- Proof That Girls Are Absolute Evil
Mathematical Proof That Girls Are Evil.
in Educational > Mathematics - Elementary Topology: Second Edition by Michael C. Gemignani
Superb introduction to rapidly expanding area of mathematical thought. Fundamentals of metric spaces, topologies, convergence, compactness, connectedness, homotopy theory and other essentials. Numerous exercises, plus section on paracompactness and complete regularity. References throughout. Includes 107 illustrations.
Amazon.com: Elementary Topology: Second Edition (Dover Books on Mathematics) (9780486665221): Michael C. Gemignani: Books
0486665224 20724441 books dover edition elementary gemignani geometry mathematics michael publications science second topology
in Educational > Mathematics > Topology Books
Note: Recommended by John Banks. - Euler Played Sudoku Too! - Dr Ian Wanless
Maths lecture I went to on Sudoku. Eighteenth century Swiss mathematician Leonard Euler was prolific in every sense. He fathered 13 children and probably just as many branches of mathematics. One of his many legacies is the name "Latin square" to describe a matrix in which each row and column forms a permutation of the numbers 1,2,3,...,n. He was the original Sudoku addict! Like Euler, Ian Wanless discovered that playing with Latin squares is fun a long time before it became fashionable. In this colloquium he will explain some of his recent extensions of Euler's fundamental discoveries.
in Educational > Mathematics - Introduction to General Topology by Joshi - amazon.com
K. D. Joshi, Introduction to General Topology. A Halsted Press Book. John Wiley & Sons, Inc., New York, 1983. xii+412 pp. ISBN: 0-470-27556-1. K D Joshi obtained his Ph D in Mathematics from Indiana University,USA in 1972 and has been teaching mathematics at IIT Bombay since 1975. He has been involved with the conduct of the Joint Entrance Examination (JEE) in various capacities for over two decades. He has many books to his credit one of which is Calculus for Scientists and Engineers published by Narosa Publishing House in 2002.
Amazon.com: Introduction to General Topology (9780852264447): K.D. Joshi: Books
0852264445 2853116 and general introduction john joshi k.d ltd sons topology wiley
in Educational > Mathematics > Topology Books
Note: Really good book. Lots of explaining of motivation, wordy in a good way. His personal homepage is found here: http://www.math.iitb.ac.in/~kdjoshi/ Melbourne Uni Maths library has a copy. - Topology (2nd Edition) - by James Munkres - amazon.com
This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.
in Educational > Mathematics > Topology Books
Note: John Banks recommended it. More formal than gemignani's 'elementary topology'. - Proof: "any topological space with the fixed point property is connected" - PlanetMath
Theorem Any topological space with the fixed-point property is connected. Proof. We will prove the contrapositive. ....
in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups
Note: A decent explanation of the fixed point property: http://planetmath.org/encyclopedia/FixedPointProperty.html - Fixed Point Theorem Finite-Closed - Topology Q+A Board
Does a space which has the finite closed topology have the fixed-point property? I really don't know how to go about this, but my initial thoughts are: - This should be related to continuous functions and connectedness.
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 - 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 - Musings of the Masters: An Anthology of Miscellaneous Reflections by Raymond Ayoub
The anthology is a collection of articles contiguous to the humanities written by renowned mathematicians of the twentieth century. The articles cover a variety of topics that, for want of a better name, shall be referred to as humanistic. An important criterion, thereby limiting the choice, is that the articles should be accessible to the literate reader who may or may not have technical knowledge of mathematics. The articles span roughly a century in time and a wide range in subject. They are by mathematicians acknowledged by their peers as outstanding creators whose work has added richly to the discipline. Each article is preceded by a brief biographical sketch of the author and a brief indication of the content.
Amazon.com: Musings of the Masters: An Anthology of Mathematical Reflections (Spectrum) (9780883855492): Raymond Ayoub: Books
0883855496 amer anthology assn ayoub bkk-04214825-m masters mathematical musings raymond reflections so sociology spectrum the
in Educational > Mathematics > Textbooks/Books
Note: Melbourne maths library got it (of course!): http://cat.lib.unimelb.edu.au/search/XMusings+of+the+Masters+An+Anthology+of+Miscellaneous+Reflection&f=&searchscope=30&m=&l=&Da=&Db=&p=&SORT=D/XMusings+of+the+Masters+An+Anthology+of+Miscellaneous+Reflection&f=&searchscope=30&m=&l=&Da=&Db=&p=&SORT=D&SUBK ...moreEY=Musings%20of%20the%20Masters%20An%20Anthology%20of%20Miscellaneous%20Reflection/1%2C32000%2C32000%2CB/frameset&FF=XMusings+of+the+Masters+An+Anthology+of+Miscellaneous+Reflection&SORT=D&1%2C1%2C - 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. - 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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