The Mathematician's Brain

A Personal Tour Through the Essentials of Mathematics and Some of the Great Minds Behind Them
Author: David Ruelle
Publisher: Princeton University Press
ISBN: 0691190305
Category: Mathematics
Page: N.A
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The Mathematician's Brain poses a provocative question about the world's most brilliant yet eccentric mathematical minds: were they brilliant because of their eccentricities or in spite of them? In this thought-provoking and entertaining book, David Ruelle, the well-known mathematical physicist who helped create chaos theory, gives us a rare insider's account of the celebrated mathematicians he has known-their quirks, oddities, personal tragedies, bad behavior, descents into madness, tragic ends, and the sublime, inexpressible beauty of their most breathtaking mathematical discoveries. Consider the case of British mathematician Alan Turing. Credited with cracking the German Enigma code during World War II and conceiving of the modern computer, he was convicted of "gross indecency" for a homosexual affair and died in 1954 after eating a cyanide-laced apple--his death was ruled a suicide, though rumors of assassination still linger. Ruelle holds nothing back in his revealing and deeply personal reflections on Turing and other fellow mathematicians, including Alexander Grothendieck, René Thom, Bernhard Riemann, and Felix Klein. But this book is more than a mathematical tell-all. Each chapter examines an important mathematical idea and the visionary minds behind it. Ruelle meaningfully explores the philosophical issues raised by each, offering insights into the truly unique and creative ways mathematicians think and showing how the mathematical setting is most favorable for asking philosophical questions about meaning, beauty, and the nature of reality. The Mathematician's Brain takes you inside the world--and heads--of mathematicians. It's a journey you won't soon forget.

Elliptic Curves, Modular Forms, and Their L-functions


Author: Alvaro Lozano-Robledo
Publisher: American Mathematical Soc.
ISBN: 0821852426
Category: Mathematics
Page: 195
View: 660

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Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. The original simply stated problem can be obscured in the depth of the theory developed to understand it. This book is an introduction to some of these problems, and an overview of the theories used nowadays to attack them, presented so that the number theory is always at the forefront of the discussion. Lozano-Robledo gives an introductory survey of elliptic curves, modular forms, and $L$-functions. His main goal is to provide the reader with the big picture of the surprising connections among these three families of mathematical objects and their meaning for number theory. As a case in point, Lozano-Robledo explains the modularity theorem and its famous consequence, Fermat's Last Theorem. He also discusses the Birch and Swinnerton-Dyer Conjecture and other modern conjectures. The book begins with some motivating problems and includes numerous concrete examples throughout the text, often involving actual numbers, such as 3, 4, 5, $\frac{3344161}{747348}$, and $\frac{2244035177043369699245575130906674863160948472041} {8912332268928859588025535178967163570016480830}$. The theories of elliptic curves, modular forms, and $L$-functions are too vast to be covered in a single volume, and their proofs are outside the scope of the undergraduate curriculum. However, the primary objects of study, the statements of the main theorems, and their corollaries are within the grasp of advanced undergraduates. This book concentrates on motivating the definitions, explaining the statements of the theorems and conjectures, making connections, and providing lots of examples, rather than dwelling on the hard proofs. The book succeeds if, after reading the text, students feel compelled to study elliptic curves and modular forms in all their glory.

Anatomy & Physiology

The Unity of Form and Function
Author: Kenneth Saladin
Publisher: McGraw-Hill Higher Education
ISBN: 0077676718
Category: Science
Page: 1248
View: 6069

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With Saladin, students make connections through learning outcomes and assessments, integrated media, and a writing style that clearly depicts anatomy and physiology processes. A consistent set of chapter learning tools helps students identify and retain key concepts while the stunning visual program provides a realistic view of body structures and processes. Saladin's text requires no prior knowledge of college chemistry or cell biology, and is designed for a two-semester A&P course.

