American Mathematical Society, the Society for Industrial and Applied Mathematics, and the American Statistical Association. It was proclaimed in 1986 by then-President Ronald Reagan for a week, and expanded to a full month in 1999. Originally, the week was celebrated nationally by such organizations as the Smithsonian Institution. More recently, the activities became local and regional, with emphasis on the importance, value, and even the beauty of mathematics. In addition, each year, there is a certain mathematical theme to the celebration. For example, in 2011 the theme was “Unraveling Complex Systems,” emphasizing such entities as power grids, transportation systems, and the Internet to mathematical models of environment, such as flocks of birds and schools of fish. To find the MAM’s Website, log on to http://www.mathaware.org/index.html.

Another example is the Max Planck Institute for Mathematics (MPIM at http://www.mis.mpg.de/) in Bonn, Germany, one of about 80 other research facilities that are part of the Max Planck Society (http://www.mpg.de/en), all internationally recognized for their basic research in the sciences, mathematics, and humanities. Mathematicians from all over the world visit the MPIM, which offers visitors the ability to discuss mathematical problems or exchange ideas with colleagues.

For a long list of U.S. and international mathematical institutions, see the following websites: The American Mathematical Society’s listings at http://www.ams.org/mathweb/mi-inst.html and the International Mathematical Union’s site at http:// www.mathunion.org/information/math-societies/.

What are some clubs and honorary organizations for students interested in math?

There are many student math organizations, including the following:

Mu Alpha Theta—This organization is sponsored by the MAA, the National Council of Teachers of Mathematics, and the Society for Industrial and Applied Mathematics. It is a mathematics club for high school and two-year college students who enjoy mathematical problems, articles, and puzzles. Mu Alpha Theta publishes a journal, The Mathematical Log, and holds regional and national meetings. Web address: http://www.mualphatheta.org/.

Pi Mu Epsilon—This group is an Honorary National Mathematics Society. Its purpose is the promotion of scholarly activities in mathematics among the students in academic institutions, and it has more than 300 chapters at colleges and universities throughout the United States. Web address: http:// www.pme-math.org/.

Kappa Mu Epsilon—This group is also a national mathematics honor society, but is specialized. It was founded in 1931 to promote the interest of mathematics among undergraduate students in the United States, and as of this writing has around 144 chapters and over 75,000 members. It also has an official journal called The Pentagon; the web address is http://www.kappamuepsilon.org/index.php.

Sigma Zeta—This group is a national science and mathematics honor society that encourages and fosters knowledge in the natural and computer sciences, as well as mathematics. You can view their website at http://www.sigmazeta.org/.

In addition to these national honor societies, some colleges and universities offer their own special mathematical groups. For example, the Archimedean Society at Fairleigh-Dickinson University in New Jersey offers support, events, and lectures in mathematics for students interested in the subject.

ORGANIZATIONS AND SOCIETIES

What are some mathematics societies and organizations in the United States?

The following lists some of these groups, along with contact information:

American Institute of Mathematics

360 Portage Ave.

Palo Alto, CA 94306-2244

Fax: 650-845-2074

Website: http://www.aimath.org/

American Mathematical Society

201 Charles St.

Providence, RI 02904-2294

Phone: 401-455-4000 worldwide; 800-321-4AMS in the United States and Canada

Fax: 401-331-3842

E-mail: ams@ams.org

Website: http://www.ams.org

American Statistical Association

732 North Washington St.

Alexandria, VA 22314-1943

Phone: 703-684-1221

Toll-free: 888-231-3473

Fax: 703-684-2037

E-mail: asainfo@amstat.org

Website: http://www.amstat.org/

Association for Symbolic Logic

Box 742, Vassar College

124 Raymond Ave.

Poughkeepsie, NY 12604

Phone: 845-437-7080

Fax: 845-437-7830

E-mail: asl@vassar.edu

Website: http://www.aslonline.org

Mathematical Association of America

1529 Eighteenth St. NW

Washington, DC 20036-1358

Phone: 202-387-5200; 1-800-741-9415

Fax: 202-265-2384

E-mail: maahq@maa.org

Website: http://www.maa.org

Society for Industrial and Applied Mathematics (SIAM)

3600 Market St., Sixth Floor

Philadelphia, PA 19104-2688

Phone: 215-382-9800; 1-800-447-SIAM (in the U.S. and Canada)

Fax: 215-386-7999

E-mail: service@siam.org

Website: http://www.siam.org/

Are there any international societies devoted to mathematics?

