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Author: Mubeen Junaid
Publisher: Simon and Schuster
ISBN: 1639362576
Category : Mathematics
Languages : en
Pages : 215
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Book Description
A fresh exploration into the 'human nature versus technology’ argument, revealing an unexpected advantage that humans have over our future robot masters: we’re actually good at mathematics. There’s so much discussion about the threat posed by intelligent machines that it sometimes seems as though we should simply surrender to our robot overlords now. But Junaid Mubeen isn’t ready to throw in the towel just yet. As far as he is concerned, we have the creative edge over computers, because of a remarkable system of thought that humans have developed over the millennia. It’s familiar to us all, but often badly taught in schools and misrepresented in popular discourse—math. Computers are, of course, brilliant at totting up sums, pattern-seeking, and performing mindless tasks of, well, computation. For all things calculation, machines reign supreme. But Junaid identifies seven areas of intelligence where humans can retain a crucial edge. And in exploring these areas, he opens up a fascinating world where we can develop our uniquely human mathematical talents. Just a few of the fascinating subjects covered in MATHEMATICAL INTELLIGENCE include: -Humans are endowed with a natural sense of numbers that is based on approximation rather than precise calculation. Our in-built estimation skills complement the precision of computers. Interpreting the real world depends on both. -What sets humans apart from other animals is language and abstraction. We have an extraordinary ability to create powerful representations of knowledge— more diverse than the binary language of computers. -Mathematics confers the most robust, logical framework for establishing permanent truths. Reasoning shields us from the dubious claims of pure pattern-recognition systems. -All mathematical truths are derived from a starting set of assumptions, or axioms. Unlike computers, humans have the freedom to break free of convention and examine the logical consequences of our choices. Mathematics rewards our imagination with fascinating and, on occasion, applicable concepts that originate from breaking the rules. -Computers can be tasked to solve a range of problems, but which problems are worth the effort? Questioning is as vital to our repertoire of thinking skills as problem-solving itself.
Author: Peter Hilton
Publisher: Springer Science & Business Media
ISBN: 1475736819
Category : Mathematics
Languages : en
Pages : 344
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Book Description
This book collects nine related mathematical essays which will intrigue and inform. From the reviews: "The authors put their writing where their talents are, and students get to see just how alive mathematics is...there is much to commend the book. It contains plenty of interesting mathematics, often going in unusual directions. I like the diagrams; the authors have chosen mathematics that involves especially pretty ones." --THE MATHEMATICAL ASSOCIATION OF AMERICA
Author: Peter Hilton
Publisher: Springer Science & Business Media
ISBN: 1461219329
Category : Mathematics
Languages : en
Pages : 367
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Book Description
A relaxed and informal presentation conveying the joy of mathematical discovery and insight. Frequent questions lead readers to see mathematics as an accessible world of thought, where understanding can turn opaque formulae into beautiful and meaningful ideas. The text presents eight topics that illustrate the unity of mathematical thought as well as the diversity of mathematical ideas. Drawn from both "pure" and "applied" mathematics, they include: spirals in nature and in mathematics; the modern topic of fractals and the ancient topic of Fibonacci numbers; Pascals Triangle and paper folding; modular arithmetic and the arithmetic of the infinite. The final chapter presents some ideas about how mathematics should be done, and hence, how it should be taught. Presenting many recent discoveries that lead to interesting open questions, the book can serve as the main text in courses dealing with contemporary mathematical topics or as enrichment for other courses. It can also be read with pleasure by anyone interested in the intellectually intriguing aspects of mathematics.
Author: Titu Andreescu
Publisher: American Mathematical Soc.
