Spending symmetry.
Terence Tao

In preparation

Last updated: May 15, 2020

This continues my series of books derived from my blog. The preceding books in this series were “Structure and Randomness“, “Poincaré’s legacies“, “An epsilon of room“, “An introduction to measure theory“, “Topics in random matrix theory“, “Higher order Fourier analysis“, “Compactness and contradiction“, and “Hilbert’s fifth problem and related topics“.

A draft version of the MS can be found here.

Pre-errata  (to be corrected in the published version):

• Page ix: the parenthetical reference to “compactness and contradiction” should be deleted.
• Page 34: On line 6, “Let now analyse” should be “Let us now analyse”.
• Page 45: In Section 2.2.5, one should use the tensor product ${\bf C}^2 \otimes {\bf C}^2$ instead of the direct sum ${\bf C}^2 \oplus {\bf C}^2$, making the necessary changes to the formulae (e.g. replacing $(v,w)$ by $v \otimes w$).
• Page 55: In line 4 of the statement of Theorem 4.1.1: “exactly one of the following statements hold” should be “exactly one of the following statements holds”.
• Page 89: “Converge almost everywhere” should be “Converges almost everywhere”.
• Page 144: On the third line before Conjecture 7.2.4, a space is missing after [BoSo1978].
• Page 199: $x^2+y^2+z^2$ should be $x^2+y^2+z^2=1$.
• Page 208: In Lemma 8.5.1 and its proof, one should replace $A+B$ with a measurable superset $C$, since $A+B$ might not itself be measurable.
• Page 233: The references [Ba1967,Ba1967b] were puvblished in 1967 rather than 1966; also [BoSaZi2011] has been publishhed.
• Page 235: The reference [Er1979] should be Erdős, Paul Some unconventional problems in number theory. Math. Mag. 52 (1979), no. 2, 67–70.

Thanks to Alan Chang, Nick Gill, Gerry Myerson, Ho Boon Suan, and Po Lam Yung for corrections.