## A record of gremlin achievement

These errors survive in the 2nd printing. Errors of punctuation and of English are omitted, since the reader will be easily able to supply the correction her- or himself.
• Page 7. Proof of Proposition 1.1. Last line should read M(y-x) and not My -x.
• Page 46. Line 3 of the proof of Lemma 2.1: the multiplication dot should be raised above the line of the bottom of the letters. (thanks to Nicolai Vorobjov, University of Bath). N.B. This error survives in the 2nd printing.
• Page 52. Proof (sketch). Replace the pompous but inaccurate though it would be a remarkable first-year undergraduate...' by since 2p (p) = p^2 + p^2'. (thanks to Ewart Shaw of the University of Warwick, England). Note that this idiocy survives into the 3rd printing!
• Page 63. The displayed equation should end 13/2 rather than 11/2. (thanks to Dave Johnson, University of the West Indies).
• Page 65. The field axioms; 0+a = a = a+0 and 1*a = a = a*1. (thanks to Dave Johnson and to Andriy Oliinyk of Toronto, Canada).
• Page 69. This equation is missing something crucial. Append the symbols =0', (thanks to Charles Cruickshank). N.B. This error survives into the 3rd printing!
• Page 76. Second paragraph. The angles of a triangle sum to pi, and not to 2pi. Ouch! (Dave Johnson).
• Page 77. Last line. Insert sin(alpha - beta) instead of sin(alpha + beta) (Dave Johnson).
• Page 82. Line 2 Replace log(nx) by log(x^n). ( Andriy Oliinyk). Note that this howler survives into the 3rd printing!
• Page 82. Definition 3.11. The quantity e is not a natural number (thanks to Edward Fraenkel). Note that this howler survives into the 3rd printing!
• Page 88. First line after the displayed equation. Replace inversion'' by integration'' (Dave Johnson).
• Page 89. Last line of third paragraph. Integral multiple of 2pi should read integral multiple of 2pi/n.
• Page 91. 5th paragraph. x=y=e^(2*pi*i/3) so xy=e^(4*pi*i/3)=e^(-2*pi*i/3). (Andriy Oliinyk). N.B. This error survives in the 3rd printing..
• Page 92. Line 16. Chapter 7 should read Chapter 6.
• Page 99. Equation 4.5 should read ||lambda x || = |lambda| dot ||x|| (Dave Johnson).
• Page 100. Last line of proof. |u|| should be ||u||.
• Page 101. Question 4.1 should read `(4.5) to (4.10)'' since one cannot justify a definition!
• Page 146. Proof of Proposition 5.7. It is better to replace m by n throughout the proof (Dave Johnson).
• Page 172. The proof of Proposition 6.4 is garbled.(Dave Johnson).
• Page 188 Line 14 (first line of the second paragraph of the proof), D_M should be \overline{T_M}. (thanks to Victoria Gould, University of York).
• Page 195. Remark 7.1. Replace z by b twice (Dave Johnson).
• Page 197-198, Proposition 7.2 and the preamble. This is not an error, but a matter of mathematical hygiene. It would have been better to define f(0) to be the gcd of 0 and 1, and so f(0)=1. With this variation f would be (just when you thought that it was safe to get back into the water) continuous at all irrational points and discontinuous at all rational points (thanks to my colleague Geoffrey Burton of the University of Bath).
• Page 199 Definition 8.2. The final symbol for the natural numbers on the last line should be just a capital N (Dave Johnson).
If you find an unrecorded glitch in the book, please send an email to G.C.Smith@bath.ac.uk and get yourself thanked here and in any reprinted edition.