ISBN: 1470434644
Category : Juvenile Nonfiction
Languages : en
Pages : 137
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Book Description
This book starts with simple arithmetic inequalities and builds to sophisticated inequality results such as the Cauchy-Schwarz and Chebyshev inequalities. Nothing beyond high school algebra is required of the student. The exposition is lean. Most of the learning occurs as the student engages in the problems posed in each chapter. And the learning is not “linear”. The central topic of inequalities is linked to others in mathematics. Often these topics relate to much more than algebraic inequalities. There are also “secret” pathways through the book. Each chapter has a subtext, a theme which prepares the student for learning other mathematical topics, concepts, or habits of mind. For example, the early chapters on the arithmetic mean/geometric mean inequality show how very simple observations can be leveraged to yield useful and interesting results. Later chapters give examples of how one can generalize a mathematical statement. The chapter on the Cauchy-Schwarz inequality provides an introduction to vectors as mathematical objects. And there are many other secret pathways that the authors hope the reader will discover—and follow. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Author: Mubeen Junaid
Publisher: Simon and Schuster
ISBN: 1639362576
Category : Mathematics
Languages : en
Pages : 215
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Book Description
A fresh exploration into the 'human nature versus technology’ argument, revealing an unexpected advantage that humans have over our future robot masters: we’re actually good at mathematics. There’s so much discussion about the threat posed by intelligent machines that it sometimes seems as though we should simply surrender to our robot overlords now. But Junaid Mubeen isn’t ready to throw in the towel just yet. As far as he is concerned, we have the creative edge over computers, because of a remarkable system of thought that humans have developed over the millennia. It’s familiar to us all, but often badly taught in schools and misrepresented in popular discourse—math. Computers are, of course, brilliant at totting up sums, pattern-seeking, and performing mindless tasks of, well, computation. For all things calculation, machines reign supreme. But Junaid identifies seven areas of intelligence where humans can retain a crucial edge. And in exploring these areas, he opens up a fascinating world where we can develop our uniquely human mathematical talents. Just a few of the fascinating subjects covered in MATHEMATICAL INTELLIGENCE include: -Humans are endowed with a natural sense of numbers that is based on approximation rather than precise calculation. Our in-built estimation skills complement the precision of computers. Interpreting the real world depends on both. -What sets humans apart from other animals is language and abstraction. We have an extraordinary ability to create powerful representations of knowledge— more diverse than the binary language of computers. -Mathematics confers the most robust, logical framework for establishing permanent truths. Reasoning shields us from the dubious claims of pure pattern-recognition systems. -All mathematical truths are derived from a starting set of assumptions, or axioms. Unlike computers, humans have the freedom to break free of convention and examine the logical consequences of our choices. Mathematics rewards our imagination with fascinating and, on occasion, applicable concepts that originate from breaking the rules. -Computers can be tasked to solve a range of problems, but which problems are worth the effort? Questioning is as vital to our repertoire of thinking skills as problem-solving itself.
Author: David F. Hayes
Publisher: American Mathematical Soc.
ISBN: 1470457415
Category : Mathematics
Languages : en
Pages : 306
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Book Description
Author: Jeffrey Hoffstein
Publisher: Springer Science & Business Media
ISBN: 0387779949
Category : Mathematics
Languages : en
Pages : 533
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Book Description
An Introduction to Mathematical Cryptography provides an introduction to public key cryptography and underlying mathematics that is required for the subject. Each of the eight chapters expands on a specific area of mathematical cryptography and provides an extensive list of exercises. It is a suitable text for advanced students in pure and applied mathematics and computer science, or the book may be used as a self-study. This book also provides a self-contained treatment of mathematical cryptography for the reader with limited mathematical background.
Author: Peter Hilton
Publisher: Cambridge University Press
ISBN: 1139489070
Category : Mathematics
Languages : en
Pages :
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Book Description
This easy-to-read 2010 book demonstrates how a simple geometric idea reveals fascinating connections and results in number theory, the mathematics of polyhedra, combinatorial geometry, and group theory. Using a systematic paper-folding procedure it is possible to construct a regular polygon with any number of sides. This remarkable algorithm has led to interesting proofs of certain results in number theory, has been used to answer combinatorial questions involving partitions of space, and has enabled the authors to obtain the formula for the volume of a regular tetrahedron in around three steps, using nothing more complicated than basic arithmetic and the most elementary plane geometry. All of these ideas, and more, reveal the beauty of mathematics and the interconnectedness of its various branches. Detailed instructions, including clear illustrations, enable the reader to gain hands-on experience constructing these models and to discover for themselves the patterns and relationships they unearth.
Author: David A Cox
Publisher: Springer Science & Business Media
ISBN: 0387356509
Category : Mathematics
Languages : en
Pages : 565
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Book Description
This book details the heart and soul of modern commutative and algebraic geometry. It covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes: a significantly updated section on Maple; updated information on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR; and presents a shorter proof of the Extension Theorem.
Author: A. V. Balakrishnan
Publisher: Optimization Software Incorporated Publications
ISBN:
Category : Mathematics
Languages : en
Pages : 408
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Book Description
Author: Eric Schechter
Publisher: Academic Press
ISBN: 0080532993
Category : Mathematics
Languages : en
Pages : 907
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Book Description
Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/