As befits a major branch of science, there are many international mathematical societies. A few are listed below:

Association for Automated Reasoning

Institutt for informatikk

Postboks 1080 Blindern

N-0316 Oslo

Norway

E-mail: secretary@aarinc.org

Website: http://www.aarinc.org/

Canadian Mathematical Society

577 King Edward, Suite 109

Ottawa, ON

Canada K1N 6N5

Phone: 613-562-5702

Fax: 613-565-1539

E-mail: office@cms.math.ca

Website: http://www.cms.math.ca

The European Mathematical Society (EMS)

Contact: Professor Dr. Bernd Wegner

Editor-in-Chief of Zentralblatt MATH

Zentralblatt MATH / FIZ Karlsruhe

Franklinstr. 11

D-10587 Berlin

Germany

E-mail: zblwegner@netscape.net

Website: http://www.emis.de/

London Mathematical Society

De Morgan House

57-58 Russell Square

London WC1B 4HS

England

Phone 020 7637 3686

Fax: 020 7323 3655

E-mail: lms@lms.ac.uk

Website: http://www.lms.ac.uk

The New Zealand Mathematical Society

c/o Dr. Alex James (NZMS Secretary)

Department of Mathematics and Statistics

University of Canterbury

Private Bag 4800

Christchurch 8140

New Zealand

E-mail: a.james@math.canterbury.ac.nz

Website: http://www.math.waikato.ac.nz/NZMS/NZMS.html

St. Petersburg Mathematical Society

Fontanka 27,

St. Petersburg, 191023,

Russia

Phones: 7 (812) 312 8829, 312 4058

Fax: 7 (812) 310 5377

E-mail: see website

Website: http://www.mathsoc.spb.ru/index-e.html

MUSEUMS

What museum is devoted exclusively to mathematics?

At one time, the Goudreau Museum of Mathematics in Art and Science, located in New Hyde Park, New York, was devoted exclusively to math and offered hands-on, interactive exhibits, along with workshops and programs. Mathematics teacher and engineer Bernard Goudreau founded the museum in 1980. But in 2008, the museum closed its doors to the public (although its website is old, but still working, at http://www.mathmuseum.org).

But now, to fill in the gap, is The Museum of Mathematics in New York City, first opened in 2012. It is the brainchild of Glen Whitney, president of the Math Factory (www.mathfactory.org), a group that developed the interactive, hands-on, permanent museum of mathematics. Similar to the Goudreau, and as the new museum claims, “The Museum of Mathematics strives to enhance public understanding and perception of mathematics. Its dynamic exhibits and programs will stimulate inquiry, spark curiosity, and reveal the wonders of mathematics. The museum’s activities will lead a broad and diverse audience to understand the evolving, creative, human, and aesthetic nature of mathematics.” The museum can be contacted at the following addresses:

The Museum of Mathematics

134 West 29th St., Suite 709/710

New York, NY 10001

Phone: 212-542-0566

E-mail: info@momath.org

Website: http://www.momath.org

What major museums around the world feature online exhibits dealing with math?

There are several museums around the world that offer mathematically oriented online exhibits. The following lists just a few:

Are there any traveling mathematical museums?

Yes, there is one such museum, the Museum of Mathematics’ Math Midway. It is a part of the new museum called The Museum of Mathematics in New York City (see above). Mainly for middle-school children, the Math Midway travels the country, offering mathematics through hands-on, visual experience, including a circus- and carnival-like atmosphere that uses such activities as simulated roller coasters and giant blocks—even a square-wheel tricycle—all explained through the use of mathematics. You can see more about this traveling museum at the website http://mathmidway.org/.

Museo Galileo: Istituto e Museo di Storia della Scienza (The Institute and Museum of the History of Science)—Located in Florence, Italy, this museum’s website offers an online look at the mathematics behind Galileo Galilei. For example, one part examines Galileo’s compass, which includes lessons on angles and proportions. The website is http://www.imss.fi.it/museo/index.html.

The Museum of the History of Science—Located in Oxford, England, this museum offers information about the history of mathematics and mathematical applications, including Albert Einstein’s blackboard. They also have many online exhibits, including The Measurers: A Flemish Image of Mathematics in the Sixteenth Century, Using an Astrolabe to Tell the Time, and The Geometry of War 1500-1750. The website is located at http://www.mhs.ox.ac.uk/.

Library of Congress Vatican Exhibit Mathematics Room—This website contains annotated Greek and Latin manuscripts of mathematics and astronomy; it also has special images, including (under “Greek Mathematics”) a ninth-century version of Euclid’s Elements (showing the Pythagorean theorem), and thirteenth- and fifteenth-century versions of Archimedes’s works. It is located at the web address http://sunsite.unc.edu/expo/vatican.exhibit/exhib-it/d-mathematics/Mathematics.html.

Virtual Math Museum —This site offers a look at the details of mathematics, put together by the 3DXM Consortium, an international volunteer group of mathematicians. You can reach it at website http://virtualmathmuseum.org/gallery4.html.

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The Library of Congress created the Vatican Exhibit Mathematics Room, a website that contains fascinating resources about Greek and Latin mathematics.

POPULAR RESOURCES

Are there any magazines devoted to mathematics?

The following lists a few print magazines about math:

Mathematical Gazette

The Mathematical Association

259 London Rd.

Leicester LE2 3BE

England

Phone: 0116 221 0013

Fax: 0116 212 2835

E-mail: office@m-a.org.uk

Website: http://www.m-a.org.uk

The primary focus of this gazette is teaching and learning mathematics. It is free to members of the association, and also available on a subscription basis.

Mathematics Magazine

The MAA Service Center

P.O. Box 91112

Washington, DC 20090-1112

Phone: 800-331-1622; 301-617-7800

Fax: 301-206-9789

E-mail: maaservice@maa.org

Website: http://www.maa.org/pubs/mathmag.html

Published by the Mathematical Association of America for members, it offers readable and lively expositions on a wide range of mathematical topics.

