## 113 Geometric Inequalities from the AwesomeMath Summer Program

**Author**: Adrian Andreescu,Titu Andreescu,Oleg Mushkarov

**Publisher:**N.A

**ISBN:**9780979926983

**Category:**

**Page:**202

**View:**646

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For the curious reader looking to sharpen their arsenal of mathematical strategies on the Olympiad level, 113 Geometric Inequalities from the AwesomeMath Summer Program is a valuable addition. This problem-solving methodology prompts key ideas in other domains such as calculus or complex numbers as the solutions are usually nonstandard in a geometric sense. Nevertheless, trying your hand at these types of inequalities consolidates your mathematical reasoning while exposing you to a broad range of problems, all teeming with insightful inequality-type solutions.

## 115 Trigonometry Problems from the AwesomeMath Summer Program

**Author**: Titu Andreescu,Vlad Crisan

**Publisher:**N.A

**ISBN:**9780999342800

**Category:**Trigonometry

**Page:**200

**View:**7005

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Focusing on Trigonometry reveals a wealth of alternate approaches to solving intricate geometry problems while providing foundational support in other areas of mathematics such as Fourier Analysis and Differential Equations. It is time for Trigonometry to receive the attention it deserves in this stand-alone book where the theory chapter is an invaluable pedagogical resource with lots of examples and guided exercises and the subsequent chapters offer a collection of carefully selected introductory through advanced problems and solutions intended to enhance the problem-solving skills of the reader. This book is not only for those studying for mathematics Olympiads but all individuals who want a better understanding of Trigonometry so they will be more successful in different settings such as a calculus course. This book offers a comprehensive overview of the trigonometric functions and contains a collection of 115 carefully selected introductory and advanced problems in Trigonometry from world-wide renowned Olympiads and mathematical magazines, as well as original problems designed by the authors. Together with the beautiful examples and the creative solutions, the present text is a valuable resource and teaching material for anybody who wants to explore the beauty of Trigonometry.

## 116 Algebraic Inequalities from the AwesomeMath Year-Round Program

**Author**: Titu Andreescu,Marius Stanean

**Publisher:**N.A

**ISBN:**9780996874588

**Category:**Algebra

**Page:**216

**View:**3362

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## Putnam and Beyond

**Author**: Razvan Gelca,Titu Andreescu

**Publisher:**Springer Science & Business Media

**ISBN:**038768445X

**Category:**Mathematics

**Page:**798

**View:**7005

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Putnam and Beyond takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis in one and several variables, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research.

## 112 Combinatorial Problems from the AwesomeMath Summer Program

**Author**: Elizabeth Reiland,VLAD. MATEI

**Publisher:**N.A

**ISBN:**9780996874526

**Category:**

**Page:**196

**View:**6392

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This book aims to give students a chance to begin exploring some introductory to intermediate topics in combinatorics, a fascinating and accessible branch of mathematics centered around (among other things) counting various objects and sets. We include chapters featuring tools for solving counting problems, proof techniques, and more to give students a broad foundation to build on. The only prerequisites are a solid background in arithmetic, some basic algebra, and a love for learning math.

## 109 Inequalities from the AwesomeMath Summer Program

**Author**: Titu Andreescu,Adithya Ganesh

**Publisher:**Xyz Press

**ISBN:**9780988562288

**Category:**Mathematics

**Page:**203

**View:**5278

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109 Inequalities from the AwesomeMath Summer Program aims to convey the theory and techniques involved in proving algebraic inequalities. Each chapter begins with a theoretical part, in which several classical theorems are stated and proven. These include the fundamental Arithmetic-Geometric Mean and Cauchy-Schwarz inequalities, as well as the Nesbitt, Schur, Hlder, Rearrangement, and Chebyshev inequalities. Numerous examples are provided to illustrate the subtleties involved in applying these inequalities. Problems range from relatively easy to extremely challenging, benefiting both beginners and veteran problem solvers alike. To help the reader hone their skills, 109 inequality problems are provided, of which 54 are introductory and 55 are advanced. Detailed solutions to all of these problems are given, in which an eclectic medley of ideas are employed.

## Number Theory

*Concepts and Problems*

**Author**: Titu Andreescu,Gabriel Dospinescu,Oleg Mushkarov

**Publisher:**N.A

**ISBN:**9780988562202

**Category:**Number theory

**Page:**686

**View:**7189

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Challenge your problem-solving aptitude in number theory with powerful problems that have concrete examples which reflect the potential and impact of theoretical results. Each chapter focuses on a fundamental concept or result, reinforced by each of the subsections, with scores of challenging problems that allow you to comprehend number theory like never before. All students and coaches wishing to excel in math competitions will benefit from this book as will mathematicians and adults who enjoy interesting mathematics.

