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Web Links
- Math Thinking in the Real World - overviews
- "Heart of Mathematics" applets
- Describing Nature With Math - a "Nova beta" article describing how scientists use mathematics to define reality.
- 10 Coolest Mathematics Results - one list-maker's thoughts. Several of these are discussed in Math 1250!
- Just for fun: How Eratosthenes estimated the circumference of the earth in 240 B.C.E.
- Math does not have to be complex - a "Scientific American" blog post about the nature of mathematics contrasted with its public perception as defined in the mass media.
- The Singular Mind of Terry Tao - a "New York Times Magazine" article about one of the world's most accomplished mathematicians that also explores what it means to do mathematics at the research level.
- To Live Your Best Life, Do Mathematics - an interview in "Quanta" with Francis Su, past president of the Mathematical Association of America.
- Chapter 1
- Click and Clack posed a "two glasses of water" puzzle; more puzzles from "Car Talk" in their archive.
- Scene from "Die Hard III" in which 4 gallons of water are required using a 3 gallon and a 5 gallon container.
- Scroll down to find an online Flash game for the prisoners and wardens puzzle (look for the "cannibals and missionaries" puzzle). (That page has other similar puzzles, so try them, too!)
- Chapter 2
- A series of 15 minute segments on mathematics from BBC 4 radio, narrated by Simon Singh:
- Five Numbers (zero, pi, golden ratio, imaginary numbers, infinity), first aired Tuesdays at 9.30am from September 25 to October 23, 2001
- Another Five Numbers (four, seven, the largest prime, Kepler's conjecture, game theory), first aired Tuesday at 9.30am, from April 22, 2003 to May 20, 2003
- A Further Five Numbers (one, two, six, 6.67 x 10-11, 1729), first aired Tuesdays at 9:30 am, from August 23 to September 20, 2005
- The on-line encyclopedia of integer sequences - useful for identifying sequences of numbers (for example, the sequence that starts 3, 0, 2, 3, 2, 5 that appeared in the October 11, 2005 comic strip "Fox Trot"; by Bill Amend)
- For Section 2.1: Examples applying the pigeon-hole principle (some are to deeper mathematics); an in-depth posting about the ""Say the sequence"" Mindscape (Number 21)
- For Section 2.2: A wealth of information and activities about Fibonacci Numbers and the Golden Ratio, another based on relationship of the Fibonacci numbers to music - thanks, Jake), a Wikipedia article about a song that uses the Fibonacci sequence as a basis for the number of syllables in the lyrics
- For Section 2.3: A prime site for prime numbers; a selection of sites about Fermat's Last Theorem as indexed at Yahoo; information about unsolved prime problems; A news release about the ABC conjecture; The Twin Prime hero - a piece about Yitang "Tom" Zhang, who proved an important result about the twin prime conjecture in 2013; an article about recent progress on prime gaps; made in Missouri - the largest known prime number
- For Section 2.4: More about UPC codes (with a link for ISBN codes); download a small book that will tell you everything you could ever want to know about UPC codes
- For Section 2.5: You, too, can use full-strength public key codes
- For Section 2.6: Wikipedia article on irrational numbers
- A series of 15 minute segments on mathematics from BBC 4 radio, narrated by Simon Singh:
- Chapter 3
- Alas, only a finite number of sites about infinity: FAQ on large numbers (at the Math Forum); a version of the Hilbert (or Cardinality) Hotel story (a page from the MegaMath project at the Los Alamos National Laboratory)
- Chapter 4
- Section 4.1: A page on the Theorem of Pythagoras that includes several more geometric proofs; another collection of proofs that includes several quotes on the theorem
- Section 4.2: An activity on the Art Gallery Theorem (a pdf document) based on its mention in the TV show NUMB3RS on the episode aired first on October 7, 2005 (episode 204, "Obsession"), the very same day we discussed this topic in class that semester! See Dr. Andrew Nestler's Analysis of NUMB3RS for more information about the appearance of the Art Gallery Theorem in the episode.
- Section 4.3: A page on the golden section in art and building; an article that appeared in Nautilus about the golden ratio
- Section 4.4: A page at the Geometry Junkyard about tiling - look at the picture at the bottom of the page!; a newly discovered tiling of the plane using pentagons; an article about recent work on the number of distinct tilings of the plane
- Section 4.5: A playground icosahedron in Scorching Bay, Wellington, New Zealand. The ""Big Bang Theory"" vanity card for the September 22, 2014 episode features a Rhombicosidodecahedron
- Section 4.7: Stretch out into the twilight zone with these sites on the fourth dimension: Links to various fourth dimension resources; the reading on Flatland, "Flatland: A Romance of Many Dimensions" by Edwin A. Abbott; the reading on a four-dimensional house "... And He Built a Crooked House --" by Robert A. Heinlein; short movies illustrating fourth dimension principles, used in a math course at Union College; short movies illustrating hyperspace structures, at Loughborough University in the U.K.; a story and movie about a video game (called "Miegakure" - under development) that is played in four dimensions; a Second-Lifer has built a hypercube house based on Heinlein's story - read about it in this blog entry, or (for those who have an account in Second Life) go visit the house; a movie about the first ten dimensions and their relationship to the universe.
- Chapter 5
- Section 5.2: Wind and Mr. Ug, a video story on a Möbius band; more twists on Möbius bands and Klein bottles: Math That Makes You Go Wow (student work for a multi-disciplinary course at Yale); an animated crab swims in the surface of a Klein bottle (see also the game site below); games played on the surface of a torus or a Klein bottle; buy a Klein bottle (or not?)
- Section 5.3: To be or knot to be - a gallery of knots; a familiar knot from a class activity, part of a display of nautical knots in Holland (photo credit: Dr. Anneke Bart).
- Section 5.4: Mudd Math Facts on the Brouwer Fixed Point Theorem
- Chapter 6
- Section 6.1: An article on Wired.com referencing the Königsberg bridge problem "Google's New Vacation App was 280 Years in the Making"
- Section 6.2: A blog article "Platonic Solids in Nature"; a page on the 3 Utilities puzzle
- Section 6.3: A brief page on the University of Illinois four colors suffice postmark (and another mathematical postmark)
- Chapter 7
- Section 7.2: Among the chaos of fractal pages, these applets by Bob Devaney (at Boston University) are gems
- Section 7.3: This page on naturally occurring fractals shows a range of excellent fractal images
- Section 7.5: Dead or alive? - sites catalogued at Yahoo for Conway's Game of Life - also for online java examples; one nice page is www.math.com's; an article published by The Guardian about John H. Conway