- Bijection, injection and surjection - Wikipedia
In mathematics, injections, surjections and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other.
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in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups
Note: Need to learn this. - Burkard Polster
Department of Mathematics and Statistics, Monash University. Areas of interest: -finite and topological geometry -combinatorial designs -group theory -history of mathematics -classical interpolation theory -computer visualisation -mathematics education and outreach -any kind of fun mathematics
personal homepage
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in Educational > Mathematics > People
Note: His homepage at Monash is: http://www.maths.monash.edu.au/staff/bpolster.html - Converting TeX to Microsoft Word? | Slashdot |
"For many years I've done almost all of my writing in TeX. This has increasingly caused problems with publishing in journals. For a long time, many journals reset what you sent them, so they didn't care what program you used. More and more, I find, they do, and in most cases, what they want is MS Word. Is there any good way to convert TeX to Word?"
belmolis asks: "For many years I've done almost all of my writing in TeX. This has increasingly caused problems with publishing in journals. For a long time, many journals reset what you sent them, so they didn't care what program you used. More and more, I find, they do, and in most cases, what th...
in Computing > Software > Office Applications - Fixed point property - Wikipedia
In mathematics, a topological space X has the fixed point property if all continuous mappings from X to X have a fixed point.
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in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups
Note: In mathematics, a fixed point (sometimes shortened to fixpoint) of a function is a point that is mapped to itself by the function... http://en.wikipedia.org/wiki/Fixed_point_%28mathematics%29 - Fixed-point theorem - Wikipedia
In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. Results of this kind are amongst the most generally useful in mathematics. The Banach fixed point theorem gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point. By contrast, the Brouwer fixed point theorem is a non-constructive result: it says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point, but it doesn't describe how to find the fixed point (See also Sperner's lemma).
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in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups - GraphFunc Online
A handy online java tool for drawing single variable graphs, you can chuck 'em on top of each other too!
in Educational > Mathematics > Software - Implicit function theorem
In multivariable calculus of mathematics the implicit function theorem says that for a suitable set of equations, some of the variables are defined as functions of the others.
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in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups - Introduction to Mathematical Logic by Elliott Mendelson
I was sufficiently fortunate to have taken Professor Emeritus Mendelson's famous logic course at Queens College, the City University of New York, just two semesters before his retirement. I was, and continue to be, astonished by Dr. Mendelson's precise yet easy style, and the beautifully efficient organization of the subjects. Everything from the expository prose to the system of notational conventions has been carefully thought through so as to make the book both very substantive and very readable. In my opinion, it's the best introduction to serious mathematical logic currently on the market, and thanks to the genius of its author, it is likely to remain so for a long time. The buyer will not be disappointed.
Amazon.com: Introduction to Mathematical Logic, Fourth Edition (9780412808302): E. Mendelson: Books
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in Educational > Mathematics > Textbooks/Books
Note: LTU lib has it (2nd edition): http://library.latrobe.edu.au/search/XIntroduction+to+Mathematical+Logic+Elliott+Mendelson&searchscope=1&SORT=A/XIntroduction+to+Mathematical+Logic+Elliott+Mendelson&searchscope=1&SORT=A&extended=0&SUBKEY=Introduction%20to%20Mathematical%20Logic%20Elliott%20Mendelson/1% ...more2C3%2C3%2CB/frameset&FF=XIntroduction+to+Mathematical+Logic+Elliott+Mendelson&SORT=A&1%2C1%2C - LaTeX
LATEX, written as LaTeX in plain text, is a document preparation system for the TeX typesetting program. It offers programmable desktop publishing features and extensive facilities for automating most aspects of typesetting and desktop publishing, including numbering and cross-referencing, tables and figures, page layout, bibliographies, and much more.
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in Computing > Software > Office Applications by 2 users - Littlewood's Miscellany: Books: Béla Bollobás (editor) - Amazon.com
Academic life in Cambridge especially in Trinity College is viewed through the eyes of one of its greatest figures. Most of Professor Littlewood's earlier work is presented along with a wealth of new material.
Amazon.com: Littlewood's Miscellany (9780521337021): John E. Littlewood, Béla Bollobás: Books
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in Educational > Mathematics > Textbooks/Books - Living Reviews
'Living Reviews' is a unique editorial concept for the publication of high-quality scientific content. 'Living' review articles are 1. as the name suggests, review articles, providing insightful surveys on research progress in the fields they cover and guiding readers to the most important literature in the field, 2. solicited from experts in the field by an international Editorial Board, 3. subject to peer-review, 4. open access publications 5. and, most important, 'living' which means that the articles are regularly being updated by their authors to incorporate the latest developments in the field.
Journal portal for peer-refereed, solely online scientific journals publishing invited review articles. Reviews are kept up to date by their authors. All reference information is collected into searchable databases. http://www.livingreviews.org/ is a free resource to the scientific community. Living Reviews in Relativity is published by the Max Planck Institute for Gravitational
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in Educational > Cosmology by 2 users - MacTutor History of Mathematics
"History of Mathematics website Most of the information for the mini history lectures given by Katherine Seaton (Brian Davey) come from the following website."
Biographies of mathematicians
in Educational > Mathematics - Mathemagics--the art of mental calculation
Dr. Arthur Benjamin is both a professor of mathematics and a magician. He has combined his two loves to create a dynamic presentation called "Mathemagics," suitable for all audiences, where he demonstrates and explains his secrets for performing rapid mental calculations faster than a calculator. Reader's Digest calls him "America's Best Math Whiz". He has presented his high energy talk on over a thousand occasions to audiences throughout the world. Dr. Benjamin has appeared on many television and radio programs, including: The Today Show, CNN, Amazing Discoveries! and National Public Radio. He has been profiled in The New York Times, Los Angeles Times, USA Today, Scientific American, Discover Magazine, Omni Magazine, Esquire Magazine, People Magazine, and
in Educational > Mathematics > People
Note: Art Benjamin (Harvey Mudd College) Szental Lecture Theatre, La Trobe University 4:00pm June 23, 2005 http://www.latrobe.edu.au/mathstats/seminars/2005_seminars.html The lecture I went to. - MathWorld
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in Educational > Mathematics by 54 users - Ned Wright's Cosmology Tutorial
Cosmology is the study of the origin, current state, and future of our Universe. This field has been revolutionized by many discoveries made during the past century. My cosmology tutorial is an attempt to summarize these discoveries.
Cosmology tutorial: an illustrated introductory guide to cosmology
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in Educational > Cosmology - Open problems in topology edited by Jan van Mill, George M. Reed.
Title: Open problems in topology / edited by Jan van Mill, George M. Reed. Published: Amsterdam [Netherlands] ; New York : North-Holland ; New York, N.Y., U.S.A : Distributors for the U.S. and Canada, Elsevier Science Pub. Co., 1990.
in Educational > Mathematics > Topology Books
Note: Doesn't seem like they got to their third edition, despite saying it was due around 1995. Need to know a lot more topology before I can understand the problems. - Optimnem Blog
The Blog of Daniel Tammet. (wiki) Daniel Paul Tammet (born January 31, 1979) is a British autistic savant (though he has learnt how to manage social interaction) gifted with a facility for mathematics problems, sequence memory, and natural language learning. He was born with congenital childhood epilepsy. Experiencing numbers as colors or sensations is a well-documented form of synesthesia, but Tammet is unique in how specific and detailed his mental imagery of numbers is. He claims that in his mind each number, up to 10,000, has its own unique shape and feel, and he can "sense" whether a number is prime or composite and "see" results of calculations as landscapes in his mind.
in Computing > Blogs - Prisoner's Dilemma, William Poundstone - Fishpond.com.au
John von Neumann invented the digital computer, played a key role in the development of the atom bomb, constructed a branch of mathematics known as game theory, and became a defender of a movement to bomb the Russians before they could bomb us. Now comes a biography of this controversial genius and an exploration of his greatest idea--one that nearly triggered a nuclear war in 1950. Photographs.
in Educational > Mathematics > Textbooks/Books
Note: Grant recommended it; good light (populist) reading. - Range (mathematics) - Wikipedia
In mathematics, the range of a function is the set of all "output" values produced by that function. Sometimes it is called the image, or more precisely, the image of the domain of the function....The range should not be confused with the codomain B. The range is a subset of the codomain, but is not necessarily equal to the codomain, since there may be elements of the codomain which are not elements of the range. The codomain is sometimes taken to be the range, but more often is some standard set, such as the real numbers or the complex numbers, which contains the range. A function whose range equals its codomain is called onto or surjective.
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in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups - Separation axiom - Wikipedia
In topology and related fields of mathematics, there are several restrictions that one often makes on the kinds of topological spaces that one wishes to consider. Some of these restrictions are given by the separation axioms. These are sometimes called Tychonoff separation axioms, after Andrey Tychonoff. The separation axioms are axioms only in the sense that, when defining the notion of topological space, you could add these conditions as extra axioms to get a more restricted notion of what a topological space is. The modern approach is to fix once and for all the axiomatization of topological space and then speak of kinds of topological spaces.
in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups
Note: See also: The precise meanings of the terms associated with the separation axioms has varied over time, as explained in History of the separation axioms... http://en.wikipedia.org/wiki/History_of_the_separation_axioms
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