Math Horizons

Mathematical Association of America

P.O. Box 91112

Washington, DC 20090-1112

Phone: 800-331-1622; 301-617-7800

Fax: 301-206-9789

E-mail: maaservice@maa.org

Website: http://www.maa.org/Mathhorizons/

This is from the Mathematical Association of America; it is mainly intended for undergraduate students interested in mathematics.

The World of Mathematics Magazine

P.O. Box 5385

Takoma Park, MD 20913

Phone: 301-275-4771

Website: http://www.theworldofmathematics.com/home.html

This is directed towards students in the upper years of secondary school, and anyone with an interest in mathematics.

What other magazines often contain mathematical content?

There are many magazines that often contain news about math or mathematical content. The following lists just a few (notice most of these magazines are science-oriented):

Astronomy

21027 Crossroads Circle

P.O. Box 1612

Waukesha, WI 53187

Phone: 800-533-6644

Website: http://www.astronomy.com

Discover

90 Fifth Ave.

New York, NY 10011

Website: http://www.discovermagazine.com

New Scientist

Lacon House

Who is Martin Gardner?

Martin Gardner (1914–2010) was an American recreational mathematician and author. For decades, he was the “Mathematical Games” columnist for Scientific American; he was also the author of over 70 books and countless articles. Some of his titles include: My Best Mathematical and Logic Puzzles (Dover Publications, 1994); The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems (W.W. Norton & Company, 2001); Entertaining Mathematical Puzzles (Dover Publications, 1986); Mathematics, Magic and Mystery (Dover Publications,1977); and When You Were a Tadpole and I Was a Fish and Other Speculations about This and That (Hill and Wang, 2009).

84 Theobald’s Rd.

London WC1X 8NS

England

Website: http://www.newscientist.com

Popular Science

2 Park Ave., 9th Floor

New York, NY 10016

Phone: 212-779-5000

Fax: 212-779-5108

Website: http://www.popsci.com/popsci/

Science News

1719 N Street NW

Washington, DC 20036

Phone: 202-785-2255

Website: http://www.sciencenews.org

Science News For Kids

1719 N Street, N.W.

Washington, DC 20036

Phone: 202-785-2255

Website: http://www.sciencenewsforkids.org/

Scientific American

Scientific American, Inc.

415 Madison Ave.

New York, NY 10017

Phone: 212-754-0550

Website: http://www.sciam.com

What are some nonfiction books about mathematicians?

The following books are just a sampling of those available about the lives of mathematicians:

A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash by Sylvia Nasar (Simon & Schuster, 2001; ISBN: 0743224574)—The fascinating biography of John Nash, the mathematical genius who descended into schizophrenia for decades, losing his sanity, career, and wife. He ultimately recovered from this illness, and was subsequently awarded the Nobel Prize for his early work. There was also a movie adaptation of this book (see below).

The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth by Paul Hoffman (Hyperion, 1999; ISBN: 0786884061)—The story of a mathematician who had no home, no wife, and no life other than numbers. Living out of two suitcases for more than 60 years, Erdos passionately chased mathematical problems over four continents, thinking and working for 19 hours per day, while interacting with the leading scientists of his day.

Incompleteness: The Proof and Paradox of Kurt Gödel by Rebecca Goldstein (W. W. Norton & Company, 2005; ISBN: 0393051692)—This book explores the remarkable theorem of incompleteness and the eccentric genius behind its discovery, Kurt Gödel.

The Man of Numbers: Fibonacci’s Arithmetic Revolution by Keith Devlin (Walker, 2011; ISBN: 0802778127). This is the story of Fibonacci (a.k.a. Leonardo of Pisa) the 13th-century mathematician who published Liber abbaci (Book of Calculation) in 1202, which introduced the numbers 0 to 9 to Europe—the Hindu-Arabic numbering system we’re all familiar with today.

How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics by William Byers (Princeton University Press, 2010; ISBN: 9780691145990). This book by a mathematician presents readers with the human part of mathematics, including how such people think and create through their world of numbers.

Fascinating Mathematical People: Interviews and Memoirs, edited by Donald J. Albers and Gerald L. Alexanderson (Princeton, 2011; ISBN: 0691148295). This book highlights how, over time and in their own words, various major research mathematicians advanced the field of mathematics.

What are some nonfiction books about specific numbers?

Although most people wouldn’t think that a book about a number would be interesting, the following shows that’s not always true:

The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number by Mario Livio (Broadway Books, 2003; ISBN: 0767908163)—A history of the number phi (1.6180339887), also known as the golden ratio or divine proportion. There are examples from nature, as well as phi’s use in architecture and art throughout human history.

Pi: A Biography of the World’s Most Mysterious Number by Alfred S. Posamentier and Ingmar Lehmann (Prometheus Books, 2004; ISBN: 1591022002)—The story of the number pi throughout history, from the Old Testament to modern politics. An epilogue has pi expressed to 100,000 decimal places.

e: The Story of a Number by Eli Major (Princeton University Press, 2009; ISBN: 9780691141343). In this new edition of his book, Major traces “e” from the 16th century to the present, winding his story around the properties of this well-known number.

