Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the various tactics involved in solving mathematical problems at the Mathematical Olympiad level. Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout. Assuming only a basic level of mathematics, the text is ideal for students of 14 years and above in pure mathematics.

Solving Mathematical Problems: A Personal Perspective

Science & Math

TAO, TERENCE

Mathematics

Oxford University Press

Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the various tactics involved in solving mathematical problems at the Mathematical Olympiad level. Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout. Assuming only a basic level of mathematics, the text is ideal for students of 14 years and above in pure mathematics.

Additive Combinatorics (Cambridge Studies in Advanced Mathematics, Series Number 105)

Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemerédi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.

Cambridge University Press

A graduate-level text bringing together the tools from different fields used in additive combinatorics.

Additive Combinatorics ICM Edition (Cambridge Studies in Advanced Mathematics)

Vu, Van H.

Poincare's Legacies: Pages from Year Two of a Mathematical Blog

American Mathematical Society(RI)

In 2007 Terry Tao began a mathematical blog to cover a variety of topics, ranging from his own research and other recent developments in mathematics, to lecture notes for his classes, to nontechnical puzzles and expository articles. The first two years of the blog have already been published by the American Mathematical Society. The posts from the third year are being published in two volumes. The present volume consists of a second course in real analysis, together with related material from the blog. The real analysis course assumes some familiarity with general measure theory, as well as fundamental notions from undergraduate analysis. The text then covers more advanced topics in measure theory, notably the Lebesgue-Radon-Nikodym theorem and the Riesz representation theorem, topics in functional analysis, such as Hilbert spaces and Banach spaces, and the study of spaces of distributions and key function spaces, including Lebesgue's $L^p$ spaces and Sobolev spaces. There is also a discussion of the general theory of the Fourier transform. The second part of the book addresses a number of auxiliary topics, such as Zorn's lemma, the Carathéodory extension theorem, and the Banach-Tarski paradox. Tao also discusses the epsilon regularisation argument--a fundamental trick from soft analysis, from which the book gets its title. Taken together, the book presents more than enough material for a second graduate course in real analysis. The second volume consists of technical and expository articles on a variety of topics and can be read independently.

An Epsilon of Room, I: Real Analysis: Pages from Year Three of a Mathematical Blog (Graduate Studies in Mathematics)

Amer Mathematical Society

An Introduction To Measure Theory

Orient Blackswan

Winner of the 2015 Prose Award for Best Mathematics Book!In the fifth of his famous list of 23 problems, Hilbert asked if every topological group which was locally Euclidean was in fact a Lie group. Through the work of Gleason, Montgomery-Zippin, Yamabe, and others, this question was solved affirmatively; more generally, a satisfactory description of the (mesoscopic) structure of locally compact groups was established. Subsequently, this structure theory was used to prove Gromov's theorem on groups of polynomial growth, and more recently in the work of Hrushovski, Breuillard, Green, and the author on the structure of approximate groups.In this graduate text, all of this material is presented in a unified manner, starting with the analytic structural theory of real Lie groups and Lie algebras (emphasising the role of one-parameter groups and the Baker-Campbell-Hausdorff formula), then presenting a proof of the Gleason-Yamabe structure theorem for locally compact groups (emphasising the role of Gleason metrics), from which the solution to Hilbert's fifth problem follows as a corollary. After reviewing some model-theoretic preliminaries (most notably the theory of ultraproducts), the combinatorial applications of the Gleason-Yamabe theorem to approximate groups and groups of polynomial growth are then given. A large number of relevant exercises and other supplementary material are also provided.

Hilbert's Fifth Problem and Related Topics (Graduate Studies in Mathematics, 153)

L'art de résoudre les problèmes de mathématiques

CASSINI

See the best price to sell, buy, or rent books by TAO, TERENCE. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by TAO, TERENCE

See the best price to sell, buy, or rent books by TAO, TERENCE. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Solving Mathematical Problems: A Personal Perspective

Solving Mathematical Problems: A Personal Perspective

Additive Combinatorics (Cambridge Studies in Advanced Mathematics, Series Number 105)

Additive Combinatorics ICM Edition (Cambridge Studies in Advanced Mathematics)

Additive Combinatorics (Cambridge Studies in Advanced Mathematics, Series Number 105)

Poincare's Legacies: Pages from Year Two of a Mathematical Blog

An Epsilon of Room, I: Real Analysis: Pages from Year Three of a Mathematical Blog (Graduate Studies in Mathematics)

An Introduction To Measure Theory

Hilbert's Fifth Problem and Related Topics (Graduate Studies in Mathematics, 153)

L'art de résoudre les problèmes de mathématiques