Polynomial Methods and Incidence Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Polynomial Methods and Incidence Theory write by Adam Sheffer. This book was released on 2022-03-24. Polynomial Methods and Incidence Theory available in PDF, EPUB and Kindle. A thorough yet accessible introduction to the mathematical breakthroughs achieved by using new polynomial methods in the past decade.
Polynomial Methods and Incidence Theory
Polynomial Methods and Incidence Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Polynomial Methods and Incidence Theory write by Adam Sheffer. This book was released on 2022-03-24. Polynomial Methods and Incidence Theory available in PDF, EPUB and Kindle. The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdős's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. There has also been significant progress on a variety of problems from additive combinatorics, discrete geometry, and more. This book gives a detailed yet accessible introduction to these new polynomial methods and their applications, with a focus on incidence theory. Based on the author's own teaching experience, the text requires a minimal background, allowing graduate and advanced undergraduate students to get to grips with an active and exciting research front. The techniques are presented gradually and in detail, with many examples, warm-up proofs, and exercises included. An appendix provides a quick reminder of basic results and ideas.
Polynomial Methods in Combinatorics
Polynomial Methods in Combinatorics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Polynomial Methods in Combinatorics write by Larry Guth. This book was released on 2016-06-10. Polynomial Methods in Combinatorics available in PDF, EPUB and Kindle. This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book.
Polynomial Methods in Statistical Inference
Polynomial Methods in Statistical Inference - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Polynomial Methods in Statistical Inference write by Yihong Wu. This book was released on 2020-10-12. Polynomial Methods in Statistical Inference available in PDF, EPUB and Kindle. The authors of this monograph survey a suite of techniques based on the theory of polynomials, collectively referred to as polynomial methods. These techniques provide useful tools not only for the design of highly practical algorithms with provable optimality, but also for establishing the fundamental limits of inference problems through moment matching. The authors demonstrate the effectiveness of the polynomial method using concrete problems such as entropy and support size estimation, distinct elements problem, and learning Gaussian mixture models. This monograph provides a comprehensive, yet concise, overview of the theory covering topics such as polynomial approximation, polynomial interpolation and majorization, moment space and positive polynomials, orthogonal polynomials and Gaussian quadrature. The authors proceed to show the applications of the theory in statistical inference. Polynomial Methods in Statistical Inference provides students, and researchers with an accessible and complete treatment of a subject that has recently been used to solve many challenging problems in statistical inference.
Graph Theory and Additive Combinatorics
Graph Theory and Additive Combinatorics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Graph Theory and Additive Combinatorics write by Yufei Zhao. This book was released on 2023-07-31. Graph Theory and Additive Combinatorics available in PDF, EPUB and Kindle. An introductory text covering classical and modern developments in graph theory and additive combinatorics, based on Zhao's MIT course.