Zero: The Biography of a Dangerous Idea by Charles Seife and Matt Zimet (Penguin Books, 2000; ISBN: 0140296476)—An entertaining story about (literally) nothing. The development and use of nothing, or zero, is covered in detail from ancient times to the present.

An Imaginary Tale: The Story of [the Square Root of Minus One] by Paul Nahin (Princeton University Press, 2010; ISBN: 9780691146003). This instructive book will take the reader through not only the history of complex numbers, but why such imaginary numbers are important to mathematics.

And a book about the importance of all numbers:

Cosmic Numbers: The Numbers that Define Our Universe by James D. Stein (Basic Books, 2011; ISBN: 0465021980). This book traces the power of numbers, noting the “discovery, evolution, and interrelationship of figures that define our world.” In other words, it gives the reader a good reason why numbers are so important to everyone.

What are some nonfiction books about mathematical problems?

Tales of epic quests to solve some of the most difficult mathematical problems ever considered are served up in the following books:

Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem by Simon Singh (Anchor Books; 1998; ISBN: 0385493622). The epic quest to solve Fermat’s theorem is recounted—replete with human drama and tragedy.

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire (Plume Books; 2004; ISBN: 0452285259). Math, history, and biography are intertwined in this story of a mathematical mystery that remains unsolved today.

Four Colors Suffice: How the Map Problem Was Solved by Robin Wilson (Princeton University Press; 2004; ISBN: 0691120234). A seemingly simple problem that perplexed amateur and professional mathematicians for over one hundred years is recounted in this interesting work.

What are some other interesting nonfiction books about mathematics?

There are hundreds, if not thousands, of nonfiction books devoted to mathematics. And it’s true—math can be both fun and interesting, as the following books illustrate:

Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter (Basic Books, Inc., 1999; ISBN: 0465026567). The classic work on human creativity and thought, bringing together the mathematics of Gödel, the art of Escher, and the music of Bach.

The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse by Jennifer Ouellette (Penguin, reprinted, 2010; ISBN: 0143117378). The author helps you learn to love math by taking you through your everyday life with mathematics in mind.

The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century by David Salsburg (Henry Holt & Company, 2002; ISBN: 0805071342). As the title suggests, this is the story of how statistics changed the way science was done in the 20th century. The methods of statistics are covered in easily understood terms, and there are short biographies of the major contributors to this field.

The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math by Steven Strogatz (Princeton University Press, reprinted, 2010; ISBN: 0691150389). This book highlights 30 years of letters between a teacher and his student.

Is God a Mathematician? by Mario Livio (Simon & Schuster, 2009; ISBN: 074329405X). This book traces the evolution of mathematical reasoning from Pythagoras to the 21st century.

Mathematics in 10 Lessons: The Grand Tour by Jerry P. King (Prometheus Books, 2009; ISBN: 1591026865). This introduction to mathematics allows the reader to understand not only mathematical methods, but how to think mathematically.

Here’s Looking at Euclid: A Surprising Excursion through the Astonishing World of Math by Alex Bellos (Free Press, 2010; ISBN: 1416588256). This book takes the reader off the beaten mathematical path, using examples and amazing stories to explain mathematics.

The Mathematics of Life by Ian Stewart (Basic Books, 2011; ISBN: 0465022383). This is an overview of biology, all with an emphasis on the mathematical connections, such as life’s origins.

The Playful Brain: The Surprising Science of How Puzzles Improve Your Mind by Richard Restak and Scott Kim (Riverhead Books, 2011; ISBN: 9781594487774). This book, written by a neuroscientist, shows how working on puzzles is not only fun but can help your brain’s thinking processes.

The Math Instinct: Why You’re a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs) by Kevin Delvin (Thunder’s Mouth Press, 2005; ISBN: 0641976321). Written by National Public Radio’s “Math Guy,” this entertaining book looks at the innate mathematical abilities found in humans and other animals on the planet.

How has mathematics been used in fiction?

There are, of course, hundreds of fiction books that use mathematics as a theme, a mathematician as protagonist, or have a mathematical solution (the more recent ones seem to be mostly science fiction). There are also numerous sites on the Internet that specialize in mathematics and fiction. For example, the MathFiction site (http://kasmana.people.cofc.edu/MATHFICT/browse.php) run by Alex Kasman at the College of Charleston has an entire collection of not only books, but movies and other media featuring math in fiction. The following is merely a small taste of such titles, past and recent:

1 to 999—This book is by famous science fiction (and nonfiction) writer Isaac Asimov, who once earned a living as a chemist. In this book, cryptologists try to break a simple code, with one of the key clues being the frequency with which letters appear.

Sixty Million Trillion Combinations—Another book by Asimov, in which one of his recurring characters in his “Black Widower” mystery series, Tom Trumbull, tries to convince an eccentric mathematician that his secret password is not safe. Asimov had several more books with mathematical connections, which are a strong emphasis in many of his short story collections and over 500 published books.

Kepler: A Novel—This John Banville book gives a fictionalized, yet somewhat accurate, portrayal of the Renaissance mathematician and astronomer—from his work to determine the orbits of the planets to some more eccentric ideas, such as why there are only six planets in the solar system in terms of Platonic solids.

