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103 Trigonometry Problems by Titu Andreescu,Zuming Feng Pdf
* 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
102 Combinatorial Problems by Titu Andreescu,Zuming Feng Pdf
"102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.
104 Number Theory Problems by Titu Andreescu,Dorin Andrica,Zuming Feng Pdf
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.
Geometry with Trigonometry Second Edition is a second course in plane Euclidean geometry, second in the sense that many of its basic concepts will have been dealt with at school, less precisely. It gets underway with a large section of pure geometry in Chapters 2 to 5 inclusive, in which many familiar results are efficiently proved, although the logical frame work is not traditional. In Chapter 6 there is a convenient introduction of coordinate geometry in which the only use of angles is to handle the perpendicularity or parallelism of lines. Cartesian equations and parametric equations of a line are developed and there are several applications. In Chapter 7 basic properties of circles are developed, the mid-line of an angle-support, and sensed distances. In the short Chaper 8 there is a treatment of translations, axial symmetries and more generally isometries. In Chapter 9 trigonometry is dealt with in an original way which e.g. allows concepts such as clockwise and anticlockwise to be handled in a way which is not purely visual. By the stage of Chapter 9 we have a context in which calculus can be developed. In Chapter 10 the use of complex numbers as coordinates is introduced and the great conveniences this notation allows are systematically exploited. Many and varied topics are dealt with , including sensed angles, sensed area of a triangle, angles between lines as opposed to angles between co-initial half-lines (duo-angles). In Chapter 11 various convenient methods of proving geometrical results are established, position vectors, areal coordinates, an original concept mobile coordinates. In Chapter 12 trigonometric functions in the context of calculus are treated. New to this edition: The second edition has been comprehensively revised over three years Errors have been corrected and some proofs marginally improved The substantial difference is that Chapter 11 has been significantly extended, particularly the role of mobile coordinates, and a more thorough account of the material is given Provides a modern and coherent exposition of geometry with trigonometry for many audiences across mathematics Provides many geometric diagrams for a clear understanding of the text and includes problem exercises for many chapters Generalizations of this material, such as to solid euclidean geometry and conic sections, when combined with calculus, would lead to applications in science, engineering, and elsewhere
Compiled and Solved Problems in Geometry and Trigonometry by Florentin Smarandache Pdf
This book is a translation from Romanian of "Probleme Compilate şi Rezolvate de Geometrie şi Trigonometrie" (University of Kishinev Press, Kishinev, 169 p., 1998), and includes problems of 2D and 3D Euclidean geometry plus trigonometry, compiled and solved from the Romanian Textbooks for 9th and 10th grade students.
115 Trigonometry Problems from the AwesomeMath Summer Program by Titu Andreescu,Vlad Crisan Pdf
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.
In a sense, trigonometry sits at the center of high school mathematics. It originates in the study of geometry when we investigate the ratios of sides in similar right triangles, or when we look at the relationship between a chord of a circle and its arc. It leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. It also has many applications to physics, astronomy, and other branches of science. It is a very old subject. Many of the geometric results that we now state in trigonometric terms were given a purely geometric exposition by Euclid. Ptolemy, an early astronomer, began to go beyond Euclid, using the geometry of the time to construct what we now call tables of values of trigonometric functions. Trigonometry is an important introduction to calculus, where one stud ies what mathematicians call analytic properties of functions. One of the goals of this book is to prepare you for a course in calculus by directing your attention away from particular values of a function to a study of the function as an object in itself. This way of thinking is useful not just in calculus, but in many mathematical situations. So trigonometry is a part of pre-calculus, and is related to other pre-calculus topics, such as exponential and logarithmic functions, and complex numbers.
Trigonometry by Margaret L. Lial,John Hornsby,David I. Schneider Pdf
Allowing students to focus on real-life applications of mathematics. Selected examples feature traditional algebraic as well as optional graphing calculator solutions. We have taken great care to only use this format in examples where the graphing calculator can naturally be used to support and/or enhance the algebraic solution. For those interested in Mathematics.
Mathematical Olympiad Treasures by Titu Andreescu,Bogdan Enescu Pdf
Mathematical Olympiad Treasures aims at building a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts in undergraduate mathematics. The book contains a stimulating collection of problems in the subjects of algebra, geometry, trigonometry, number theory and combinatorics. While it may be considered a sequel to "Mathematical Olympiad Challenges," the focus is on engaging a wider audience to apply techniques and strategies to real-world problems. Throughout the book students are encouraged to express their ideas, conjectures, and conclusions in writing. The goal is to help readers develop a host of new mathematical tools that will be useful beyond the classroom and in a number of disciplines.
A Path to Combinatorics for Undergraduates by Titu Andreescu,Zuming Feng Pdf
This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions. Topics encompass permutations and combinations, binomial coefficients and their applications, bijections, inclusions and exclusions, and generating functions. Each chapter features fully-worked problems, including many from Olympiads and other competitions, as well as a number of problems original to the authors; at the end of each chapter are further exercises to reinforce understanding, encourage creativity, and build a repertory of problem-solving techniques. The authors' previous text, "102 Combinatorial Problems," makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book's unusual problems and examples will interest seasoned mathematicians as well. "A Path to Combinatorics for Undergraduates" is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.
A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.
Learning Trigonometry By Problem Solving by Alexander Rozenblyum,Leonid Rozenblyum Pdf
In this book, trigonometry is presented mainly through the solution of specific problems. The problems are meant to help the reader consolidate their knowledge of the subject. In addition, they serve to motivate and provide context for the concepts, definitions, and results as they are presented. In this way, it enables a more active mastery of the subject, directly linking the results of the theory with their applications. Some historical notes are also embedded in selected chapters.The problems in the book are selected from a variety of disciplines, such as physics, medicine, architecture, and so on. They include solving triangles, trigonometric equations, and their applications. Taken together, the problems cover the entirety of material contained in a standard trigonometry course which is studied in high school and college.We have also added some interesting, in our opinion, entertainment problems. To solve them, no special knowledge is required. While they are not directly related to the subject of the book, they reflect its spirit and contribute to a more lighthearted reading of the material.
CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.
