{"title":"Ellina Grigorieva","description":null,"products":[{"product_id":"methods-of-solving-complex-geometry-problems-book-ellina-grigorieva-9783319007045","title":"Methods of Solving Complex Geometry Problems","description":"This book is a unique collection of challenging geometry problems and detailed solutions that will build students’ confidence in mathematics. By proposing several methods to approach each problem and emphasizing geometry’s connections with different fields of mathematics, Methods of Solving Complex Geometry Problems serves as a bridge to more advanced problem solving.  Written by an accomplished female mathematician who struggled with geometry as a child, it does not intimidate, but instead fosters the reader’s ability to solve math problems through the direct application of theorems.     Containing over 160 complex problems with hints and detailed solutions, Methods of Solving Complex Geometry Problems can be used as a self-study guide for mathematics competitions and for improving problem-solving skills in courses on plane geometry or the history of mathematics. It contains important and sometimes overlooked topics on triangles, quadrilaterals, and circles such as the Menelaus-Ceva theorem, Simson’s line, Heron’s formula, and the theorems of the three altitudes and medians. It can also be used by professors as a resource to stimulate the abstract thinking required to transcend the tedious and routine, bringing forth the original thought of which their students are capable.     Methods of Solving Complex Geometry Problems will interest high school and college students needing to prepare for exams and competitions, as well as anyone who enjoys an intellectual challenge and has a special love of geometry. It will also appeal to instructors of geometry, history of mathematics, and math education courses.","brand":"WoB","offers":[{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50246843171089,"sku":"CIN3319007041VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3319007041.jpg?v=1751252610"},{"product_id":"methods-of-solving-complex-geometry-problems-book-ellina-grigorieva-9783319375625","title":"Methods of Solving Complex Geometry Problems","description":"This book is a unique collection of challenging geometry problems and detailed solutions that will build students’ confidence in mathematics. By proposing several methods to approach each problem and emphasizing geometry’s connections with different fields of mathematics, Methods of Solving Complex Geometry Problems serves as a bridge to more advanced problem solving.  Written by an accomplished female mathematician who struggled with geometry as a child, it does not intimidate, but instead fosters the reader’s ability to solve math problems through the direct application of theorems.     Containing over 160 complex problems with hints and detailed solutions, Methods of Solving Complex Geometry Problems can be used as a self-study guide for mathematics competitions and for improving problem-solving skills in courses on plane geometry or the history of mathematics. It contains important and sometimes overlooked topics on triangles, quadrilaterals, and circles such as the Menelaus-Ceva theorem, Simson’s line, Heron’s formula, and the theorems of the three altitudes and medians. It can also be used by professors as a resource to stimulate the abstract thinking required to transcend the tedious and routine, bringing forth the original thought of which their students are capable.     Methods of Solving Complex Geometry Problems will interest high school and college students needing to prepare for exams and competitions, as well as anyone who enjoys an intellectual challenge and has a special love of geometry. It will also appeal to instructors of geometry, history of mathematics, and math education courses.","brand":"WoB","offers":[{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50396853174545,"sku":"CIN3319375628VG","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52588201541905,"sku":"NLS9783319375625","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52761245155601,"sku":"NIN9783319375625","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3319375628.jpg?v=1751030763"},{"product_id":"methods-of-solving-number-theory-problems-book-ellina-grigorieva-9783319909141","title":"Methods of Solving Number Theory Problems","description":"Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory. Every technique is followed by problems (as well as detailed hints and solutions) that apply theorems immediately, so readers can solve a variety of abstract problems in a systematic, creative manner. New solutions often require the ingenious use of earlier mathematical concepts - not the memorization of formulas and facts. Questions also often permit experimental numeric validation or visual interpretation to encourage the combined use of deductive and intuitive thinking.   The first chapter starts with simple topics like even and odd numbers, divisibility, and prime numbers and helps the reader to solve quite complex, Olympiad-type problems right away.   It also covers properties of the perfect, amicable, and figurate numbers and introduces congruence.  The next chapter begins with the Euclidean algorithm, explores therepresentations of integer numbers in different bases, and examines continued fractions, quadratic irrationalities, and the Lagrange Theorem. The last section of Chapter Two is an exploration of different methods of proofs. The third chapter is dedicated to solving Diophantine linear and nonlinear equations and includes different methods of solving Fermat’s (Pell’s) equations. It also covers Fermat’s factorization techniques and methods of solving challenging problems involving exponent and factorials. Chapter Four reviews the Pythagorean triple and quadruple and emphasizes their connection with geometry, trigonometry, algebraic geometry, and stereographic projection.  A special case of Waring’s problem as a representation of a number by the sum of the squares or cubes of other numbers is covered, as well as quadratic residuals, Legendre and Jacobi symbols, and interesting word problems related to the properties of numbers. Appendices provide a historic overview of number theory and its main developments from the ancient cultures in Greece, Babylon, and Egypt to the modern day.   