{"title":"Avner Ash","description":"\u003cp\u003eAvner Ash’s works invite readers into the fascinating world of mathematics, blending rigorous concepts with accessible storytelling. His books, such as \u003cem\u003eElliptic Tales\u003c\/em\u003e and \u003cem\u003eFearless Symmetry\u003c\/em\u003e, explore deep mathematical ideas with clarity and engaging narrative, making complex subjects approachable for both enthusiasts and scholars.\u003c\/p\u003e\n\n\u003cp\u003eSituated at the crossroads of education and science, Ash’s writings illuminate number theory and advanced mathematics while honouring their historical and cultural contexts. These titles serve as a thoughtful introduction to mathematical beauty and logical wonder for curious minds.\u003c\/p\u003e","products":[{"product_id":"fearless-symmetry-by-robert-gross-9780691138718","title":"Fearless Symmetry","description":"\u003cdiv class=\"book-description\"\u003e\n\u003cp\u003eMathematicians solve equations, or try to. But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, \u003cem\u003eFearless Symmetry\u003c\/em\u003e is the first popular math book to discuss these elegant and mysterious patterns and the ingenious techniques mathematicians use to uncover them.\u003c\/p\u003e\n\n\u003cp\u003eHidden symmetries were first discovered nearly two hundred years ago by French mathematician Évariste Galois. They have been used extensively in the oldest and largest branch of mathematics—number theory—for such diverse applications as acoustics, radar, and codes and ciphers. They have also been employed in the study of Fibonacci numbers and to tackle well-known problems such as Fermat's Last Theorem, Pythagorean Triples, and the ever-elusive Riemann Hypothesis.\u003c\/p\u003e\n\n\u003cp\u003eMathematicians are still devising techniques for teasing out these mysterious patterns, and their uses are limited only by the imagination. The first popular book to address representation theory and reciprocity laws, \u003cem\u003eFearless Symmetry\u003c\/em\u003e focuses on how mathematicians solve equations and prove theorems. It discusses rules of mathematics and why they are just as important as those in any game one might play.\u003c\/p\u003e\n\n\u003cp\u003eThe book starts with basic properties of integers and permutations and reaches current research in number theory. Along the way, it takes delightful historical and philosophical digressions. Required reading for all math buffs, the book will appeal to anyone curious about popular mathematics and its myriad contributions to everyday life.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"NewSouth Books","offers":[{"title":"Default Title","offer_id":46998079504620,"sku":"9780691138718","price":86.0,"currency_code":"NZD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0705\/7784\/8556\/files\/1374323482434.jpg?v=1763207732"},{"product_id":"elliptic-tales-by-robert-gross-9780691163505","title":"Elliptic Tales","description":"\u003cdiv class=\"book-description\"\u003e\n\u003cp\u003e\u003cem\u003eElliptic Tales\u003c\/em\u003e describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics—the Birch and Swinnerton-Dyer Conjecture.\u003c\/p\u003e\n\n\u003cp\u003eIn this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjecture lies in elliptic curves, which may appear simple, but arise from some very deep—and often very mystifying—mathematical ideas.\u003c\/p\u003e\n\n\u003cp\u003eUsing only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and, in the process, venture to the very frontiers of modern mathematics.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"NewSouth Books","offers":[{"title":"Default Title","offer_id":47460720312556,"sku":"9780691163505","price":50.0,"currency_code":"NZD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0705\/7784\/8556\/files\/9780691163505-elliptic-tales.jpg?v=1774951915"},{"product_id":"summing-it-up-by-robert-gross-9780691178516","title":"Summing It Up","description":"\u003cdiv class=\"book-description\"\u003e\n\u003cp\u003eWe use addition on a daily basis—yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? \u003cem\u003eSumming It Up\u003c\/em\u003e uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems.\u003c\/p\u003e\n\n\u003cp\u003eMathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research. Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds.\u003c\/p\u003e\n\n\u003cp\u003eEmploying college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series—long sums that can only be defined by the concept of limit, as in the example of 1+1\/2+1\/4+...=?\u003c\/p\u003e\n\n\u003cp\u003eWith the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms—the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem.\u003c\/p\u003e\n\n\u003cp\u003eAppropriate for numbers novices as well as college math majors, \u003cem\u003eSumming It Up\u003c\/em\u003e delves into mathematics that will enlighten anyone fascinated by numbers.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"NewSouth Books","offers":[{"title":"Default Title","offer_id":47471653617900,"sku":"9780691178516","price":70.0,"currency_code":"NZD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0705\/7784\/8556\/files\/9780691178516-summing-it-up.jpg?v=1775248767"}],"url":"https:\/\/bookhero.pro\/collections\/avner-ash.oembed","provider":"Book Hero","version":"1.0","type":"link"}