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mathematics

general mathematics resources
links	comments
mathematics chronology	Provided by the School of Mathematics and Statistics University of St Andrews, Scotland. Includes subject glossary, biographies and a subject index. See also their script which tells you Mathematicians alive on a given date. Useful for deciding on something to celebrate at a party is Mathematicians' anniversaries throughout the year.
MSC 2000	2000 Mathematics Subject Classification. I prefer to use their MSC 2000 directory browsing. Hosted by the Fachinformationszentrum Karlsruhe, which includes some useful mathematics links.
Mathematical atlas	Includes a set of articles on the areas of mathematics arranged by AMS classification (MSC). Includes differential geometry. Includes such detailed things as an example of a topological space which is locally Euclidean but not Hausdorff.
Geometry.net links	A very useful-looking large set of links to mathematics sites. They also seem to run a search engine (called `Copernic'?) for finding mathematics sites on the web.
AMS maths in media	AMS archive of maths that appears in the media.
Math Forum	A web site with a useful general discussion groups and research discussion groups for mathematics.
sci.math	sci.math.* news groups at Google.
science oxygen	2005-11-26: Includes tensor analysis and Lie Groups and Lie Algebras and differential geometry. This seems to be an automatically generated set of links from Google searches.
wikiversity	2008-2-28: A wiki for university level mathematics, but there is not much material here yet. See also philosophy of mathematics, analysis and differential geometry (not yet started).
free download books, lecture notes, research papers
links	comments
halfvalue.com textbooks	2007-2-26: Free mathematics textbooks online.
maths textbooks	2005-3-1: A really big list of free online textbooks on mathematics collected by Alexandre Stefanov. See also his links to other lists of maths books online. 2008-1-31: There seems to be a new version of this list here: mathbooks.110mb.com This list is duplicated at algebra.com. See also http://www.trillia.com/online-math/.
freebookcentre.net	2008-11-7: Includes free mathematics books.
Le MathsLinker	2005-3-1: An index of maths resources (such as free books) on the web in French and English.
Lyon	2007-3-14: Archive des rapports de stages des étudiants de l'École Normale Supérieure de Lyon.
maths books	2008-4-27: Free textbooks on mathematics and computer science at theassayer.org.
textbook revolution	2008-4-27: A small set of online free maths textbooks.
maths texts	2008-4-27: A small set of elementary maths texts at opentextbook.org.
inktextbooks	2008-4-27: A small set of elementary maths texts at inktextbooks.com.
books.pspxworld.com	2007-2-12: An index of free mathematics books. They seem to be elementary.
geometry and topology	The net advance of physics. A big list of maths and physics documents for download from the net.
archimedeans	2008-1-25: Lots of lecture notes, including these maths lecture notes. However, most of the material seems to be blocked to people outside Cambridge University.
Norbury e-books	Several free online books in PDF format by John W. Norbury. Includes a book on general relativity.
Sean O'Hagan's list	2004-6-27: A list of free downloadable maths books, mostly on algebraic topology and differential geometry.
citeseer.ist.psu.edu	2005-3-18: CiteSeer. Scientific Literature Digital Library. Lots of online science/engineering literature including mathematics, nicely indexed.
Rincón Matemático	2007-4-30: Spanish-language web site for mathematics students. Uses SMF (Simple Machines Forum) software.
college algebra	2008-1-25: Notes by Ken Kubota, who just happened to be one of my computer administrators when I was teaching at University of Kentucky in 1985/86.
pure maths books	2008-1-24: This is a rather amazing, large list of books which are useful for learning mathematics and mathematical physics. Some of the books on this list are marked as being free. Includes this list of mathematics resources on the web.
6370243.blogfa.com	2008-3-5: A big, quirky page of free mathematics books/notes links, written in English, Arabic, and a bit of Hebrew. Some or all of this web page is copied from other sources without attribution, like from my web site for example.
See also free online download differential geometry textbooks and notes.
See also general free textbooks.
mathematics journals
links	comments
GANG	Geometry Analysis Numerics Graphics journal preprints. Includes these papers by Evans and Spruck on motion by mean curvature.
DG e-prints	Online reprints of papers in a large number of DG topics.
JDG	2005-3-20: Journal of Differential Geometry. See also JDG article submission.
arXiv.org e-Print archive	Some sort of archive of maths and physics publications. Includes a paper on Manyfold universe theory. See also arxiv.org/archive/math.
WorldSciNet	A site with a big collection of journals, including on maths and physics. Includes International Journal of Mathematics.
analysis and differential geometry
links	comments
geometry.net DG links	A big set of useful links on differential geometry.
the Spivak book	The 3rd edition (1999) of Michael Spivak's 5-volume DG book. Costs US$145 for the set.
TCAEP	Amazon book-selling of DG books via the constants and equations pages.
DG/PDE seminars	Info on University of Washington seminars. Includes this postscript abstract of a talk by John McCuan (MSRI) in Fall 1998 on applications of convexity maximum principles to problems of constant sectional curvature. Also refers to a paper by Alvarez, Lasry and Lions (1997) which gives an improved convexity maximum principle.
DG book draft	Alan Kennington's free online differential geometry book draft, including differentiable manifolds, fibre bundles, connections and riemannian manifolds.
DG and GR notes	DG and general relativity lecture notes by Stefan Waner.
DG lecture notes	A set of differential geometry lecture notes by Sergei Yakovenko.
mathematics institutions and organisations
links	comments
Uni Tübingen	Department of Maths, University of Tübingen. Includes Gerhard Huisken.
University of Sevilla	Department of Geometry and Topology.
UK mathematics	Home page of University of Kentucky mathematics department. Includes staff web pages.
Brandeis Maths Dept	Massachusetts.
SINTEF	Applied Mathematics institute in Trondheim, Norway.
IMAG	Institut d'Informatique et Mathématiques Appliquées de Grenoble.
UTSA	Division of Mathematics and Statistics, University of Texas at San Antonio.
Aust Math Soc	See also Australian Math Society Welcome Page.
Australian University mathematics departments
links	comments
SMS ANU	School of mathematical sciences, ANU.
