Sum of Squares: Theory and Applications - 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 Sum of Squares: Theory and Applications write by Pablo A. Parrilo. This book was released on . Sum of Squares: Theory and Applications available in PDF, EPUB and Kindle. This volume is based on lectures delivered at the 2019 AMS Short Course “Sum of Squares: Theory and Applications”, held January 14–15, 2019, in Baltimore, Maryland. This book provides a concise state-of-the-art overview of the theory and applications of polynomials that are sums of squares. This is an exciting and timely topic, with rich connections to many areas of mathematics, including polynomial and semidefinite optimization, real and convex algebraic geometry, and theoretical computer science. The six chapters introduce and survey recent developments in this area; specific topics include the algebraic and geometric aspects of sums of squares and spectrahedra, lifted representations of convex sets, and the algorithmic and computational implications of viewing sums of squares as a meta algorithm. The book also showcases practical applications of the techniques across a variety of areas, including control theory, statistics, finance and machine learning.
Sums of Squares of Integers
Sums of Squares of Integers - 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 Sums of Squares of Integers write by Carlos J. Moreno. This book was released on 2005-12-09. Sums of Squares of Integers available in PDF, EPUB and Kindle. Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's element
Sums of Squares of Integers
Sums of Squares of Integers - 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 Sums of Squares of Integers write by Carlos J. Moreno. This book was released on 2005-12-09. Sums of Squares of Integers available in PDF, EPUB and Kindle. Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's elementary methods with the analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representations of an integer n as the sum of s squares of integers for any s and n. It is also the first book to give a proof of Szemeredi's theorem, and is the first number theory book to discuss how the modern theory of modular forms complements and clarifies the classical fundamental results about sums of squares. The book presents several existing, yet still interesting and instructive, examples of modular forms. Two chapters develop useful properties of the Bernoulli numbers and illustrate arithmetic progressions, proving the theorems of van der Waerden, Roth, and Szemeredi. The book also explains applications of the theory to three problems that lie outside of number theory in the areas of cryptanalysis, microwave radiation, and diamond cutting. The text is complemented by the inclusion of over one hundred exercises to test the reader's understanding.
From Great Discoveries in Number Theory to Applications
From Great Discoveries in Number Theory to Applications - 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 From Great Discoveries in Number Theory to Applications write by Michal Křížek. This book was released on 2021-09-21. From Great Discoveries in Number Theory to Applications available in PDF, EPUB and Kindle. This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital signatures, hashing functions, generators of pseudorandom numbers, and the RSA method based on large prime numbers. A diverse array of topics is covered, from the properties and applications of prime numbers, some surprising connections between number theory and graph theory, pseudoprimes, Fibonacci and Lucas numbers, and the construction of Magic and Latin squares, to the mathematics behind Prague’s astronomical clock. Introducing a general mathematical audience to some of the basic ideas and algebraic methods connected with various types of natural numbers, the book will provide invaluable reading for amateurs and professionals alike.
From Polynomials to Sums of Squares
From Polynomials to Sums of Squares - 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 From Polynomials to Sums of Squares write by T.H Jackson. This book was released on 2023-05-09. From Polynomials to Sums of Squares available in PDF, EPUB and Kindle. From Polynomials to Sums of Squares describes a journey through the foothills of algebra and number theory based around the central theme of factorization. The book begins by providing basic knowledge of rational polynomials, then gradually introduces other integral domains, and eventually arrives at sums of squares of integers. The text is complemented with illustrations that feature specific examples. Other than familiarity with complex numbers and some elementary number theory, very little mathematical prerequisites are needed. The accompanying disk enables readers to explore the subject further by removing the tedium of doing calculations by hand. Throughout the text there are practical activities involving the computer.