Plant Biomechanics

An Engineering Approach to Plant Form and Function
Author: Karl J. Niklas
Publisher: University of Chicago Press
ISBN: 9780226586311
Category: Science
Page: 607
View: 5069

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In this first comprehensive treatment of plant biomechanics, Karl J. Niklas analyzes plant form and provides a far deeper understanding of how form is a response to basic physical laws. He examines the ways in which these laws constrain the organic expression of form, size, and growth in a variety of plant structures, and in plants as whole organisms, and he draws on the fossil record as well as on studies of extant species to present a genuinely evolutionary view of the response of plants to abiotic as well as biotic constraints. Well aware that some readers will need an introduction to basic biomechanics or to basic botany, Niklas provides both, as well as an extensive glossary, and he has included a number of original drawings and photographs to illustrate major structures and concepts. This volume emphasizes not only methods of biomechanical analysis but also the ways in which it allows one to ask, and answer, a host of interesting questions. As Niklas points out in the first chapter, "From the archaic algae to the most derived multicellular terrestrial plants, from the spectral properties of light-harvesting pigments in chloroplasts to the stacking of leaves in the canopies of trees, the behavior of plants is in large part responsive to and intimately connected with the physical environment. In addition, plants tend to be exquisitely preserved in the fossil record, thereby giving us access to the past." Its biomechanical analyses of various types of plant cells, organs, and whole organisms, and its use of the earliest fossil records of plant life as well as sophisticated current studies of extant species, make this volume a unique and highly integrative contribution to studies of plant form, evolution, ecology, and systematics.

Modular Functions and Dirichlet Series in Number Theory


Author: Tom M. Apostol
Publisher: Springer Science & Business Media
ISBN: 1461209994
Category: Mathematics
Page: 207
View: 7700

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A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.

Functions and Graphs


Author: I. M. Gelfand,E. G. Glagoleva,E. E. Shnol
Publisher: Courier Corporation
ISBN: 0486317137
Category: Mathematics
Page: 112
View: 7807

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This text demonstrates the fundamentals of graph theory. The 1st part employs simple functions to analyze basics; 2nd half deals with linear functions, quadratic trinomials, linear fractional functions, power functions, rational functions. 1969 edition.

Algebra: Form and Function


Author: William G. McCallum,Eric Connally,Deborah Hughes-Hallett
Publisher: Wiley Global Education
ISBN: 0470927763
Category: Mathematics
Page: 576
View: 7946

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Algebra is fundamental to the working of modern society, yet its origins are as old as the beginnings of civilization. Algebraic equations describe the laws of science, the principles of engineering, and the rules of business. The power of algebra lies in its efficient symbolic representation of complex ideas, and this also presents the main difficulty in learning it. It is easy to forget the underlying structure of algebra and rely instead on a surface knowledge of algebraic manipulations.

Mathematics and Its History


Author: John Stillwell
Publisher: Springer Science & Business Media
ISBN: 144196052X
Category: Mathematics
Page: 662
View: 525

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From a review of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.

Introduction to the Arithmetic Theory of Automorphic Functions


Author: Gorō Shimura
Publisher: Princeton University Press
ISBN: 9780691080925
Category: Mathematics
Page: 267
View: 7827

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After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.

Introducing Philosophy of Mathematics


Author: Michele Friend
Publisher: Routledge
ISBN: 1317493788
Category: Philosophy
Page: 240
View: 6386

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What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.

Introduction to Elliptic Curves and Modular Forms


Author: N. Koblitz
Publisher: Springer Science & Business Media
ISBN: 1468402552
Category: Mathematics
Page: 248
View: 9924

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This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. The ancient "congruent number problem" is the central motivating example for most of the book. My purpose is to make the subject accessible to those who find it hard to read more advanced or more algebraically oriented treatments. At the same time I want to introduce topics which are at the forefront of current research. Down-to-earth examples are given in the text and exercises, with the aim of making the material readable and interesting to mathematicians in fields far removed from the subject of the book. With numerous exercises (and answers) included, the textbook is also intended for graduate students who have completed the standard first-year courses in real and complex analysis and algebra. Such students would learn applications of techniques from those courses, thereby solidifying their under standing of some basic tools used throughout mathematics. Graduate stu dents wanting to work in number theory or algebraic geometry would get a motivational, example-oriented introduction. In addition, advanced under graduates could use the book for independent study projects, senior theses, and seminar work.

Modular Forms: A Classical Approach


Author: Henri Cohen,Fredrik Strömberg
Publisher: American Mathematical Soc.
ISBN: 0821849476
Category: Forms (Mathematics).
Page: 700
View: 1699

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The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and “fun” subject in itself and abounds with an amazing number of surprising identities. This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin–Lehner–Li theory of newforms and including the theory of Eisenstein series, Rankin–Selberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms. Some “gems” of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Li's little-known theorem on the diagonalization of the full space of modular forms, and explicit algorithms due to the second author for computing Maass forms. This book is essentially self-contained, the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on being given in a separate chapter.

Loose Leaf for Anatomy and Physiology: The Unity of Form and Function


Author: Kenneth S. Saladin, Dr.
Publisher: McGraw-Hill Education
ISBN: 9781260151947
Category: Science
Page: 1248
View: 4676

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Master the story of Anatomy & Physiology with Saladin's Anatomy & Physiology: The Unity of Form and Function! Saladin's A&P helps students make connections by telling a story that will intrigue, engage, and inspire them. Saladin expertly weaves together science, clinical applications, history and evolution of the body with vibrant photos and art to convey the beauty and excitement of the subject. A consistent set of chapter learning tools helps students identify and retain key concepts while the stunning visual program provides a realistic view of body structures and processes. Saladin's text requires no prior knowledge of college chemistry or cell biology, and is designed for a two-semester A&P course.

Mathematics

Its Content, Methods and Meaning
Author: A. D. Aleksandrov,A. N. Kolmogorov,M. A. Lavrent’ev
Publisher: Courier Corporation
ISBN: 0486157873
Category: Mathematics
Page: 1120
View: 7056

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Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.

Secrets of Mental Math

The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks
Author: Arthur Benjamin,Michael Shermer
Publisher: Three Rivers Press
ISBN: 9780307347466
Category: Mathematics
Page: 224
View: 2538

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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.

Tasks in Primary Mathematics Teacher Education

Purpose, Use and Exemplars
Author: Barbara Clarke,Barbro Grevholm,Richard Millman
Publisher: Springer Science & Business Media
ISBN: 0387096698
Category: Education
Page: 310
View: 1247

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Tasks in Primary Mathematics Teacher Education is intended to advance relevant research and innovative international practices in the preparation and professional development of mathematics teachers. Emerging from discussion at the ICMI study on teacher professional development, this volume, focused on primary and elementary teachers, culls a richness that can only be found by gathering wisdom from varied experiences around the world. The choice of tasks, and the associated pedagogies, is a key aspect of teaching and learning mathematics. Arguing that what students learn is largely defined by the tasks they are given, several major themes are presented. One such major strand, the form, function and focus of tasks, is discussed throughout several chapters, offering analysis, discussion of implementation, and exemplars of a broader category of illustrative techniques for developing critical understanding.

Mathematics for Chemistry and Physics


Author: George Turrell
Publisher: Elsevier
ISBN: 0080511279
Category: Mathematics
Page: 424
View: 2400

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Chemistry and physics share a common mathematical foundation. From elementary calculus to vector analysis and group theory, Mathematics for Chemistry and Physics aims to provide a comprehensive reference for students and researchers pursuing these scientific fields. The book is based on the authors many classroom experience. Designed as a reference text, Mathematics for Chemistry and Physics will prove beneficial for students at all university levels in chemistry, physics, applied mathematics, and theoretical biology. Although this book is not computer-based, many references to current applications are included, providing the background to what goes on "behind the screen" in computer experiments.