Recently Ive began to learn real analysis via Rudin. 'AMS lecture: Structure and randomness in the prime numbers'. The reference requests for analysis books have become so numerous as to blot out any usefulness they could conceivably have had. 'Obstructions to uniformity and arithmetic patterns in the primes'. 'Arithmetic progressions and the primes'. Bulletin of the American Mathematical Society. Here are three resources that inform my thinking on. 'The Green–Tao theorem on arithmetic progressions in the primes: an ergodic point of view'. The use of number theory in the teaching and learning of mathematics and in mathematics education research. 'Progressions arithmétiques dans les nombres premiers (d'après B. Providence, RI: American Mathematical Society. 'Long arithmetic progressions of primes'. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. Bulletin of the London Mathematical Society. Terence Chi-Shen 'Terry' Tao FAA FRS ( Chinese: born 17 July 1975) is an Australian-born mathematician. 'Decompositions, approximate structure, transference, and the Hahn–Banach theorem'. Conlon, David Fox, Jacob Zhao, Yufei (2014).'The Gaussian primes contain arbitrarily shaped constellations'. 'Erratum to 'The primes contain arbitrarily long polynomial progressions' '.

'The primes contain arbitrarily long polynomial progressions'. 'A short proof of the multidimensional Szemerédi theorem in the primes'. 'A Multidimensional Szemerédi Theorem in the primes via Combinatorics'. ^ Cook, Brian Magyar, Ákos Titichetrakun, Tatchai (2018).International Mathematics Research Notices. The problem can be traced back to investigations of Lagrange and Waring from around 1770. The proof is an extension of Szemerédi's theorem. In other words, for every natural number k, there exist arithmetic progressions of primes with k terms. The last three sections discuss optional topics. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. In number theory, the Green–Tao theorem, proved by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. An Introduction to Measure Theory by Terrence Tao.

Number theory terrence