a mathematical orchard problems and solutions

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A Mathematical Orchard

Author : Mark I. Krusemeyer
ISBN : 9780883858332
Genre : Mathematics
File Size : 26. 36 MB
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This volume is a republication and expansion of the much-loved Wohascum County Problem Book, published in 1993. The original 130 problems have been retained and supplemented by an additional 78 problems. The puzzles contained within, which are accessible but never routine, have been specially selected for their mathematical appeal, and detailed solutions are provided. The reader will encounter puzzles involving calculus, algebra, discrete mathematics, geometry and number theory, and the volume includes an appendix identifying the prerequisite knowledge for each problem. A second appendix organises the problems by subject matter so that readers can focus their attention on particular types of problems if they wish. This collection will provide enjoyment for seasoned problem solvers and for those who wish to hone their skills.

A Gentle Introduction To The American Invitational Mathematics Exam

Author : Scott A. Annin
ISBN : 9780883858356
Genre : Mathematics
File Size : 27. 9 MB
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This book is a celebration of mathematical problem solving at the level of the high school American Invitational Mathematics Examination. There is no other book on the market focused on the AIME. It is intended, in part, as a resource for comprehensive study and practice for the AIME competition for students, teachers, and mentors. After all, serious AIME contenders and competitors should seek a lot of practice in order to succeed. However, this book is also intended for anyone who enjoys solving problems as a recreational pursuit. The AIME contains many problems that have the power to foster enthusiasm for mathematics – the problems are fun, engaging, and addictive. The problems found within these pages can be used by teachers who wish to challenge their students, and they can be used to foster a community of lovers of mathematical problem solving! There are more than 250 fully-solved problems in the book, containing examples from AIME competitions of the 1980’s, 1990’s, 2000’s, and 2010’s. In some cases, multiple solutions are presented to highlight variable approaches. To help problem-solvers with the exercises, the author provides two levels of hints to each exercise in the book, one to help stuck starters get an idea how to begin, and another to provide more guidance in navigating an approach to the solution.

Euclidean Geometry In Mathematical Olympiads

Author : Evan Chen
ISBN : 9780883858394
Genre : Mathematics
File Size : 53. 17 MB
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This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains as selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads, or for teachers looking for a text for an honor class.


Author : James Tanton
ISBN : 9780883858363
Genre : Mathematics
File Size : 35. 25 MB
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This guide covers the story of trigonometry. It is a swift overview, but it is complete in the context of the content discussed in beginning and advanced high-school courses. The purpose of these notes is to supplement and put into perspective the material of any course on the subject you may have taken or are currently taking. (These notes will be tough going for those encountering trigonometry for the very first time!)

Fibonacci And Catalan Numbers

Author : Ralph Grimaldi
ISBN : 9781118159767
Genre : Mathematics
File Size : 23. 83 MB
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Discover the properties and real-world applications of the Fibonacci and the Catalan numbers With clear explanations and easy-to-follow examples, Fibonacci and Catalan Numbers: An Introduction offers a fascinating overview of these topics that is accessible to a broad range of readers. Beginning with a historical development of each topic, the book guides readers through the essential properties of the Fibonacci numbers, offering many introductory-level examples. The author explains the relationship of the Fibonacci numbers to compositions and palindromes, tilings, graph theory, and the Lucas numbers. The book proceeds to explore the Catalan numbers, with the author drawing from their history to provide a solid foundation of the underlying properties. The relationship of the Catalan numbers to various concepts is then presented in examples dealing with partial orders, total orders, topological sorting, graph theory, rooted-ordered binary trees, pattern avoidance, and the Narayana numbers. The book features various aids and insights that allow readers to develop a complete understanding of the presented topics, including: Real-world examples that demonstrate the application of the Fibonacci and the Catalan numbers to such fields as sports, botany, chemistry, physics, and computer science More than 300 exercises that enable readers to explore many of the presented examples in greater depth Illustrations that clarify and simplify the concepts Fibonacci and Catalan Numbers is an excellent book for courses on discrete mathematics, combinatorics, and number theory, especially at the undergraduate level. Undergraduates will find the book to be an excellent source for independent study, as well as a source of topics for research. Further, a great deal of the material can also be used for enrichment in high school courses.

Mathematics Galore

Author : James Tanton
ISBN : 9780883857762
Genre : Mathematics
File Size : 86. 31 MB
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Mathematics Galore! Showcases some of the best activities and student outcomes of the St. Mark's Institute of Mathematics and invites you to engage the mathematics yourself! Revel in the delight of deep intellectual play and marvel at the heights to which young scholars can rise. See some great mathematics explained and proved via natural and accessible means.Based on 26 essays (“newsletters”) and eight additional pieces, Mathematics Galore! offers a large sample of mathematical tidbits and treasures, each immediately enticing, and each a gateway to layers of surprising depth and conundrum. Pick and read essays in no particular order and enjoy the mathematical stories that unfold. Be inspired for your courses, your math clubs and your math circles, or simply enjoy for yourself the bounty of research questions and intriguing puzzlers that lie within.

Challenging Mathematical Problems With Elementary Solutions

Author : ?. ? ?????
ISBN : 9780486655376
Genre : Mathematics
File Size : 39. 86 MB
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Volume II of a two-part series, this book features 74 problems from various branches of mathematics. Topics include points and lines, topology, convex polygons, theory of primes, and other subjects. Complete solutions.

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