37 comments on “Blog and book updates

  1. I managed to pick up a copy of Maths 1001 for £6.99. I have many reference books on Mathematics and Science but this by far the best, very informative with clear descriptions and concise diagrams. This book will definitely provide a good supplement to my Maths and Further Maths A-Level courses. Aesthetically the book is nice and chunky and the pages are laid out very clearly (how did you know Georgia was my favourite font!)

  2. Hi Jack, thanks for taking the time to leave a comment. It’s fantastic to hear that you’re enjoying the book. I’m afraid I can’t take the credit for the choice of typeface though… those sort of decisions were all the editors.

    Thanks again, and the best of luck with all your studies!

  3. This is a micro-nano-femto nit: In the section on Fuzzy Logic, you misspelled “Lotfi Zadeh” as “Lofti Zadeh”.

    Great book, by the way!

  4. Hi Richard! Would it be possible to include the date of the errata when you post them? This way we can see which ones are new and update our copies accordingly. Cheers!

  5. Great book! Interesting and easy to digest most of the information in it. However, i do have a question as this have puzzled me for quite a while. With regards to the cubic formula,

    “The formula for the general cubic equation x^3 + ax^2 + bx + c = 0 is significantly more complicated than that for the quadratic. To give in, we first define
    q = -a^3/27 + ab/6 – c/2
    p = q^2 + (b/3 – a^2/9)^3.
    Then the first solution is given by:
    X = (q+p^(1/2)]^(1/3) + (q-p^(1/2))^(1/3) – a/3”

    as quoted from the book,
    what happens if c=0, a=12 and b=15,
    we get x^3 + 12x^2 + 15x = 0
    the answer will be x = 0, -1.41, -10.6
    However, using the formula from the book, the value of p would turn out to be -175, and the first value of x would therefore be an imaginary answer,. how is this possible?

    anyway, this is a splendid book! would recommend all my friends to read this book! 🙂

  6. Hi Lyone

    Thanks very much for your comment, and for your kind words!

    Actually, in your example, the first value of x is not imaginary. I know it may look like it, as you have to take the square root of a negative number… but in fact the imaginary parts cancel each other out.

    The point is that [q+p^(1/2)]^(1/3) will be of the form c+id (for some numbers c&d which you can work out!) and then [q-p^(1/2)]^(1/3) will be c-id. So when you add them together, you are left with just 2c, and no imaginary part.

    Please note though that unfortunately there is an error in that section, in the second formula. See the entry on my errata page:

  7. Your book Mathematics 1001 is the most interesting maths book I have ever picked up. You update with sufficient, but not overdone, detail recent results and developments that are hard to find for us numerate laymen. Very well done, sir.

  8. Hi Richard,

    I’m currently enjoying your book.

    I’ve spotted a few things which I think are incorrect.

    On page 13 you wrote “You can take logarithms to any base number, as long as it is positive”

    On page 99 you refer to a face as a side.

    Quite a few times you wrote “Highest common factor (highest common denominator)”

    If I’m wrong please excuse my ignorance. 🙂


  9. Top of page 170

    cos(theta) must be between 0 and 1.

    I hope I’m not too irritating and that these posts are helpful. I’d love to know 1/10 of the maths that you know. 🙂

  10. They’re definitely helpful, and not at all irritating! (Well, the fact that there are errors is in itself rather annoying, but that’s hardly your fault.)

    Thanks so much for letting me know.

  11. Just finished your book, really enjoyed it.

    On page 281, maybe “work algorithm” should be “word algorithm” ?

  12. On page 331 in False positives, I get

    P(Y) = 0.99 * 0.0003 + 0.05 * 0.9997 = 0.050282

    putting P(X|Y) at just under 0.6%.

  13. Hi Richard. Your book is terrific– I picked it up at a Canberra public library and am half-way through it. I will order it soon.
    I had thought that Pickover’s “The Math Book” was excellent, but
    your is much more complete and more useful, though I like them both.
    A trivial spelling error occurred on p 115, in the Quadratic Curves section. “principle” should be “principal”.
    Cheers –John Winkelman

  14. I have a question, on page , The problem of the ray, is a bit difficult for me to understand, I searched it up on the web, but could not find any explanations. Could someone explain it to me?

  15. Bought on a whim. Serendipitously, apparently. Half way through Chapter 1 I’ve only felt stumped about 5 times. Normally with “Super-Hard Stuff Made Super-Simple” books I’m there by half way through Page 2.

    The book has helped me overcome my sordid past: I once proved 1=0 on the wall of a public toilet stall. At the time, I thought I was being childish, and a vandal. Thanks to this book providing a proof that 2=1 (p. 32), I was quickly able to realize that I had simply found a more elegant expression of the same concept. So I’m feeling pretty good right now. Thanks, Doc.

  16. Can you please release a pdf version or an E-Book on amazon or google play. I use this book as a little bit of preparation before I go to the navy school for nuclear engineering. It would be amazing to pull up a paragraph on my tablet to get a better understanding of the topic.The book is amazing and very helpful. I get more out of one paragraph than I do in 3-5 pages of when i had high school txt books. Thank you


    I have Mathematics 1001, version, ISBN 13:978-1-55407-719-9. Is there a revised version of this book available? If so, how can I get it?

    I chose Mathematics 1001 instead of several others of its kind, because of its comprehensive approach to the entire realm of math. It has a well organized sequence of topics. Also, the quality of the paper and workmanship of the book itself is superior.

    I have covered roughly 40% of the book. Unfortunately, I have encountered many errors
    and I keep finding more all the time. Many of
    these errors are different from the errors in your online errata.

    I am interested in hearing your thoughts,


    Mark Burke


    I found several errors that are not listed in the online errata for
    the green hardcover book – Mathematics 1001.

    These are listed below. Any text surrounded by round brackets are my
    own comments.

    I read about a third of the book, before I stopped reading it. If I
    would keep going, I know I will find more errors. Some of these errors
    are really picky and some were just omitted words or bad English.


    Page 4 The book reads… Ruler and compass constructions…

    (The overlap the the next line looks sloppy. Maybe it
    could instead be… geometric constructions
    or the ruler and compass.)

    Page 39 it reads… reflecting al Al?Khwarizmi

    (should read… reflecting al Khwarizmi)

    Page 46 it reads… how many they are

    (should read… how many there are)

    Page 47 it reads… then that specific examples

    (should read… then specific examples)

    Page 52 it reads… so x+1 / 2

    (should read… which is x+1 / 2)

    Page 53 it reads… length is core

    (should be… length is the core)

    Page 58 the graph is misleading…

    (The graph shows what looks like a line. This is
    misleading, because it is really bent a little bit.)

    Page 84 (In the real number line diagram shouldn’t it have an
    arrow pointing left toward negative infinity also?)

    Page 85 (Wouldn’t it be better if the a and b axis were switched
    so that the coordinate system used is right-handed?)

    Page 96 it reads… outside the triangle

    (should be… outside the circle)

    Page 103 In the diagram caption
    it reads… eight octagon ring

    (should read… eight octahedron ring)

    Page 105 (The 3rd and 4th diagrams don’t show the true
    transformation of the image of the tree. The images are
    small and hard to see, but I notice the reflection of
    the tree was really just slid, not reflected.)

    Page 107 it reads… so,

    (should be… so, if)

    Page 109 it reads… irregular convex hexagon

    (should read… irregular convex hexagons)

    Page 109 it reads… meaning that a transitionally

    (should read… meaning that a translationally)

    Page 111 it reads… gyroscope of order 4

    (should read… gyration of order 4)

    Page 118 (The title heading needs to be plural, just like the
    title heading for PARABOLOIDS and HYPERBOLOIDS.)

    it reads… ELLIPSOID

    (should be… ELLIPSOIDS)

    Page 119 it reads… “2 dimensions and 1 dimension”

    (should be… “3 dimensions and 2 dimensions”)

    Page 120 (The diagrammed point “D” for (2, 3pi/2)
    is in the wrong spot.)

    Page 124 (Two problems are found that describes a circle as
    having length. A circle has a diameter or radius,
    but not length.)