University of Adelaide	Mathematics departments' web site. Includes Institute for Geometry and its Applications and Adelaide University differential geometry seminars.
mathematicians
links	comments
Halmos essay	An essay by Paul R. Halmos on How to write Mathematics.
Avner Friedman	See also this short vita.
Hyam Rubinstein	University of Melbourne. Differential geometry.
Grant Keady
Stephan Luckhaus	I met Stephan in Heidelberg (1986/87) and Bonn (1991 or 1992). He helped simplify an interior cone condition in a paper of mine on parabolic initial value problems in 1986/87.
Thorbergsson Gudlaugur	Differential geometer in the Mathematisches Institut der Universität zu Köln.
Bill Burke	Some differential geometry links. Died 1996.
A.N. Tikhonov	2005-3-11: Андрей Николаевич Тихонов (Andrei Nikolaevich Tikhonov). See also this Tikhonov biography.
queueing theorists	2007-3-17: A list of over 1400 queueing theorists. Very scary!
mathematics software
links	comments
proofweb	2008-12-9: Mathwiki: Wiki for formalized mathematics based on ProofWeb.
WIMS	WWW Interactive Mathematics Server. Lots of interactive mathematics software online.
logic software
links	comments
HOL	Automated Reasoning Group HOL page. The HOL System is an environment for interactive theorem proving in a higher-order logic. The system has a wide variety of uses from formalizing pure mathematics to verification of industrial hardware. The system is available without charge. Cambridge University.
Coq	The Coq proof assistant allows to handle calculus assertions, to check mechanically proofs of these assertions, helps to find formal proofs, extracts a certified program from the constructive proof of its formal specification. Inria, France.
Isabelle	Isabelle is a popular generic theorem proving environment developed at Cambridge University (Larry Paulson) and TU Munich (Tobias Nipkow).
mean curvature flow
links	comments
Sethian publications	Publications of J.A. Sethian.
Russell's paradox
links	comments
Stanford Encyclopedia	2005-5-4: History and significance of the paradox.
scienceworld.wolfram.com	2005-5-4: This very brief biography of Frege contains the famous quote (from the same book by E.T. Bell where I found it): A scientist can hardly encounter anything more undesirable than to have the foundation collapse just as the work is finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was almost through the press. See also Google. See also St. Andrews biography of Frege
Justin T Miller	2005-5-4: Includes discussion of Frege's reaction to Russell's paradox, and this comment: Although the foundation of his theory had been destroyed, Russell described Frege's reaction as superhuman, writing to van Heijenoort that Frege responded with intellectual pleasure clearly submerging any feelings of personal disappointment.
diagonal method	2005-5-4: Diagonal method and Russell's paradox.
ontology of mathematics
links	comments
where maths comes from	2006-12-17: A book called: Where mathematics comes from: how the embodied mind brings mathematics into being. Authors: George Lakoff & Rafael E. Núñez.
Paul Ernest	2004-4-11: Texts and the objects of mathematics. Extract from Chapter 6 of Social Constructivism as a Philosophy of Mathematics, Albany, New York: SUNY Press, 1997.
formal ontology	2008-3-2: Ontology. A Resource Guide for Philosophers, by Raul Corazzon.
mathematical logic
links	comments
Metamath	2008-1-21: Includes Metamath Proof Explorer about propositional calculus, predicate calculus and set theory axioms. Inspired by Whitehead and Russell's monumental Principia Mathematica, the Metamath Proof Explorer has over 7,000 completely worked out proofs in logic and set theory, interconnected with over a million hyperlinked cross-references. Each proof is pieced together with razor-sharp precision using a simple substitution rule that practically anyone can follow, not just mathematicians.
propositional logic	2008-1-16: From The Internet Encyclopedia of Philosophy.
mathematical logic	2008-1-16: Introduction to Mathematical Logic, Vilnis Detlovs, Karlis Podnieks, University of Latvia. This looks very useful to me.
wiki CC axiom	2007-4-20: A useful wikipedia article on countable axiom of choice. See also axiom of choice, Gödel's incompleteness theorems. For something more cheerful, see also Gödel's incompleteness theorem (in German).
planetmath.org	2005-1-28: Includes an article on countable axiom of choice stating as follows: The Axiom of Countable Choice (CC) is a weak form of the Axiom of Choice. It states that every countable set of nonempty sets has a choice function. ZF+CC (that is, the Zermelo-Fraenkel axioms together with the Axiom of Countable Choice) suffices to prove that the union of countably many countable sets is countable. It also suffices to prove that every infinite set has a countably infinite subset.
online mathematics book purchase
links	comments
maths books	2008-2-22: At an Australian web site: computeroutpost.com.au. Includes some books on logic, such as Mathematical logic by Joseph Schoenfeld.
history of mathematics
links	comments
history of notation	2008-4-25: Wikipedia: History of mathematical notation.
maths symbols history	2008-4-25: The History of Mathematical Symbols.
history of topology	A page of lecture notes on history of topology. Comes from a set of notes by E. Christopher Zeeman.
related URLs
links	comments
kleinbottle.com	These people sell Klein bottles, mugs and hats.
digits of Pi	An article on randomness of the decimal digits of Pi.
Confidence Intervals	Slide 3 of 7. Computation Physics / Carleton University.
integer sequences	Online encyclopedia of integer sequences.
math methods	The beginnings of texts (free online) on mathematical methods for physics, by Richard Scalzo.
tessellations.com	Commercial site with stuff related to tessellations.
crank.net	Links to bizarre maths on the net.
Kungl texts	Some documents on a swedish site, including this doctoral thesis on convexity by Arshak Petrosyan.
dualities in N=2 string theory	Includes differential geometry and a definition of principal fibre bundle. But the graphics files are missing!
Cardaliaguet	Some papers by Pierre Cardaliaguet, including one on strict concavity of the harmonic radius in dimension N>2.
theorème d'uniformisation de Riemann	A maths document in French. It uses some sort of TeX to PNG convertor to present maths on the web.
Millennium problems	2005-3-18: In order to celebrate mathematics in the new millennium, The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) has named seven Prize Problems. The Scientific Advisory Board of CMI selected these problems, focusing on important classic questions that have resisted solution over the years. The problems titles are: Birch and Swinnerton-Dyer Conjecture, Hodge Conjecture, Navier-Stokes Equations, P vs NP, Poincaré Conjecture, Riemann Hypothesis, Yang-Mills Theory.

