 • Proof That Girls Are Absolute Evil
Mathematical Proof That Girls Are Evil.
Vector calculus (also called vector analysis) is a field of mathematics concerned with multivariate real analysis of vectors in two or more dimensions. It consists of a suite of formulas and problem solving techniques very useful for engineering and physics. Vector analysis has its origin in quaternion analysis, and was formulated by the American scientist, J. Willard Gibbs . It concerns vector fields, which associate a vector to every point in space, and scalar fields, which associate a scalar to every point in space. For example, the temperature of a swimming pool is a scalar field: to each point we associate a scalar value of temperature. The water flow in the same pool is a vector field: to each point we associate a velocity vector.
calculus chain change continuous curl derivative differential dimension function geometry mathematics rule variables vector

Note: The summary of gradient, curl and divergence is particularly good.
• College Algebra - Math 116 - Lecture Notes by James Jones
These notes were written during the Fall 1997 semester to accompany Larson's College Algebra: A Graphing Approach, 2nd edition text. We have moved on to Larson's 4th edition and some sections have changed but I have left them where they are since many people on the Internet find these useful resources. The notes were updated in the Fall 2003 semester to use Cascading Style Sheets and validate as XHTML 1.0 strict web pages. If your browser doesn't support CSS, certain pages (especially those with matrices) will not display properly.

Note: A nice book on basic algebra operations.
• Differential Equations - Wikibooks, collection of open-content textbooks
This book aims to lead the reader through the topic of differential equations, a vital area of modern mathematics and science. It is hoped that this book will provide information about the whole area of differential equations, but for the moment it will concentrate on the simpler equations.
applications bernoulli deqs differential equations exact existence first formation frobenius linear order second solution the

Note: This stuff I found to be rather good: http://en.wikibooks.org/wiki/Differential_Equations/First_Order
• 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

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.
• 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

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.
• Texas Instruments Derive™ 6 from US & CANADA
A powerful Computer Algebra System, Derive can easily solve a wide range of symbolic and numeric problems. Results can be plotted as 2-D graphs or 3-D color surfaces, enabling different approaches to problem solving.
define derive entry expression files infinite matrix plot plots productdetail surfaces toolbars unicode values worksheets
• 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.

Note: John Banks recommended it. More formal than gemignani's 'elementary topology'.
• Topology Without Tears, chapters 1-10.
"Topology Without Tears" by Sidney A. Morris. University of Ballarat, Victoria Australlia.
• Beginning Topology (Brooks/Cole Series in Advanced Mathematics) by Sue Goodman
With a nice balance of mathematical precision and accessibility, this text provides a broad introduction to the field of topology. Author Sue Goodman piques student curiosity and interest without losing necessary rigor so that they can appreciate the beauty and fun of mathematics. The text demonstrates that mathematics is an active and ever-changing field with many problems still unsolved, and students will see how the various areas of mathematics ? algebra, combinatorics, geometry, calculus, and differential equations ? interact with topology. Students learn some of the major ideas and results in the field, do explorations and fairly elementary proofs, and become aware of some recent questions.
Amazon.com: Beginning Topology (Brooks/Cole Series in Advanced Mathematics) (9780534424268): Sue Goodman: Books
0534424260 711014858-0534424260 advanced beginning brooks cole genera goodman mathematics science series sue textbooks topology

Note: A good broad introduction into some topological applications (a good 'overview' of what topology encompasses too); the four-colour problem, fixed-point theorems, fundamental theorem of algebra and knots. Glosses over point-set, seems to cover the important stuff. Her personal website can be found h ...moreere: http://www.math.unc.edu/Faculty/seg/ She recommends a history of Topology here: http://www-gap.dcs.st-and.ac.uk/~history/PrintHT/Topology_in_mathematics.html (I think Brian Davey also recommended this site)
• Elements of general topology by Donald Bushaw (2nd edition)
Author: Bushaw, Donald. Title: Elements of general topology. Published: New York : J. Wiley, .