The Difference Engine—In this science fiction, alternate reality tale by William Gibson and Bruce Sterling, mathematicians Charles Babbage and Ada Lovelace (Byron) actually succeed in making the difference engine (for more about the difference engine, see “Math in Computing”).

The Nine Billion Names of God— Arthur C. Clarke’s classic story in which two programmers hired by a Buddhist sect seek to find all true names of God by exhausting a combinatorial library of possibilities—a story that combines mathematics, computers, and religion.

Round the Moon—Written in 1870 by Jules Verne, this classic book about space travel comes complete with two chapters—chapter 4 “A Little Algebra” and chapter 15 “Hyperbola or Parabola”—containing detailed mathematics as discussed by the space-faring crew.

Adventure of the Final Problem—And of course, one can’t forget Sir Arthur Conan Doyle’s Sherlock Holmes, his sidekick Dr. Watson, and Holmes’s major adversary, Professor Moriarty. This is the first story that mentions Moriarty, introducing him as a professor of mathematics who wins fame as a young man for his extension of the binomial theorem.

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Jules Verne wrote the classic science fiction tale Round the Moon. As well as being an entertaining space travel story, it includes mathematical discussions about algebra, parabolas, and hyperbolas.

Are there any math books aimed at children and young adults?

As with adult books, there are a plethora of math books aimed at children and young adults. The following lists only a very few that enlist stories, riddles, or other methods to explain mathematics:

A to Z of Women in Science and Math by Lisa Yount (Facts on File, 2007; ISBN 10: 9780816066957) examines 150 women who have added to our knowledge of mathematics. For ages 9 to 12.

The Adventures of Penrose the Mathematical Cat by Theoni Pappas (Wide World Publishing, 1997; ISBN: 1884550142)—This story tells of Penrose the cat as he explores and experiences a variety of mathematical concepts, including infinity, the golden rectangle, and impossible figures. For ages 9 to 12.

The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger, Rotraut Susanne Berner, and Michael Henry Heim (Metropolitan Books; Reprint edition, 2000; ISBN: 0805062998)—This great humorous book for kids is about mathematics. It begins when young Robert’s dreams take a decided turn for the weird. Instead of falling down holes and such adventures typical in many children’s dreams, in Robert’s 12 dreams, he visits a bizarre magical land of number tricks with the number devil as his host. For ages 9 to 12.

The Grapes of Math by Gregory Tang (Scholastic Press, 2001; ISBN: 043921033X)—This story offers a series of counting riddles and encourages the reader to find shortcuts to determining the mathematical answers by looking for patterns, symmetries, and familiar number combinations. For ages 9 to 12.

Mummy Math: An Adventure in Geometry by Cindy Neuschwander (Square Fish, 2009; ISBN: 0312561172)—The author takes the reader on a fictional trip through a pyramid, incorporating a bit of mathematics along the way. For ages 4 to 8.

How Big Is a Foot? by Rolf Myller (Yearling; Reissue edition, 1991; ISBN: 0440404959)—A humorous picture book that begins: “Once upon a time there lived a King and his wife, the Queen….” From there, the book explains to readers ages 4 to 8 a concept in measurement—the foot—and why it’s necessary to have measurement standards.

What television show paired mathematics with crime solving?

The television show NUMB3RS, which debuted in 2005, featured a mathematical genius named Charlie, who was recruited by his FBI agent brother to help solve a wide range of crimes in Los Angeles. Inspired by real events, this show depicted how mathematics and police work can come together to provide answers to baffling cases. The show sought the help of mathematicians, and even premiered the pilot at a mathematical conference. The show was cancelled in 2010.

What movies had mathematics as their primary focus?

There are many mathematical themes seen in television and the movies, and if you want to know more, just type in “mathematics and television” or “mathematics and movies” into a search engine on the Internet. For example, there is the Mathematics in Movies site of Oliver Knill at Harvard University’s Department of Mathematics, providing a list of movies and television shows (and some interesting comments about how mathematics are “abused”—and amusing—in many shows) and video clips of each.

Just to give a few examples, the following three movies were either about mathematicians or had a dominant mathematical theme:

What popular movies pitted dinosaurs versus a mathematician?

Both Jurassic Park (1993) and The Lost World: Jurassic Park (1997) had a mathematician as one of the main (human) protagonists. Jeff Goldblum played chaos theory mathematician Dr. Ian Malcolm, who tried to sound a warning about the inherent instability of the park’s experiment with dinosaurs. Unfortunately, no one listened to him and the dinosaurs made the best of it by taking over the island. In the second movie, Dr. Malcolm has to rescue a colleague/love interest (and his daughter) on a second island from dinosaurs, and of course, evil corporate dinosaur hunters.

A Beautiful Mind (2001)—Based on the book by Sylvia Nasar (also see above about the original book), this is Hollywood’s version of John Nash’s rise, descent into mental illness, and eventual redemption. Directed by Ron Howard, it stars Russell Crowe and Ed Harris.

