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Discrete Math Lecture Notes

Discrete Math Lecture Notes

Book of Proof This book is an introduction to the standard methods of proving mathematical theorems. It has been approved by the American Institute of Mathematics' Open Textbook Initiative. Also see the Mathematical Association of America Math DL review (of the 1st edition), and the Amazon reviews. The second edition is identical to the first edition, except some mistakes have been corrected, new exercises have been added, and Chapter 13 has been extended. Order a copy from Amazon or Barnes & Noble for $13.75 or download a pdf for free here. Part I: Fundamentals Part II: How to Prove Conditional Statements Part III: More on Proof Part IV: Relations, Functions and Cardinality Thanks to readers around the world who wrote to report mistakes and typos! Instructors: Click here for my page for VCU's MATH 300, a course based on this book. I will always offer the book for free on my web page, and for the lowest possible price through on-demand publishing.

11 cheap gifts guaranteed to impress science geeks Science comes up with a lot of awesome stuff, and you don't need a Ph.D, a secret lab, or government funding to get your hands on some of the coolest discoveries. We've got a list of 11 mostly affordable gifts that are guaranteed to blow your mind, whether or not you're a science geek. Click on any image to see it enlarged. 1. Aerogel Also known as frozen smoke, Aerogel is the world's lowest density solid, clocking in at 96% air. Aerogel isn't just neat, it's useful. Price: $35 2. Inside these sealed glass balls live shrimp, algae, and bacteria, all swimming around in filtered seawater. EcoSpheres came out of research looking at ways to develop self-contained ecosystems for long duration space travel. Price: $80 3. NASA has been trying to figure out how to get a sample of rock back from Mars for a while now. Every once in a while, a meteorite smashes into Mars hard enough to eject some rocks out into orbit around the sun. Price: $70+ 4. Price: $150 5. Price: $110 6. Price: $80 7. Price: $15 8.

How to Become a Pure Mathematician (or Statistician) Home - Math 106 Visualizing a function can give a mathematician enormous insight into the function's algebraic and geometrical properties. The easiest way to see what a function looks like is to use a computer as a graphing tool. At times, this technique is the most useful, but drawing the function yourself is always the best way to get a feeling for why the function looks the way it does when graphed. All of you are by now familiar with graphing one-variable functions in the plane and hopefully can easily predict the shape of any fairly simple 2D function just by analyzing its equation. This knowledge came from graphing similar functions over and over again to get a feel for their general shape and critical points.

Game Theory 101: Game Theory Made Easy Langtons Ant -- from Wolfram MathWorld - StumbleUpon A 4-state two-dimensional Turing machine invented in the 1980s. The ant starts out on a grid containing black and white cells, and then follows the following set of rules. 1. If the ant is on a black square, it turns right and moves forward one unit. 2. 3. When the ant is started on an empty grid, it eventually builds a "highway" that is a series of 104 steps that repeat indefinitely, each time displacing the ant two pixels vertically and horizontally. (right figure) steps.

- StumbleUpon Algebra is the language of modern mathematics. This course introduces students to that language through a study of groups, group actions, vector spaces, linear algebra, and the theory of fields. The lectures videos The recorded lectures are from the Harvard Faculty of Arts and Sciences course Mathematics 122, which was offered as an online course at the Extension School. The Quicktime and MP3 formats are available for download, or you can play the Flash version directly. Review of linear algebra Groups. Permutations Cosets, Z/nZ. Quotient groups, first isomorphism theorem Abstract fields, abstract vectorspaces. Abstract linear operators and how to calculate with them Properties and construction of operators. Orthogonal groups Isometrics of plane figures Cyclic and dihedral groups. Group actions Basic properties and constructions. A5 and the symmetries of an icosahedron Sylow theorems. Rings Examples of rings. Extensions of rings Quotient rings. Special lecture Euclidean domains, PIDs, UFDs Wrap-up

[ wu :: riddles(hard) ] - StumbleUpon There are three puzzlers in the puzzle forum: A Newbie, a Senior Riddler, and an Uberpuzzler. All three are honest, but can only give answers to the best of their knowledge. Newbies are confused creatures. Senior Riddlers have great powers of perception, but are not yet infallible. Uberpuzzlers are omniscient beings who are your greatest allies in the Puzzle Forum!!! The Uberpuzzler can exert Influence arbitrarily often. Furthermore, an Uberpuzzler only uses his power of Influence in a very specific way. (Thus, he employs a strategy defined as a mapping f : S3 x {(T|F)*} -> {0,1}, which can be interpreted as follows: for each ordering of the puzzlers "sigma" (a permutation in S3, e.g. Note that this is different from saying that the puzzler chooses when the Uberpuzzler applies Influence! Determine with proof the minimum number of questions which will allow you to identify which puzzler is which. [* The Newbie does not make any new posts during questioning. ;) ]