Note: A really good, well worded account on point set topology, gives a good sketch of the motivation behind definitions. LTU Bundy's got it: https://alpha2.latrobe.edu.au/patroninfo/1119178/item&1287918
• Laws of Logarithms
Do you have trouble remembering the laws of logarithms? Do you know why you can change log(x)+log(y) to a different form, but not log(x+y)? This page helps you make sense out of the laws of logarithms.
The laws of logarithms, and how to remember them (Stan Brown)
• Maplesoft
Command the Brilliance. Makers of Maple.
Maplesoft is a world leader in mathematical and analytical software. The Maple system embodies advanced technology such as symbolic computation, infinite precision numerics, innovative Web connectivity and a powerful 4GL language for solving a wide range of mathematical problems encountered in modeling and simulation.
algebra computation computer education maple maplesoft mathematical mathematics modeling software symbolic teaching waterloo
by 2 users
• 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. ....

Note: A decent explanation of the fixed point property: http://planetmath.org/encyclopedia/FixedPointProperty.html
• A Mathematician's Apology (Canto) (Paperback) by G. H. Hardy, C. P. Snow (Foreword)
A Mathematician's Apology is a profoundly sad book, the memoir of a man who has reached the end of his ambition, who can no longer effectively practice the art that has consumed him since he was a boy. But at the same time, it is a joyful celebration of the subject--and a stern lecture to those who would sully it by dilettantism or attempts to make it merely useful. "The mathematician's patterns," G.H. Hardy declares, "like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics."
Amazon.com: A Mathematician's Apology (Canto) (9780521427067): G. H. Hardy, C. P. Snow: Books
0521427061 apology calculus cambridge canto general hardy mathematicians mathematics nw321843 press science snow university
• Andrew Wiles, Wikipedia
Sir Andrew John Wiles (born April 11, 1953) is a British-American mathematician, the Eugene Higgins Professor of Mathematics at Princeton University, Princeton mathematics department chair, and member of scientific advisory board of the Clay Mathematics Institute. One of the major highlights of his career has been an announcement of a proof of Fermat's Last Theorem in 1993 and a discovery of a beautiful method to complete that proof in 1994.
9999 adam alberto alma andrew andrey andré anne ast calderón kolmogorov mater otter riess search sofie special von weil wiles
• Australian Mathematical Sciences Institute
The Australian Mathematical Sciences Institute was established in November 2002 with initial funding of \$1M from the Victorian Government's Science, Technology and Innovation Infrastructure grants program and matching funds from a member consortium of Australian universities and other mathematical organizations. AMSI's premises were provided by the University of Melbourne and are located at 111 Barry Street, Carlton. AMSI's mission is to become a nationally and internationally recognised centre for the mathematical sciences, providing service to its member institutions, improving the international competitiveness of Australian industry and commerce and enhancing the national level of school mathematics, by the provision and support of mathematical and stati
AMSI - Australian Mathematical Sciences Institute
amsi australian collaboration education industry institute mathematical maths national sciences the
• Bachelor of Mathematical and Statistical Science (SBMSS) - Melbourne (Bundoora) - La Trobe University
In the last 50 years, mathematics has found widespread applications in areas as diverse as information technology, economics, management, finance and biology, as well as deepening its traditional relationships with physics, chemistry and engineering. Statistical science plays a crucial role in providing the tools necessary for the understanding of scientific, engineering and economic data. Demand for mathematicians and statisticians is currently high. This degree course provides the opportunity for students to combine significant studies in mathematics and statistics with units from a wide variety of disciplines, including those with which mathematics and statistics have not traditionally been associated. In doing this, students have the opportunity to desi
• Bijection - wikipedia
In mathematics, a bijection, or a bijective function is a function f from a set X to a set Y with the property that, for every y in Y, there is exactly one x in X such that f(x) = y. Alternatively, f is bijective if it is a one-to-one correspondence between those sets; i.e., both one-to-one (injective) and onto (surjective). (See also Bijection, injection and surjection.)
2009 articles axiomatic bijection bijective cardinal cardinality from lacking march number numeration proof set sources theory