Spending symmetry.
Terence Tao

In preparation

Last updated: Feb 14, 2017

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 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 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 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, Gerry Myerson, and Po Lam Yung for corrections.