    1st reads… triple the length

    (should be… triple the diameter)

    2nd reads… quadruple the length

    (should be… quadruple the diameter)

    Page 127 (The bee diagram is in conflict with the text.
    The diagram shows 3 rhombuses so the text should
    read… three rhombuses, not 4)

    Page 132 it reads… mobius strips featured heavily
    (should read… mobius strips are featured heavily)

    Page 133 it reads… keep pinching holes
    (should read… keep punching holes)

    Page 133 (The double-torus in the diagram is too small and out
    of proportion with the other two pictures. It looks

    Page 140 it reads… might the same true

    (should read… might the same “be” true,
    or… might the same “prove” true)

    Page 142 it reads… unkot

    (should read… unknot)

    Page 146 it reads… principal

    (should be… principle)

    Page 154 it reads… unable to prove

    (should read… able to prove)

    Page 168 it reads… is further to travel

    (should read… it is further to travel)

    Page 169 it reads… ||u|| = sqrt(2) 2 = 2

    (should be the equation for ||v||
    should read… ||v|| = 2)

    Page 170 it reads… appears in many placed

    (should be… appears in many places)

    Page 176 it reads… zero determinant

    (should be… a zero determinant)

    Page 196 it reads… shortest path probelm

    (should be… shortest path problem)

    Page 198 it reads… if every pair of edges is connected to an edge

    (should be… if every pair of vertices…)

    Page 207 It reads 3n —> – oo as n —> -oo,

    (should be… 3n —> – oo as n —> +oo)

    Page 235 (The “firstly” argument is weak, because the equations
    on this page can be done with any base besides e.
    The “second” argument is ok.)

    Page 250 it reads… as is it is by no means

    (should be… as it is by no means)

    Page 252 (The 2nd diagram equation is wrong)

    it reads… y = sin y

    (should be… y = sin t)

    Page 252 (The word “saw-tooth” needs no hyphen.)

    Page 253 (The word “saw-tooth” needs no hyphen.)

    Page 271 it reads… abstract types of function

    (should be… abstract types of functions)

    Page 281 it reads… work algorithm

    (should be… word algorithm)

    Page 405 (There is a 5×5 Knight’s tour, but it is not reentrant.)

    As you can see, a lot of the errors or inefficiencies are pretty
    picky, but it sometimes makes for hard reading.

    I am interested in hearing your thoughts,


    Mark Burke

  19. I am interested in hearing your thoughts,

    Ok. My thoughts are as follows.

    The Errors

    Some of these are minor typographical errors I was aware of but haven’t included in the online errata because they do not obstruct understanding.

    Some of these are typographical errors I was not aware of but will mention to the publisher so they can be put right in future printings (e.g. “gyroscope”). I am grateful to you for bringing them to my attention.

    Some are more significant errors I was not aware of and am very grateful for your having brought to my attention.(e.g. the caption on the diagram on P252.) I have added those in this category to the Errata.

    One of these (the one on P96) is a significant error which, contrary to your assertion, already appears in the online Errata.

    The Non-Errors

    Some of these not errors at all (e.g. the first) but are your suggestions for improving the phrasing or layout. Whilst I am grateful for your thoughts, I would be more so if you hadn’t mischaracterised their nature.

    Some of these are not my errors but yours (e.g. the notion of arc-length means that one can reasonably and rigorously talk about a circle’s “length”).

  20. Hey Richard,

    On page 122, under the section of ‘surfaces of higher degree’ , i believe the equation of a super ellipse is ‘… y/b…’ and not’…y/a…’ .

    It’s still a fantastic book.

  21. Hi, I read the book in its Japanese translation and found some errors.

    On page 100, all examples other than strombic hexecontahedron are not Catalan solids.
    See: http://mathworld.wolfram.com/CatalanSolid.html

    On page 101, in the section of Kepler-poinsot polyhedra you asked “Are the Platonic solids the only solids with identical faces of regular polygons?” and answered “it depends on definitions”, but for example Triangular bipyramid is definitely a solid with identical faces of regular polygons, which has no false edges.

    Such solids are called Deltahedron: http://mathworld.wolfram.com/Deltahedron.html

  22. Loved your 1001 book. Read it thru. One thing however…I was disappointed to find nothing about discrete calculus (I.e. differentiation and integration of integer functions). I need a reference to a treatise on this. This is related to game theory and zero sum games (aka – gambler’s ruin).
    Thanks again for your definitive work.
    Jerry Hogsett. ghogsett@aol.com

  23. Well, the wallpaper reminds me of the dazzling reflections of the sun’s light on convexly curved surfaces such as car bumpers and a certain type of garden decoration which is just a polished sphere of some suitable metal such as chromium. These surfaces show not only the radian pattern which your wall paper presents, but they show also concentric rings of what seem to be probability waves, generally moving outward but with concentric phases that move inward and outward at the same time. I say probability waves because they seem to be conjugate to the radiating patterns you present. (I worked in radar and other wavelengths throughout the spectrum, from Gamma rays to VLF.

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