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Multipoint Methods for Solving Nonlinear Equations
This book is the first on the topic and explains the most cutting-edge methods needed for precise calculations and explores the development of powerful algorithms to solve research problems. Multipoint methods have an extensive range of practical applications significant in research areas such as signal processing, analysis of convergence rate, fluid mechanics, solid state physics, and many others. The book takes an introductory approach in making qualitative comparisons of different multipoint methods from various viewpoints to help the reader understand applications of more complex methods. Evaluations are made to determine and predict efficiency and accuracy of presented models useful to ...
Point Estimation of Root Finding Methods
This book sets out to state computationally verifiable initial conditions for predicting the immediate appearance of the guaranteed and fast convergence of iterative root finding methods. Attention is paid to iterative methods for simultaneous determination of polynomial zeros in the spirit of Smale's point estimation theory, introduced in 1986. Some basic concepts and Smale's theory for Newton's method, together with its modifications and higher-order methods, are presented in the first two chapters. The remaining chapters contain the recent author's results on initial conditions guaranteing convergence of a wide class of iterative methods for solving algebraic equations. These conditions are of practical interest since they depend only on available data, the information of a function whose zeros are sought and initial approximations. The convergence approach presented can be applied in designing a package for the simultaneous approximation of polynomial zeros.
Impossible Folding Puzzles and Other Mathematical Paradoxes
Do all problems have solutions? Is complexity synonymous with difficulty? This original collection of mathematical puzzles and paradoxes proves that things aren't always what they seem! Readers will discover that nothing is as easy or as difficult as it looks and that puzzles can have one, several, or no solutions. The fun-filled puzzles begin with The Tricky Hole, a challenge that involves pushing a large coin through a small hole in a sheet of paper without ripping or making any cuts in the paper. Advance to the Elastic Playing Card, in which it's possible to cut a hole into a playing card big enough for someone to climb through. Other incredible puzzles include Elephants and Castles, Trianglized Kangaroo, Honest Dice and Logic Dice, Mind-reading Powers, and dozens more. Complete solutions explain the mathematical realities behind the fantastic-sounding challenges.
Figures for Fun
Originally published in English by: Moscow: Foreign Languages Pub. House, 1957.
Challenging Math Problems
This best-of compilation features 101 of the most entertaining and challenging math puzzles ever published. No advanced knowledge of mathematics is necessary, just solid thinking and puzzle-solving skills. Includes complete solutions.
Paradoxes in Mathematics
Compiled by a prominent educator and author, this volume presents an intriguing mix of mathematical paradoxes — phenomena with surprising outcomes that can be resolved mathematically. Students and puzzle enthusiasts will get plenty of enjoyment mixed with a bit of painless mathematical instruction from 30 conundrums, including The Birthday Paradox, Aristotle's Magic Wheel, and A Greek Tragedy.
The Godelian Puzzle Book
These recreational logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. Written by a distinguished mathematician and creator of numerous popular puzzle books, this volume requires no background in formal logic and will delight readers of all ages.
The Stumbling Progress of 20th Century Science
The 70 years from 1880 to 1950 witnessed the final ascent of humankind into the modern age. Historically, this period is characterized by deep political, social and economic crises. However, parallel to this and much less known in the public, rational scientific thinking also experienced the darkest and deepest crisis of its own history. All the great modern scientific discoveries like quantum theory, genetics and neurology are products of this. Ground-breaking discoveries, profound crises, revolutionary thoughts, refutation of previously unshakable beliefs - these years are marked by scientific achievements of numerous great minds, who overturned our understanding of the world, of space, ti...
The Big Brain Puzzle Book
Originally published in 2009, with a new introduction.
