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- Search for pages identified with six dots-and-spaces . . . . . . and add them to this page.
- Check for broken hyperlinks, and fix them; find unlinked pages by looking at the end of sitemap_source
- Check page titles, descriptions, and keywords to see that they're right (checked through the F's)
- Look for U-Page="page reference" in the Navigation webbot
- Look for <style>, which interferes with application of the theme
- update sitemaps in this subweb and the mcraefamily website
- Look for href="http://2000clicks.com and src="http://2000clicks.com, and change most instances of
href="http://2000clicks.com/ to href="../
src="http://2000clicks.com/Links/ to src="linkg/
Eventually, after 2000clicks.com/Links has all been moved, delete unlinked graphics, rename the others, and "flatten" the structure by moving the links out of the folders.- Check for pages created / updated since 1/1/2009 to ensure the title and description are accurate
- Change -> to −> in the source code
- use "favorites" from both computers to update fun pages, math sites, etc.
- Do systematic changes from "symbol" to approved internet standard values
- Submit selected pages to Google
All the following PDF files are available as a "mirror" on the website in case they might be withdrawn later.
The pdf files below contain versions of course notes that I have written over the past decade or so. I am making them available for the benefit of anyone who wishes to make use of them. Please let me know if you find them useful or otherwise and let me know of any errors (mathematical, typesetting,...) that you find. All files are formatted for A4 sized paper. If you experience problems printing these files please contact me.
Look in the Wikipedia article on Fermat Numbers, especially the section "other theorems about Fermat numbers". There, you will see references to Lagrange's theorem and other factoids, which should be made into pages.
NumberFourthsAndSquares.htm -- a collection of half-baked proofs that x4+y4=z2 has no solution. One splits up the world into umpteen cases, and then wrestles each one to the ground using infinite descent. Another also uses infinite descent. This page needs to be worked into the hierarchy of pages, probably in the Math Help −> Number Theory −> Squares section.
Friendly Sets question: The answer to the Friendly Sets puzzle is missing cases 5 and 6: PuzzleFriendlySetsAnswer.htm
BasicNumberMagicSquareOfSquares.htm
NumberArithmeticSequenceOfFourSquares1.htm
NumberArithmeticSequenceOfFourSquares2.htm
NumberPrimeInfinitudeOfPrimes.htm
PuzzleFriendlySetsAnswer.htm -- questions 5 and 6 don't have answers yet.
Hamming Code Prisoner Puzzle Pages -- 20080131PuzzleTPS200801HammingCodeInfo.htm needs to be clarified, as does 20080131PuzzleTPS200801HammingCodeInfo.htm -- needs to be summarized. (The page is currently a dump of several web pages)
There are a number of puzzles related to the fact that starting with a/b, we can generate new fractions a/(a+b) and b/(a+b), and thus generate all fractions, essentially running the Euclidean Algorithm in reverse. The GeometryTrigEquivBrokenCalculatorPuzzle.htm puzzle uses this trick. There is also a puzzle PuzzleTPS200806ASetOfRationalNumbersAnswer.htm in which there is a set that contains 1/2, and if x is an element of S, then both 1/(x+1) is an element of S and x/(x+1) is an element of S. Prove that S contains all rational numbers in the interval 0<x<1. The trick is letting x=(q-p)/p, in which case 1/(x+1) = p/q; or if x=p/(q-p), then x/(x+1) = p/q
Unsolved problems needs to be fixed up from doc.xls
PuzzleThreeCirclesAndTriangleAnswer.htm
20080331PuzzleTPS200902RadicalThinking.htm
20080131PuzzleTPS200801PrisonerColorHatGuessProbabilityExecutedPuzzleAnswer.htm
BasicLogicProof.htm -- elaborate on the various types of proof
BasicAA.htm is nothing more than a title. It needs at least a table of contents (!) and its sub-page BasicAARings.htm needs work, too. Is there more to Abstract Algebra than rings? What about groups?
BasicAAGroup.htm was created, but a lot of information is in BasicSetGroup.htm, so these pages need to be coordinated (BasicSetGroup.htm should be elementary, with more advanced theory in BasicAAGroup.htm.)
Add to mathhelp: markov chains and stationary distributions, which are tools that help analyze probabilities of sequences of events.
AlgebraOnline/a020515CountPolynomials.htm
CountingTetris.htm -- use the spreadsheet that has the VBA program for counting solutions to update the method in this page, and update CountingPolyominoes.htm to include the 7-omino case.
BasicRecurrenceRelationsFibonacci.htm -- complete the proof that considering all products of two Fibonacci numbers, arranged in sequence, the difference of successive Fibonacci Products is a Fibonacci number.
BasicSequenceGeneratingFunction.htm -- (add information from the cut-the-knot reference, and from spreadsheet PuzzleNumberOfNondecreasingSequencesSumNA049988.xls and PuzzleGeneratingFunction.xls)
CountingPowerSeries.htm -- Add information in all the various sections on power series...
Infinite Base Numbers
Arbitrary Base Numbers
Product of Formal Power Series
Inverse (Reciprocal) of a Formal Power Series
Convolution
Counting Ways to Make Change
Counting Scores of a Football GameOEIS -- BasicSequenceOEIS.htm
The whole statistics.htm section needs to be de-imaged and then filled out with actual information
BasicWordLinearProgramming.htm needs to be created, with information about this topic -- example problems, "objective function", why check the corners, etc.
ProceduresPolynomialDivision.htm gives a procedure for dividing one polynomial by another. It needs some fixing up to give examples of non-monic and higher degree divisors.
Related Rate Problems -- BasicWordRelatedRates.htm
CalculusIntegralDifferentiationUnderTheIntegralSign.htm
CalculusIntegralTrigSubstitution.htm
CalculusIntegralPartialFractions.htm
CalculusIntegralIntegrationByParts.htm
Proof needed that (sin θ)/θ is strictly increasing on the interval (0,π/2)
Table of integrals -- CalculusIntegralTableOfIntegrals.htm
1/(1+sqrt(x²-1)) =
sqrt(x²-1)/(x²-2) - 1/(x²-2)Needs proof of integral, which is given as
(-1/sqrt(2)) arctan(x/sqrt(2x^2-2)) + ln(x+sqrt(x^2-1)) +
(ln(x+sqrt(2))-ln(sqrt(2)-x))/(2sqrt(2))The derivative of the second half is right -- derivative of (ln(x+sqrt(2))-ln(sqrt(2)-x))/(2sqrt(2)) is
(1/(x+sqrt(2))+1/(sqrt(2)-x))/(2 sqrt(2)) = -1/(x^2-2)But I can't make the first half of the integral add up when I differentiate it.
(1) Derivative of (-1/sqrt(2)) arctan(x/sqrt(2x^2-2)) is
-(1/sqrt(2x^2-2)-2x^2/(2x^2-2)/sqrt(2x^2-2))/sqrt(2)/(x^2/(2x^2-2)+1)
= 1/sqrt(x^2-1)/(3x^2-2)(2) Derivative of ln(x+sqrt(x^2-1)) is
1/sqrt(x^2-1)
= sqrt(x^2-1)/(x^2-1)(1) + (2) should equal sqrt(x²-1)/(x²-2), but they don't seem to be.
GeometryConicRotationOfAxes.htm -- find the coefficients a', b', 2g', 2f', and c' of the rotated conic section. You might like to also fix the ConicSection1.htm conic sections page to provide more information about the rotated axes.
GeometryTrigEquivIdentities00.htm#triple -- Summary of Identities -- cos((n+1)x)=2cos(x)cos(nx)-cos((n-1)x) is a recurrence relation for cosine, which parlays into the table given here... Is there a similar recurrence relation for sin((n+1)x) ? (I asked the question in "Onwards and Upwards" NRICH.
GeometryPolygonFTDSF.htm -- Fundamental Theorem of Directly Similar Figures (FTDSF) -- needs to be fixed up to show a good proof by similar triangles, with some diagrams.
Add a page for this puzzle question, found on Dr.Math http://mathforum.org/library/drmath/view/54760.html -- Let ABCD be a convex quadrilateral and M, N, P, Q points on AB, BC, CD, DA respectively, such as BM = CN = DP = AQ. Prove that, if MNPQ is a square then ABCD is a square.
After it is presented on TPS, fix the filename of 20080229PuzzleTPS200901CircleAndChordsAnswer.htm, and provide the Puzzle Question page as well, and include these in the GeometryTheorem-Summary.htm summary.
"Equilateroid" (a word that aught to go in the geometry glossary!) with Rational Height -- AlgebraOnline/p040901N-DimensionalTetrahedron.htm
GeometryTriangleAreaVector.htm has four sections without very descriptive names -- these need to be fixed, and moreover the word "determinant" in the fourth section needs to be clarified to explain that it's a value derived from a 2*n matrix.
Finish editing the third rendition of a puzzle (or delete it, as far as I care!).
BasicSimplifyingNestedRadicalsCube.htm
PuzzleThreeCirclesAndTriangleAnswer.htm
My effort to explain this one never got off the ground. Is it really that hard? This page needs to be updated with the proof supplied in the cut-the-knot reference.
GeometryConicSectionInversion.htm
should describe orthogonal circles and the inversion circle, and such things as the angle preservation property etc.
GeometryConicSectionBrianchonHexagon.htm needs fixing up -- it proves the following: Given a hexagon ABCDEF with all sides equal and such that the angles A+C+E=B+D+F, show that AD,BE,CF are concurrent. Is it related to GeometryTriangleCyclicBrianchon.htm?
GeometryConicSectionPappusChain.htm
GeometryTriangleCenterOrthocenter.htm
The orthocenter needs to be described on this page, along with some of its properties and internet references (cut-the-knot, mathworld, wikipedia).
A page on Barycentric Coordinates should be added, cross-referencing their use in determining whether a point is inside a triangle on page GeometryPointAndTriangle3.htm.
GeometryTriangleDiagonalsOfNGon.htm
GeometryTriangleCyclicPascal.htm
GeometryTriangleCyclicPappus.htm
GeometryTriangleInscribedAngleCircle2.htm
GeometryTriangleCenterInscribedCircle2.htm
The webmaster and author of this Math Help site is Graeme McRae.