Drawing from cases collected by an accomplished female mathematician, Methods in Solving Number Theory Problems is designed as a self-study guide or supplementary textbook for a one-semester course in introductory number theory. It can also be used to prepare for mathematical Olympiads. Elementary algebra, arithmetic and some calculus knowledge are the only prerequisites. Number theory gives precise proofs and theorems of an irreproachable rigor and sharpens analytical thinking, which makes this book perfect for anyone looking to build their mathematical confidence.","brand":"WoB","offers":[{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50397277847825,"sku":"CIN3319909142VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3319909142.jpg?v=1751221159"},{"product_id":"methods-of-solving-sequence-and-series-problems-book-ellina-grigorieva-9783319456850","title":"Methods of Solving Sequence and Series Problems","description":"This book aims to dispel the mystery and fear experienced by students surrounding sequences, series, convergence, and their applications. The author, an accomplished female mathematician, achieves this by taking a problem solving approach, starting with fascinating problems and solving them step by step with clear explanations and illuminating diagrams.  The reader will find the problems interesting, unusual, and fun, yet solved with the rigor expected in a competition. Some problems are taken directly from mathematics competitions, with the name and year of the exam provided for reference.  Proof techniques are emphasized, with a variety of methods presented.  The text aims to expand the mind of the reader by often presenting multiple ways to attack the same problem, as well as drawing connections with different fields of mathematics. Intuitive and visual arguments are presented alongside technical proofs to provide a well-rounded methodology.  With nearly 300 problems including hints, answers, and solutions, Methods of Solving Sequences and Series Problems is an ideal resource for those learning calculus, preparing for mathematics competitions, or just looking for a worthwhile challenge. It can also be used by faculty who are looking for interesting and insightful problems that are not commonly found in other textbooks.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":51323118453009,"sku":"CIN3319456857G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3319456857.jpg?v=1750773154"},{"product_id":"methods-of-solving-solid-geometry-problems-book-ellina-grigorieva-9783031869686","title":"Methods of Solving Solid Geometry Problems","description":"This textbook completes the author’s series of books on solving complex math problems and is aimed at developing readers' geometric thinking to master the skills of solving solid geometry problems. Written in a friendly manner, it discusses many important and sometimes overlooked topics about polyhedra such as their cross sections, unfolding, inscribed and circumscribed solids, and figures of revolution. Over 350 unique problems with detailed solutions and hints are presented throughout the text, many of which are solved in multiple ways to aid readers with different mathematical backgrounds. If the problem is of historical significance or can be related to a similar problem solved in ancient times, its original solution, historical information about its creation and origin of its methods are also included.   Various applications of stereometry are also explored, including those to chemistry, molecular structures, and crystallography. For example, using Euler's formula for a convex polyhedron, the reader will learn how to explain the structure of various chemical compounds, such as how to predict the shape of the truncated icosahedron for the C60 fullerene molecule (the most powerful antioxidant known today) and to prove why the surface of any fullerene C2n consists of n -10 regular hexagons and always only 12 regular pentagons.   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Numerous strategies and techniques are presented that can be used to solve intriguing and challenging problems of the type often found in competitions.  The author uses a friendly, non-intimidating approach to emphasize connections between different fields of mathematics and often proposes several different ways to attack the same problem.  Topics covered include functions and their properties, polynomials, trigonometric and transcendental equations and inequalities, optimization, differential equations, nonlinear systems, and word problems.   Over 360 problemsare included with hints, answers, and detailed solutions.    Methods of Solving Nonstandard Problems will interest high school and college students, whether they are preparing for a math competition or looking to improve their mathematical skills, as well as anyone who enjoys an intellectual challenge and has a special love for mathematics.  Teachers and college professors will be able to use it as an extra resource in the classroom to augment a conventional course of instruction in order to stimulate abstract thinking and inspire original thought.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52500844478737,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":52500845199633,"sku":"NGR9783319369013","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319369013.jpg?v=1760139036"},{"product_id":"methods-of-solving-number-theory-problems-book-ellina-grigorieva-9783030081300","title":"Methods of Solving Number Theory Problems","description":"A special case of Waring's problem as a representation of a number by the sum of the squares or cubes of other numbers is covered, as well as quadratic residuals, Legendre and Jacobi symbols, and interesting word problems related to the properties of numbers.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52595083739409,"sku":"NLS9783030081300","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783030081300.jpg?v=1761070488"}],"url":"https:\/\/www.worldofbooks.com\/en-gb\/collections\/author-books-by-ellina-grigorieva.oembed","provider":"World of Books ","version":"1.0","type":"link"}