## The Geometry of Remarkable Elements

*Points, Lines, and Circles*

**Author**: Constantin Mihalescu

**Publisher:**N.A

**ISBN:**9780996874519

**Category:**

**Page:**580

**View:**8617

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The book we are proposing here to the English-speaking reader is one that would have qualified at the beginning of the previous century as a book of "Modern Geometry" of the triangle and quadrilateral. Most of the results were obtained in the second half of the 19th century and the first half of the 20th century. The author was a retired artillery colonel and an enthusiastic amateur mathematician. This should come as no surprise, as for any artillery officer mathematics (and, especially, geometry) plays an important part in his formation. As the title surely suggests, this book is a rich collection of some of the most important properties of numerous points, lines, and circles related to triangles and quadrilaterals, as they were known by the mid-1950s. These include the nine-point circle, the Simson line, the orthopolar triangles, the orthopole, the Gergonne and Nagel points, the Miquel point and circle, the Carnot circle, the Brocard points, the Lemoine point and circles, the Newton-Gauss line, and many others. It was, probably, one of the most complete descriptions of the subject at the moment of the writing. The book was primarily addressed to young students but will be of interest to problem solvers in elementary geometry as well. Even geometers will find here new problems to inspire them.

## Problems from the Book

**Author**: Titu Andreescu,Gabriel Dospinescu

**Publisher:**Amer Mathematical Society

**ISBN:**9780979926907

**Category:**Mathematics

**Page:**554

**View:**4093

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## 103 Trigonometry Problems

*From the Training of the USA IMO Team*

**Author**: Titu Andreescu,Zuming Feng

**Publisher:**Springer Science & Business Media

**ISBN:**9780817644321

**Category:**Mathematics

**Page:**214

**View:**8330

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* Problem-solving tactics and practical test-taking techniques provide in-depth enrichment and preparation for various math competitions * Comprehensive introduction to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry * A cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training

## 111 Problems in Algebra and Number Theory

**Author**: Adrian Andreescu,Vinjai Vale

**Publisher:**N.A

**ISBN:**9780996874502

**Category:**

**Page:**230

**View:**7584

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Algebra plays a fundamental role not only in mathematics, but also in various other scientific fields. Without algebra there would be no uniform language to express concepts such as numbers' properties. Thus one must be well-versed in this domain in order to improve in other mathematical disciplines. We cover algebra as its own branch of mathematics and discuss important techniques that are also applicable in many Olympiad problems. Number theory too relies heavily on algebraic machinery. Often times, the solutions to number theory problems involve several steps. Such a solution typically consists of solving smaller problems originating from a hypothesis and ending with a concrete statement that is directly equivalent to or implies the desired condition. In this book, we introduce a solid foundation in elementary number theory, focusing mainly on the strategies which come up frequently in junior-level Olympiad problems.

## 110 Geometry Problems for the International Mathematical Olympiad

**Author**: Titu Andreescu,Cosmin Pohoata

**Publisher:**Xyz Press

**ISBN:**9780988562226

**Category:**Mathematics

**Page:**249

**View:**4040

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110 Geometry Problems for the International Mathematical Olympiads represents a collection of carefully selected geometry problems designed for passionate geometers and students preparing for the IMO. Assuming the theory and the techniques presented in 106 and 107, the book presents a multitude of beautiful synthetic solutions that are meant to give a sense of how one should think about difficult geometry problems. On average, each problem comes with at least two such solutions and with additional remarks about the underlying configuration.

## Cuban Math Olympiad

**Author**: Robert Bosch

**Publisher:**N.A

**ISBN:**9780996874540

**Category:**

**Page:**200

**View:**1487

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## 104 Number Theory Problems

*From the Training of the USA IMO Team*

**Author**: Titu Andreescu,Dorin Andrica,Zuming Feng

**Publisher:**Springer Science & Business Media

**ISBN:**9780817645618

**Category:**Mathematics

**Page:**204

**View:**7989

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This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.

## Number Theory

*Structures, Examples, and Problems*

**Author**: Titu Andreescu,Dorin Andrica

**Publisher:**Springer Science & Business Media

**ISBN:**9780817646455

**Category:**Mathematics

**Page:**384

**View:**1425

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This introductory textbook takes a problem-solving approach to number theory, situating each concept within the framework of an example or a problem for solving. Starting with the essentials, the text covers divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Included are sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems. By emphasizing examples and applications the authors motivate and engage readers.

