Structure and Randomness: Pages from Year One of a Mathematical BlogAmerican Mathematical Soc. - 298 pages "In 2007, Terry Tao began a mathematical blog, as an outgrowth of his own website at UCLA. This book is based on a selection of articles from the first year of that blog. These articles discuss a wide range of mathematics and its applications, ranging from expository articles on quantum mechanics, Einstein's equation E = mc[superscript 2], or compressed sensing, to open problems in analysis, combinatorics, geometry, number theory, and algebra, to lecture series on random matrices, Fourier analysis, or the dichotomy between structure and randomness that is present in many subfields of mathematics, to more philosophical discussions on such topics as the interplay between finitary and infinitary in analysis. Some selected commentary from readers of the blog has also been included at the end of each article. |
Table des matières
| 1 | |
X | 10 |
XI | 17 |
XII | 30 |
XIII | 38 |
XIV | 57 |
XV | 69 |
XVI | 83 |
XXIX | 180 |
XXX | 188 |
XXXI | 211 |
XXXV | 213 |
XXXVI | 216 |
XXXVII | 220 |
XXXVIII | 234 |
XXXIX | 239 |
XVII | 94 |
XVIII | 103 |
XIX | 110 |
XX | 118 |
XXI | 123 |
XXII | 130 |
XXIII | 139 |
XXIV | 146 |
XXV | 155 |
XL | 243 |
XLI | 249 |
XLII | 255 |
XLIII | 259 |
XLIV | 273 |
XLV | 278 |
| 283 | |
Autres éditions - Tout afficher
Structure and Randomness: Pages from Year One of a Mathematical Blog Terence Tao Aucun aperçu disponible - 2008 |
Expressions et termes fréquents
additive combinatorics algebraic algorithm analogue argument arithmetic progressions article was originally basically blowup coefficients compute conjecture constant convex density discuss dyadic model eigenvalues energy ensemble equation ergodic ergodic theory Euclidean exists exponential fact finitary finite formula Fourier transform function f geometric global graph hard analysis Hilbert transform inequality infinitary infinite convergence principle instance integers Lara Lebesgue linear lower bound Math mathematics matrix measure multiplicative natural numbers Navier-Stokes non-dyadic non-linear non-standard non-standard analysis non-trivial non-zero notation Nullstellensatz number theory obtain orbit originally posted orthogonal pigeonhole principle polynomial prime number prime number theorem problem proof pseudorandom quantities quantum random real numbers regularity lemma result sequence sieve theory singular values SO(Q soft analysis solution space standard Strategy structure subgroup subset sum-product symmetry Szemerédi's theorem theorem Tomb twin prime twin prime conjecture ultrafilter unipotent vector wavelets zero