113 Geometric Inequalities from the AwesomeMath Summer Program


Author: Adrian Andreescu,Titu Andreescu,Oleg Mushkarov
Publisher: N.A
ISBN: 9780979926983
Category:
Page: 202
View: 3626
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.

112 Combinatorial Problems from the AwesomeMath Summer Program


Author: Elizabeth Reiland,VLAD. MATEI
Publisher: N.A
ISBN: 9780996874526
Category:
Page: 196
View: 4462
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.

    • Trigonometry

115 Trigonometry Problems from the AwesomeMath Summer Program


Author: Titu Andreescu,Vlad Crisan
Publisher: N.A
ISBN: 9780999342800
Category: Trigonometry
Page: 200
View: 8692
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.

The Geometry of Remarkable Elements

Points, Lines, and Circles
Author: Constantin Mihalescu
Publisher: N.A
ISBN: 9780996874519
Category:
Page: 580
View: 2552
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.

    • Mathematics

Putnam and Beyond


Author: Razvan Gelca,Titu Andreescu
Publisher: Springer Science & Business Media
ISBN: 038768445X
Category: Mathematics
Page: 798
View: 319
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.

    • Mathematics

109 Inequalities from the AwesomeMath Summer Program


Author: Titu Andreescu,Adithya Ganesh
Publisher: Xyz Press
ISBN: 9780988562288
Category: Mathematics
Page: 203
View: 8161
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.

    • Mathematics

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: 9442
* 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

    • Mathematics

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: 8476
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.

    • Mathematics

Problems from the Book


Author: Titu Andreescu,Gabriel Dospinescu
Publisher: Amer Mathematical Society
ISBN: 9780979926907
Category: Mathematics
Page: 554
View: 5079

111 Problems in Algebra and Number Theory


Author: Adrian Andreescu,Vinjai Vale
Publisher: N.A
ISBN: 9780996874502
Category:
Page: 230
View: 6766
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.

Cuban Math Olympiad


Author: Robert Bosch
Publisher: N.A
ISBN: 9780996874540
Category:
Page: 200
View: 9088

    • Number theory

Number Theory

Concepts and Problems
Author: Titu Andreescu,Gabriel Dospinescu,Oleg Mushkarov
Publisher: N.A
ISBN: 9780988562202
Category: Number theory
Page: 686
View: 3006
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.

    • Mathematics

110 Geometry Problems for the International Mathematical Olympiad


Author: Titu Andreescu,Cosmin Pohoata
Publisher: Xyz Press
ISBN: 9780988562226
Category: Mathematics
Page: 249
View: 2655
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.

    • Mathematics

Straight from the Book


Author: Titu Andreescu,Gabriel Dospinescu
Publisher: Amer Mathematical Society
ISBN: 9780979926938
Category: Mathematics
Page: 590
View: 3006
This book is a compilation of many suggestions, much advice, and even more hard work. Its main objective is to provide solutions to the problems which were originally proposed in the first 12 chapters of Problems from the Book. The volume is far more than a collection of solutions. The solutions are used as motivation for the introduction of some very clear mathematical expositions. This is absolutely state-of-the-art material. Everyone who loves mathematics and mathematical thinking should acquire this book.

    • Mathematics

Number Theory

Structures, Examples, and Problems
Author: Titu Andreescu,Dorin Andrica
Publisher: Springer Science & Business Media
ISBN: 9780817646455
Category: Mathematics
Page: 384
View: 482
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.

    • Mathematics

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: 6635
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

    • Mathematics

Essential Linear Algebra with Applications

A Problem-Solving Approach
Author: Titu Andreescu
Publisher: Springer
ISBN: 0817646361
Category: Mathematics
Page: 491
View: 3357
Rooted in a pedagogically successful problem-solving approach to linear algebra, the present work fills a gap in the literature that is sharply divided between elementary texts and books that are too advanced to appeal to a wide audience. It clearly develops the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality, while simultaneously emphasizing applications and connections to fields such as biology, economics, computer graphics, electrical engineering, cryptography, and political science. Ideal as an introduction to linear algebra, the extensive exercises and well-chosen applications also make this text suitable for advanced courses at the junior or senior undergraduate level. Furthermore, it can serve as a colorful supplementary problem book, reference, or self-study manual for professional scientists and mathematicians. Complete with bibliography and index, "Essential Linear Algebra with Applications" is a natural bridge between pure and applied mathematics and the natural and social sciences, appropriate for any student or researcher who needs a strong footing in the theory, problem-solving, and model-building that are the subject’s hallmark.

Solving Problems in Geometry

Insights and Strategies
Author: Kim Hoo Hang,Haibin Wang
Publisher: World Scientific Publishing Company
ISBN: 9814583766
Category:
Page: 356
View: 9077
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

    • Mathematics

Complex Numbers from A to ... Z


Author: Titu Andreescu,Dorin Andrica
Publisher: Springer Science & Business Media
ISBN: 0817684158
Category: Mathematics
Page: 391
View: 4078
* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory