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Author: Ellina Grigorieva
Publisher: Birkhäuser
ISBN: 3319909150
Category : Mathematics
Languages : en
Pages : 405
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Book 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 the representations 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.
Author: Arthur Benjamin
Publisher: Crown
ISBN: 030734746X
Category : Mathematics
Languages : en
Pages : 306
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Book Description
These simple math secrets and tricks will forever change how you look at the world of numbers. Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun. Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.
Author: Nelson Dellis
Publisher: Abrams
ISBN: 1683357760
Category : Juvenile Nonfiction
Languages : en
Pages : 259
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Book Description
A kid’s guide to amazing feats of memorization with “a variety of engaging memory exercises [and] methods for all different types of learners.” —Kirkus Reviews Nelson Dellis, the four-time USA Memory Champion, reveals the secrets to his phenomenal ability to remember almost anything. From presidents to state capitals, from mathematical theorems to the periodic table, kids have so much to remember for school! This incredibly helpful book is structured as an entertaining and fantastical narrative in which the author guides the reader as they attempt to climb Mount Foreverest. Up there, the goal is to defeat the Memory Thief, a villain plotting to steal everyone’s memories. On the journey, while encountering pirates, forest dwarves, and mummies, you’ll also find tools and tricks to remember the US presidents in order, foreign word meanings, countries and capitals, the periodic table, long numbers, and multiplication tables. These easily understandable exercises can help build skills to remember any kinds of words, lists, numbers, or concepts. Whether you’re trying to become a better student or just want to amaze friends and family, Memory Superpowers! is one unforgettable book. “[Steph] Stilwell’s bright illustrations accompany this book that’s full of useful tips that will help students enjoy learning to study better.” ?Booklist
Author: Susan R. Greenwald
Publisher: Longevity Publishing
ISBN: 0977732304
Category : Addition
Languages : en
Pages : 259
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Book Description
This supplementary workbook is for children ages six and up, and has reproducible pages to give students an opportunity to learn the math facts. The addition and subtraction facts to 18 are taught in an original way-not just drill and practice, but by grouping and associating them with easy-to-learn methods and tricks. Each page was carefully designed; the facts are introduced with a trick and then those facts are practiced by trick name with previously learned facts, also identified by their trick name. After initial instruction, teachers/parents can assign workbook pages for class work or homework to give children practice and review. Not all students will need to do all of the pages. Cumulative practice pages include most, if not all, of the tricks taught to that point. The children will see that they can be successful in completing pages without counting on fingers or using a chart. This book will complement any mathematics curriculum, and is a perfect resource for parents, teachers, special education, and home school programs.Included in the book: Introduction, How to Use the Book, 232 workbook pages, Answer keys, Certificate of Mastery, Record-Keeping pages, Index
Author: Sanjoy Mahajan
Publisher: MIT Press
ISBN: 0262265591
Category : Education
Languages : en
Pages : 152
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Book Description
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.
Author: Kalid Azad
Publisher:
ISBN: 9781519711540
Category :
Languages : en
Pages : 98
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Book Description
Math, Better Explained is an intuitive guide to the math fundamentals. Learn math the way your teachers always wanted.
Author: Mathivanan Palraj
Publisher: PartridgeIndia
ISBN: 9781482873337
Category :
Languages : en
Pages : 0
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Book Description
The unique feature of this book is problem-solving techniques that will help the students get top scores. The first part of this book deals with theory, examples, and exercises. In the examples, wherever it is required, I have shown the problem-solving techniques that will help you tackle a problem and solve it in the shortest way. In addition, I have included many problems that are generally not given in GMAT guidebooks. The purpose is to equip you to face any situation in the actual test. The second part of this book is designed as a workbook to help you apply the problem-solving techniques that you have studied in the first part. Every problem solving has a technique, and a particular technique can be applied to different types of problems. You will have to study and master them. A successful student will not only learn the techniques but also learn how to apply the appropriate technique for a particular problem.
Author: Ellina Grigorieva
Publisher: Birkhäuser
ISBN: 3319909150
Category : Mathematics
Languages : en
Pages : 405
Get Book Here
Book 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 the representations 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.
Author:
Publisher: National Academies
ISBN:
Category : Mathematics
Languages : en
Pages : 102
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Book Description
Author: Brock Eide
Publisher: Hachette Books
ISBN: 1401384781
Category : Family & Relationships
Languages : en
Pages : 419
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Book Description
An incredibly reassuring approach by two physicians who specialize in helping children overcome their difficulties in learning and succeeding in school For parents, teachers, and other professionals seeking practical guidance about ways to help children with learning problems, this book provides a comprehensive look at learning differences ranging from dyslexia to dysgraphia, to attention problems, to giftedness. In The Mislabeled Child, the authors describe how a proper understanding of a child's unique brain-based strengths can be used to overcome many different obstacles to learning. They show how children are often mislabeled with diagnoses that are too broad (ADHD, for instance) or are simply inaccurate. They also explain why medications are often not the best ways to help children who are struggling to learn. The authors guide readers through the morass of commonly used labels and treatments, offering specific suggestions that can be used to help children at school and at home. This book offers extremely empowering information for parents and professionals alike. The Mislabeled Child examines a full spectrum of learning disorders, from dyslexia to giftedness, clarifying the diagnoses and providing resources to help. The Eides explain how a learning disability encompasses more than a behavioral problem; it is also a brain dysfunction that should be treated differently.
Author: Nelda W. Roueche
Publisher: Prentice Hall
ISBN:
Category : Business & Economics
Languages : en
Pages : 530
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Book Description
