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The heart of mathematics is its elegance; the way it all fits together. Unfortunately, its beauty often eludes the vast majority of people who are intimidated by fear of the difficulty of numbers. Mathematical Elegance remedies this. Using hundreds of examples, the author presents a view of the mathematical landscape that is both accessible and fascinating. At a time of concern that American youth are bored by math, there is renewed interest in improving math skills. Mathematical Elegance stimulates students, along with those already experienced in the discipline, to explore some of the unexpected pleasures of quantitative thinking. Invoking mathematical proofs famous for their simplicity and brainteasers that are fun and illuminating, the author leaves readers feeling exuberant-as well as convinced that their IQs have been raised by ten points. A host of anecdotes about well-known mathematicians humanize and provide new insights into their lofty subjects. Recalling such classic works as Lewis Carroll's Introduction to Logic and A Mathematician Reads the Newspaper by John Allen Paulos, Mathematical Elegance will energize and delight a wide audience, ranging from intellectually curious students to the enthusiastic general reader.
Theorems and their proofs lie at the heart of mathematics. In speaking of the purely aesthetic qualities of theorems and proofs, G. H. Hardy wrote that in beautiful proofs 'there is a very high degree of unexpectedness, combined with inevitability and economy'. Charming Proofs presents a collection of remarkable proofs in elementary mathematics that are exceptionally elegant, full of ingenuity, and succinct. By means of a surprising argument or a powerful visual representation, the proofs in this collection will invite readers to enjoy the beauty of mathematics, and to develop the ability to create proofs themselves. The authors consider proofs from topics such as geometry, number theory, inequalities, plane tilings, origami and polyhedra. Secondary school and university teachers can use this book to introduce their students to mathematical elegance. More than 130 exercises for the reader (with solutions) are also included.
This book serves as a very good resource and teaching material for anyone who wants to discover the beauty of Induction and its applications, from novice mathematicians to Olympiad-driven students and professors teaching undergraduate courses. The authors explore 10 different areas of mathematics, including topics that are not usually discussed in an Olympiad-oriented book on the subject. Induction is one of the most important techniques used in competitions and its applications permeate almost every area of mathematics.
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
What's the most radical idea possible, the one least likely to be understood by humanity, the one so far beyond humanity's level of intelligence that whoever champions it is likely to be regarded as insane? Go on, if you're smart you ought to be conceive of a connection so unobvious, so invisible to the masses, so improbable in relation to any other idea, that it will be almost universally rejected. That idea – despised, mocked and reviled by practically everyone – will be the No.1 candidate for being the authentic answer to existence. Pythagoras was the genius that delivered this idea – 2,500 years ago! – when he said, "All things are numbers." The last connection that the average person would ever make when they look at the world is that what they are actually seeing, beyond the level of superficial appearance, is nothing but numbers. That is the ultimate unthinkable thought. God is Mathematics.
“Mathematics in Everyday Life -The hidden Language of the World” is a textbook for Undergraduate and Post Graduate students to develop problem solving skills with the advent of logical thinking. Here the authors’ objective is how mathematics will be useful in the fields we come across in Science, Economics, Engineering and Technology by keeping the syllabi of various prestigious universities. The major subfields it covers Mathematical modeling, model theory, proof theory, set theory, recursion theory, Financial Mathematics, Statistics and probability in decision-making, Mathematics in Technology and Communication Engineering etc.,. It also useful in Cryptography and Encryption, Algorithm and coding development. Here the authors were focused on mathematical theory which is a mathematical model of a branch of mathematics that is based on a set of axioms and they emphasized, it can also concurrently be a body of knowledge. This textbook has been written with great effort made by referring text books written on the modern trend of Applicable Mathematics. The topics covered in this book are practical for a scholar who starts learning education in Economics, Sciences ,Technology & Engineering fields.. The mathematical concepts are written from the basic level to reach out to a wide range of student fraternities and teachers in every walk of life more particularly in industrial-related challenging problems
The Web Designer's Roadmap is a full-color book about the creative process and the underlying principles that govern that process. While other books cover the nuts 'n' bolts of how to design the elements that make up websites, this book outlines how effective designers go about their work, illustrating the complete creative process from start to finish. As well as how-to content, the book draws on interviews with a host of well-known design gurus, including Shaun Inman, Daniel Burka, Meagan Fisher, Donald Norman and Dan Rubin. A non-academic book, this is a fun and easy read packed with practical information.
Over 155 truly challenging conundrums for the expert puzzlist. Algebraic amusements, geometric exercises, diophantine diversions, problems in logic and deduction, probability posers, insight puzzles, and assorted number theory problems. Advanced mathematical skills are only sporadically required, the majority of problems are accessible to just about anyone. 130 woodcut illustrations by Ed Kysar.
The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection