If you notice any mistakes in the book, big or small, please send an email to the author at weissman AT ucsc DOT edu.
Please include the subject line ERRATUM (or ERRATA if plural, I guess!).
Before submitting your erratum, please look through the list below to see if it has already been caught.
When submitting errata, please include the following information:
Your full name, especially if you would like acknowledgment in future editions and on this errata page.
The page and location (e.g., line 10, beginning of the Proof, etc.) of the mistake.
A brief description of the mistake, and how you might fix it (optional).
Any other relevant information, e.g., how many students worked all night on an impossible exercise because of my error.
All accepted errata will be acknowledged on this page, and also in future editions of the text. Thank you to all the colleagues and students who caught errata before the first edition was published!
Thank you to Spencer Martin, at Cleveland State University, who found the first post-publication erratum. Thank you to Dr. Paul Stanford, at the University of Texas, Dallas, who found around 30 errata (!) and made excellent suggestions which I hope will be incorporated into the second edition someday.
Current errata (mathematical errors in red)
Chapter 0: Seeing arithmetic
Page 1 (darnit)
The word "myred" should be "red". Long story on this one: You might notice that some red text/dots in the text are more orange-ish than red. The reason is that screen-red (RGB) looks orange when printed. I thought I took care of this by creating a good print-red (in CMYK colorspace) which I called "myred". Indeed, I changed lots of red to "myred". But I missed some dots and text. And I accidentally changed the word "red" to "myred" on page 1. Whoops.
The stacking-corners diagram is 13+1 dots by 13+1 dots, but the labels suggest that it is 14+1 dots by 14+1 dots. (Thanks to Spencer Martin, August 2017.)
Marginnote, top-right: Zero is also typically considered a triangular number.
Marginnote, first sentence: "triangles" should be "triangle". (Thanks to Chris Shelley, November 2017.)
Just above Prop 0.13: "are form a" should be "are from a".
The end-of-proof square comes a few lines too early in Proposition 0.27.
Exercise 26: "perfect squares" should be called "squares".
Exercise 27: The parenthesis ) should be removed after "Notes". (Thanks to Chris Shelley, November 2017.)
Part I: Foundations
Chapter 1: The Euclidean algorithm
Line 13: "equaions" should be "equation".
Proposition 1.20: The integers a,b should both be nonzero.
The end-of-proof (QED) square is misplaced. It should be just above Problem 1.24.
Exercise 14: The last line should read "LCM(u^2, v^2) = LCM(u,v)^2". The final "squared" was forgotten.
Chapter 2: Prime factorization
Marginnote: A primality certificate typically refers to something more than we've described: a specific theorem and relevant parameters that rapidly guarantee primality.
The exponent of 7 should be called f_7, and not f_5, in equations (2.1), (2.2), and (2.3).
A period wandered away from 2N, at the bottom of the page.
Exercise 18(b): The period should go within the parenthesis at the end.
Chapter 3: Rational and constructible numbers
Middle figure: the r^2/d should be r^2/d^2, inside both square roots. As a result, a 1/d could be factored out of the square roots to simplify the expression a bit.
I really should have mentioned Farey sequences by name, and in the historical notes.
Sidenote 41: "...on can try..." should be "...one can try..."
Exercise 2: The triples (x,y,z) should be required to be pairwise coprime, i.e. GCD(x,y) = GCD(y,z) = GCD(x,z) = 1. Otherwise a single triple easily yields infinitely many by scaling. (Thanks to Steven Gubkin, October 2017)
Exercise 6(b): There's an extra period in "cosine.."
Chapter 4: Gaussian and Eisenstein integers
Sidenote: For the explanation to make sense, "integral domain" should have been defined. An "integral domain" is a ring in which xy = 0 implies x=0 or y=0.
Line three: "centered z" should be "centered at z."
Sidenote: In the phrase "there are infinitely many Gaussian prime numbers of the form x + i," the variable "x" is meant to refer to an ordinary integer (as in the exercise), not a Gaussian integer.
Part II: Modular Arithmetic
Chapter 5: The modular worlds
The modulus does not really need to be positive, for almost everything we do. Congruence modulo a negative m is the same as congruence modulo its absolute value. In fact, one can allow congruence "mod 0" too, which is just the same as equality!
A stray equal sign appeared, in the first centered equation. There should just be a congruence, so m is congruent to 0 mod m at the end.
Line 3 and line 8. The subscripts (1 and 2) migrated outside the absolute value. Please put them back in, next to the letter R where they belong.
Mid-page: "Linear polynomials play a special role." They do not "place" a special role.
Line 8: "degree up to 19" should be "degree up to 20".
Exercise 5: One should assume that m is nonzero. Perhaps even that m is positive, if you don't like negative moduli.
Chapter 6: Modular dynamics
In Problem 6.1, there are 7 equal signs that should be congruences instead.
In sidenote 7, "precient" should be "prescient". (Thanks to Alberto Trombetta, September 2017.)
Chapter 7: Assembling the modular worlds
Chapter 8: Quadratic residues
In the middle of the page, in the body and in the margin, I've mistakenly described the partnerships between x and -x as "(-1)-partnerships", which is incorrect. I've simply partnered each number x mod p with -x mod p. The rest of the argument (about E and O) is correct. (Thanks to Marco Schockmel, November 2017.)
Second paragraph of the proof of Lemma 8.25: The permutation alpha sends [a,b] to <a,b] (and not the other way around). (Thanks to Marco Schockmel, November 2017.)
Solution of Problem 8.28: 42 is not congruent to 1 modulo 7... change that 42 to 43. (Thanks to Firas Melaih, October 2017)
Part III: Quadratic forms
Chapter 9: The topograph
Last sentence of 3rd paragraph: there should be plus/minus (\pm) signs, to read "So we prefer \pm (0,1) over \pm (0,-1)."
Proof of Thm 9.14, end of 1st paragraph: v and w lost their over-arrows.
Top of page, "allow us transform" should be "allow us to transform".
Chapter 10: Definite forms
Chapter 11: Indefinite forms
In the two figures, the "v" should be in italics like the other variables.
There should only be one entry for Sunzi (c.220-420CE).