## Lemmas in Olympiad Geometry

**Author**: Titu Andreescu,Cosmin Pohoata,Sam Korsky

**Publisher:**N.A

**ISBN:**9780988562233

**Category:**

**Page:**369

**View:**6643

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This book showcases the synthetic problem-solving methods which frequently appear in modern day Olympiad geometry, in the way we believe they should be taught to someone with little familiarity in the subject. In some sense, the text also represents an unofficial sequel to the recent problem collection published by XYZ Press, 110 Geometry Problems for the International Mathematical Olympiad, written by the first and third authors, but the two books can be studied completely independently of each other. The work is designed as a medley of the important Lemmas in classical geometry in a relatively linear fashion: gradually starting from Power of a Point and common results to more sophisticated topics, where knowing a lot of techniques can prove to be tremendously useful. We treat each chapter as a short story of its own and include numerous solved exercises with detailed explanations and related insights that will hopefully make your journey very enjoyable.

## Mathematics Under the Microscope

*Notes on Cognitive Aspects of Mathematical Practice*

**Author**: Alexandre Borovik

**Publisher:**American Mathematical Soc.

**ISBN:**0821847619

**Category:**Mathematics

**Page:**317

**View:**8818

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The author's goal is to start a dialogue between mathematicians and cognitive scientists. He discusses, from a working mathematician's point of view, the mystery of mathematical intuition: why are certain mathematical concepts more intuitive than others? To what extent does the ``small scale'' structure of mathematical concepts and algorithms reflect the workings of the human brain? What are the ``elementary particles'' of mathematics that build up the mathematical universe? The book is saturated with amusing examples from a wide range of disciplines--from turbulence to error-correcting codes to logic--as well as with just puzzles and brainteasers. Despite the very serious subject matter, the author's approach is lighthearted and entertaining. This is an unusual and unusually fascinating book. Readers who never thought about mathematics after their school years will be amazed to discover how many habits of mind, ideas, and even material objects that are inherently mathematical serve as building blocks of our civilization and everyday life. A professional mathematician, reluctantly breaking the daily routine, or pondering on some resisting problem, will open this book and enjoy a sudden return to his or her young days when mathematics was fresh, exciting, and holding all promises. And do not take the word ``microscope'' in the title too literally: in fact, the author looks around, in time and space, focusing in turn on a tremendous variety of motives, from mathematical ``memes'' (genes of culture) to an unusual life of a Hollywood star. --Yuri I. Manin, Max-Planck Institute of Mathematics, Bonn, and Northwestern University

## Titu Andreescu and Mark Saul

**Author**: Titu Andreescu,Mark Saul

**Publisher:**American Mathematical Soc.

**ISBN:**1470434644

**Category:**Geometry, Algebraic

**Page:**124

**View:**3676

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This book starts with simple arithmetic inequalities and builds to sophisticated inequality results such as the Cauchy-Schwarz and Chebyshev inequalities. Nothing beyond high school algebra is required of the student. The exposition is lean. Most of the learning occurs as the student engages in the problems posed in each chapter. And the learning is not “linear”. The central topic of inequalities is linked to others in mathematics. Often these topics relate to much more than algebraic inequalities. There are also “secret” pathways through the book. Each chapter has a subtext, a theme which prepares the student for learning other mathematical topics, concepts, or habits of mind. For example, the early chapters on the arithmetic mean/geometric mean inequality show how very simple observations can be leveraged to yield useful and interesting results. Later chapters give examples of how one can generalize a mathematical statement. The chapter on the Cauchy-Schwarz inequality provides an introduction to vectors as mathematical objects. And there are many other secret pathways that the authors hope the reader will discover—and follow. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

## Solving Problems in Geometry

*Insights and Strategies*

**Author**: Kim Hoo Hang,Haibin Wang

**Publisher:**World Scientific Publishing Company

**ISBN:**9814583766

**Category:**

**Page:**356

**View:**2091

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This new volume of the Mathematical Olympiad Series focuses on the topic of geometry. Basic and advanced theorems commonly seen in Mathematical Olympiad are introduced and illustrated with plenty of examples. Special techniques in solving various types of geometrical problems are also introduced, while the authors elaborate extensively on how to acquire an insight and develop strategies in tackling difficult geometrical problems. This book is suitable for any reader with elementary geometrical knowledge at the lower secondary level. Each chapter includes sufficient scaffolding and is comprehensive enough for the purpose of self-study. Readers who complete the chapters on the basic theorems and techniques would acquire a good foundation in geometry and may attempt to solve many geometrical problems in various mathematical competitions. Meanwhile, experienced contestants in Mathematical Olympiad competitions will find a large collection of problems pitched at competitions at the international level, with opportunities to practise and sharpen their problem-solving skills in geometry. Request Inspection Copy