Mathematics jokes
I've heard several mathematics jokes in the last 50 years. Very few mathematical jokes actually provoke laughter. They're more like riddles where the point is to guess what they mean, not actually laugh at them. Here's one joke which almost made me laugh. Why did the chicken cross the Möbius strip? To get to the same side. Er, yes, quite... There are very few mathematics jokes which get funnier than that. No wonder mathematicians are such a glum, humourless lot! That's why you don't see groupies hovering around mathematicians at parties. Most mathematicians won't admit to being mathematicians even in private. The other mathematics joke which I found mildly amusing was this: Teacher: I give you 2 rabbits. Pupil: Yes, Sir. Teacher: Then I give you 3 rabbits. Pupil: Yes, Sir. Teacher: Now how many rabbits have you got? Pupil: 6 rabbits, Sir. Teacher: No, no! Think carefully. I give you 2 rabbits. Pupil: Yes, Sir. Teacher: Then I give you 3 rabbits. Pupil: Yes, Sir. Teacher: So now how many rabbits have you got? Pupil: 6 rabbits, Sir. Teacher: No, no, no! Don't you know how to add? Pupil: Yes, Sir. Teacher: So how do you get 6 rabbits from 2 plus 3 then? Pupil: I've already got a rabbit, Sir. I hope you found that as amusing as I did!! When I heard that joke, I naturally thought the student was multiplying and that the joke was about rabbits multiplying, because rabbits multiply and, er.... Never mind! I suppose you could count all of Zeno of Elea's paradoxes as mathematics jokes of their day. Zeno probably got a few hearty laughs down at the Gymnasium with his paradoxes. See also mathematics jokes at www.gdargaud.net.

Mathematics jokes

I've heard several mathematics jokes in the last 50 years.
Very few mathematical jokes actually provoke laughter.
They're more like riddles where the point is to guess what they mean, not actually laugh at them.
Here's one joke which almost made me laugh. Why did the chicken cross the Möbius strip?
To get to the same side.

Er, yes, quite...
There are very few mathematics jokes which get funnier than that.
No wonder mathematicians are such a glum, humourless lot!
That's why you don't see groupies hovering around mathematicians at parties.
Most mathematicians won't admit to being mathematicians even in private.

The other mathematics joke which I found mildly amusing was this:

Teacher: I give you 2 rabbits. Pupil: Yes, Sir. Teacher: Then I give you 3 rabbits. Pupil: Yes, Sir. Teacher: Now how many rabbits have you got? Pupil: 6 rabbits, Sir. Teacher: No, no! Think carefully. I give you 2 rabbits. Pupil: Yes, Sir. Teacher: Then I give you 3 rabbits. Pupil: Yes, Sir. Teacher: So now how many rabbits have you got? Pupil: 6 rabbits, Sir. Teacher: No, no, no! Don't you know how to add? Pupil: Yes, Sir. Teacher: So how do you get 6 rabbits from 2 plus 3 then? Pupil: I've already got a rabbit, Sir.

I hope you found that as amusing as I did!!
When I heard that joke, I naturally thought the student was multiplying and that the joke was about rabbits multiplying, because rabbits multiply and, er.... Never mind!

I suppose you could count all of Zeno of Elea's paradoxes as mathematics jokes of their day.
Zeno probably got a few hearty laughs down at the Gymnasium with his paradoxes.

Go to free online differential geometry textbooks.
Go to TeX typesetting software.
Go to mathematics and general science software.
Go to education links.
Go to astronomy links.
Go to physics links.
Go to science organisations and institutions.
Go to my book on differential geometry (work in progress).
Go to Alan Kennington's home page.

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MSC 2000 Wheel of Fortune

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