Pi (1998)—This dark, low-budget, black-and-white film is about a mathematician’s obsessive search for patterns in everything, while everyone from Wall Street investors to religious fundamentalists want to find and exploit him. Directed by Darren Aronofsky, it stars Sean Gullette and Mark Margolis.

Infinity (1996)—This movie about the early life of brilliant and eccentric Nobel Prize-winning physicist Richard Feynman (1918–1988), is both a tribute to the scientist and a whimsical romance. Directed by Matthew Broderick, it stars Matthew Broderick and Patricia Arquette.

In what way did a movie use partial differential equations?

Realism in movies has grown tremendously in the past decade, mainly thanks to the work of mathematicians and computer scientists. It also helps that computers have increased in power, memory, speed, and usability. Whenever you see a certain special effect, such as an exploding spacecraft in Star Wars or a swirling maelstrom in Pirates of the Caribbean, most often those seemingly real events are generated through mathematics using special computers and computer software. In many cases the movie’s physical phenomena and interactions were developed with the use of partial differential equations.

Mathematicians develop special numerical methods and algorithms to solve complex equations, while computer scientists use that information to develop the programs to find the solutions. In the past, a movie that needed to depict a whirlpool in the ocean did so with physical props and miniaturization; with faster computers and more efficient computer structures, such as supercomputers, simulations of the whirlpool and their complex interactions are “easy” to depict. Thus, the resulting computer-generated visual effects industries are one of the most sought-after businesses in today’s action-packed movie world.

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The mathematical concept of chaos theory is explained in the movie Jurassic Park in which geneticists accidentally unleash carnivorous dinosaurs like these upon the modern world.

It’s not only the special effects in movies that have grown by leaps and bounds in the past decade. Computers have also been used to create more realistic animations— from animated characters to vast skyscrapers in an alien city. These seemingly solid, computer-generated animations are actually a mathematical representation of surfaces and volumes. This means the computer animator can add such realistic features to an animation as moving wrinkles in the skin or even the movement of strands of hair—all with the use of mathematics.

When was a computer matched against humans on a television game show?

In 2011, Ken Jennings, the contestant famous for winning 74 games in a row on the television quiz show Jeopardy! played against a computer. The IBM machine, called Watson, named after IBM’s founder, Thomas J. Watson, is actually a question answering machine. This artificial intelligence comes complete with software and technologies that allowed it to understand and answer encyclopedic questions posed in a natural language. The researchers working on Watson needed to program the machine to not only answer the question, but wager bets (in something called a “daily double”), and even make educated bets on the final round.

In the end, Watson beat not only Jennings at Jeopardy, but a third player, Brad Rutter, with the final tally at $77,147 to Watson, $24,000 to Jennings, and $21,600 to Rutter. But the researchers also admitted that the machine may have benefited from what is called the “buzzer factor”—humans anticipate the buzzer to answer a question, and if they buzz too early, they can be locked out of the ability to answer by about a quarter of a second. Watson could hit the button in as little as 10 milliseconds, a time difficult for a human to beat, and in the second round Watson beat the others to the button 24 out of 30 times.

What computer scientists have won motion picture Academy Awards?

Although it seems like a stretch—from the world of complex mathematics to the fantasy worlds of movies—there are connections between these two professional worlds. One in particular has to do with developing computer programs and software to do special effects in movies. And those computer specialists/mathematicians who work on such programs have often walked away with motion picture Academy Awards.

One of the first people to work on special effects who gained recognition was Ken Perlin, who created a random distribution function that generated lifelike textures for computer graphics. But it took more than a decade for Perlin to win an Academy Award for Technical Achievement. In 1997 he finally won the award for his work in the movie Tron. Some say it was the stodginess of many people in Hollywood—and even the movie-going public—who believed using a computer for a movie was like cheating.

There have been other winners of the award, including in 2008, when Ron Fedkiw of Stanford University in California and Nick Rasmussen and Frank Lasasso Petterson of Industrial Light and Magic (the same special effects company that was started by George Lucas of Star Wars fame) won for the computer-generated special effects programs they developed for Pirates of the Caribbean and Harry Potter and the Goblet of Fire. And in 2010, Paul Debevec of the University of California’s Computer Science Department of the Viterbi School of Engineering won for developing technologies used to create believable digital faces in major motion pictures, including Spider-Man 2 and the fantasy movie Avatar. In the latter movie, his techniques included mapping the faces of live actors and putting them onto digital puppets, making the fantasy seem very real to moviegoers.

Overall, it was a victory for the field of artificial intelligence (called “the study and design of intelligent agents”), a computer science subfield that has had its share of failures over the past decades. Watson’s calculating abilities will not go unused: The researchers at IBM are now using the machine’s skills to develop a physician’s assistant service that will allow doctors to call on a “cybernetic assistant” and will eventually add voice recognition software to the service.

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The architecture of the decision tree used by IBM’s Watson computer to reach conclusions based on inputted data.

SURFING THE INTERNET

(Note: These websites were active at the time of this writing. Because content on the Internet can change rapidly, some of these sites may no longer be functional, even though they were active at press time. We apologize for any inconvenience this may cause.)

Are there any online magazines dealing with mathematics?

The following are a few of the numerous online magazines that are devoted to mathematics:

Convergence

http://mathdl.maa.org/mathDL/46/

Sponsored by the Mathematical Association of America (MAA) in cooperation with the National Council of Teachers of Mathematics. Emphasis is on teaching mathematics using its history.

The Euler Archives

http://eulerarchive.maa.org/

A publication of the Mathematical Association of America (MAA), it is a digital library dedicated to the life and mathematical studies of Leonhard Euler.

Infinity

http://www.maths.uq.edu.au/~infinity/

Online mathematics magazine from the University of Queensland, Australia.

NRICH

http://nrich.maths.org/about

Put out by a group of qualified mathematics teachers for math students 5 to 19 years old; it is also part of the Millennium Mathematics Project in the U.K.

Pi in the Sky

http://www.pims.math.ca/pi/

A periodical designed for high school students in Canada. Published by the Pacific Institute for the Mathematical Sciences.

Plus

http://plus.maths.org/index.html

This online magazine is a part of the Millennium Mathematics Project, a United Kingdom initiative based in Cambridge. Its aim is to introduce readers to the practical applications and beauty of mathematics.

What other web-based magazines also often contain mathematical content?

As with print magazines, there are many web-based magazines that often contain mathematical news or content. The following lists just a few (notice most of these sites are science-oriented):

Discovery.com

http://www.discovery.com/

A site sponsored by television’s Discovery Channel. It often carries stories about mathematicians or applications of mathematics in science.

Eureka Alert

http://www.eurekalert.org

This website is a global news service sponsored by the American Association for the Advancement of Science (AAAS). Mathematics is included under its “News by Subject” section.

Science

http://www.sciencemag.org/

This website is sponsored by the American Association for the Advancement of Science, which focuses on science and often mathematics.

Science Daily

http://www.sciencedaily.com/

This daily science journal covers the latest in the sciences—and often mathematics. Mathematics is listed under the “Topics” section.

What are some “worthwhile-to-peruse” math websites?

The following are some math websites to bookmark because you’ll be using them again and again. These are great resources, very extensive, with clear and accurate explanations for children and adults:

Cool Math

http://www.coolmath.com/

A math site for young students interested in learning more about mathematics. It includes everyday math, lessons, a dictionary, and references.

Kids Math Games

http://www.kidsmathgamesonline.com

A math site for young students that comes complete with math games and interactive learning activities. It’s very user friendly and extensive.

Mathcats

http://www.mathcats.com

Math Cats provides playful explorations of important math concepts through games, crafts, and interactive projects; it includes a magic chalkboard and an art gallery.

The Math Forum

http://mathforum.org

This site, operating under Drexel University’s School of Education, provides mathrelated materials, resources, activities, and educational products. There is even an opportunity to have your questions personally answered by “Dr. Math®.”

MathWorld

http://mathworld.wolfram.com

An extremely comprehensive and interactive mathematics encyclopedia, developed over ten years using input from mathematicians. The site is continuously updated, so everyone from the casual student to the seasoned professional will find something of interest here.

S.O.S Mathematics

http://www.sosmath.com

A math study site containing more than 2,500 pages, ranging from algebra to differential equations. Geared towards high school and college students, but equally useful to adults.

What is a good reference website if someone is interested in engineering math?

A site called eFunda, which stands for engineering Fundamentals, is an online resource site covering all the basics of engineering mathematics. Located at http://www.efunda.com/math/math_home/math.cfm, mathematical formulas are presented, along with explanations of their usage in the proper context. It also has a comprehensive list of mathematical topics, such as special functions and mathematical models.

What is the best way to search for online math resources?

The best way to find math resources online is to use a good search engine or web directory, such as Google, Lycos, Yahoo, and so on. Be specific about the topic you’re interested in; just typing “math” into the search field will result in an astronomical number of web pages that may be of little interest.

For example, if you’re curious about the mathematics behind the construction of the pyramids, try using the key words “math Egyptian pyramids construction.” You’ll get a large number of websites, but many will still be relevant to your interest. Another strategy is to peruse the websites of college and university mathematics departments and faculty web pages. They usually contain information about faculty research areas and often provide math-related links of interest. There are also some government websites that have certain information, research, or links of mathematical interest. And finally, sometimes, too, it’s more fun to just search on a whim with only a few keywords in mind and see where it leads you.

What websites offer a way to convert units of measurement?

The conversion of units of measurement are necessary, especially between same types of units (such as feet to inches) or between Standard and metric units (such as miles to kilometers). There are numerous sites on the World Wide Web to make such conversions. In most cases, just type in the number you want converted, hit the return button, and a list of the converted numbers are displayed. Among these sites are:

· http://www.onlineconversion.com

· http://www.convert-me.com/en/

· http://www.sciencemadesimple.com/conversions.html

· http://www.convertit.com/Go/ConvertIt/

What websites offer links to the history of mathematics?

The history of mathematics is an extensive topic—too much to cover in this text. Some of the best sites to explore its history are as follows.

If you want “one stop shopping” in your search for the history of mathematics, go to this comprehensive link site presented by the British Society for the History of Mathematics (BSHM), located at http://www.dcs.warwick.ac.uk/bshm/. This organization promotes research into the history of mathematics at both professional and amateur levels, and the use of that history in education.

What site has just about everything a person needs to know about an abacus?

The award-winning “Abacus: The Art of Calculating with Beads” by Luis Fernandes offers a tutorial on using the abacus. It includes pages on the history of the abacus, how to do basic math using an abacus, an interactive tutor, articles and stories, and references and links to other sites. The website is http://www.ee.ryerson.ca/~elf/abacus/.

Of course, there are other sites that offer ideas, history, and how to use an abacus. One is put out by the National Council of Teachers of Mathematics and is called the Electronic Abacus. It (and much more mathematical information) can be found at http://illuminations.nctm.org under “activites.”

Another site for history includes the Clark University’s Department of Mathematics and Computer Science’s web page http://aleph0.clarku.edu/~djoyce/mathhist/mathhist.html. Yet another mathematical historical archive with additional mathematical topics can be found at http://archives.math.utk.edu/topics/history.html.

Even more interesting is the MacTutor History of Mathematics archive from the School of Mathematics and Statistics at the University of St. Andrews, Scotland. It is an extensive resource on the history of mathematics from ancient times to the present and can be found at the websites http://www-groups.dcs.st-and.ac.uk/~history/ and http://www-history.mcs.st-and.ac.uk/.

Where can you search for the value of pi?

Do you want to know more about pi? Your answer might be on the Internet site located at http://www.angio.net/pi/piquery.html. Here resides The Pi Searches, a site that lets you search for any string of digits—up to 120 of them—in the first 200 million numbers of pi. According to the site’s “caretaker,” Dave Anderson, “The Pi Searcher uses a combination of linear search (searching each digit one by one) for small search strings and a pre-computed index for large search strings. The result is that the Pi Searcher is extremely fast —it takes less than 1/50th of a second to handle most requests.”

Anderson even mentions such fun activities (and keeps it updated) as “The Pi Day 2011.” Yes, there is a Pi Day, a holiday commemorating the mathematical constant. It is celebrated on March 14 (or 3/14 in month/day date format), since 3, 1, and 4 are the three most significant digits of π in the decimal form. In fact, it has become so popular it is celebrated by schools that join in the festivities. In 2009, the U.S. House of Representatives supported the designation of Pi Day. Not to be outdone, there is also a Pi Approximation Day on July 22 (or 22/7 in day/month date format), since the fraction 22/7 is a common approximation of pi.

What websites contain fun (and interesting) mathematical facts and activities?

If a person is interested in fun facts about math, and doesn’t want to hunt all over the Web for them, go to Mudd Math Fun Facts, located at http://www.math.hmc.edu/funfacts/. Created by Francis Edward Su of the Harvey Mudd College Math Department as a “warm-up” activity for calculus courses, these are tidbits from all areas of math. The site is definitely fun, entertaining, and addictive. If that doesn’t satisfy your mathematical questions, try “Mathematics Lessons that Are Fun,” by Cynthia Lanius, at http://math.rice.edu/~lanius/Lessons/hosted by Rice University. Here Lanius offers some simpler renditions of how to understand mathematics—mainly for young students—such as “Visualizing an Infinite Series” and “Fractals,” with links to other helpful websites.

What are some websites devoted to solving puzzles?

There are literally hundreds, if not thousands, of recreational math websites, especially those devoted to solving easy, medium, and hard puzzles. The following is just a taste of what is out there:

BrainBashers

http://www.brainbashers.com/puzzles.asp

A great site with many listings of puzzles—for younger and older puzzle aficionados.

Easy Calculation

http://www.easycalculation.com/puzzles/easy/easy1.php

This site offers what it advertizes, including puzzles that are simple to a definite challenge for some. It also offers other information about solving mathematical calculations, including many calculators (for example, a mortgage calculator) and conversion sites.

Interactive Mathematics Miscellany and Puzzles

http://www.cut-the-knot.org/content.shtml

A little bit of everything, from games and puzzles, to fallacies and visual illusions.

Mathpuzzle.com

http://www.mathpuzzle.com

Another great site for recreational math and puzzles.

Puzzles.com

http://www.puzzles.com

Illusions, puzzles, tricks, and toys can be found here. There is also a gift shop, puzzle links, and help.

Appendix 1:

Measurement Systems and Conversion Factors

The following abbreviations are used for these conversion tables: atm = atmosphere; BtuIT = British Thermal Unit (international table); cal = calorie; calIT = calorie (international table); cm = centimeter; cu ft = cubic feet; ft = feet; ft-lbf = footpound force; g = gram; gal = gallon; hp hr = horsepower-hour; in = inch; int J = international Joules; J = Joule; kg = kilogram; kgf = kilogram-force; kWh = kilowatt-hour; L = liter; lb = pound; lbf = pound-force; m = meter; mmHG = millimeters of mercury (also Torr); m ton = metric ton; N = Newton; oz = ounce; Pa = Pascal; qt = quart; yd = yard.

Units of Length

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Units of Area

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Units of Volume

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Units of Mass

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Units of Density

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Units of Energy

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Units of Pressure

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Appendix 2:

Common Formulas for Calculating Areas and Volumes of Shapes

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