The Mathematician's Brain PDF Download

Author: David Ruelle
Publisher: Princeton University Press
ISBN: 9780691129822
Category : Mathematics
Languages : en
Pages : 180

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Book Description
Examines mathematical ideas and the visionary minds behind them. This book provides an account of celebrated mathematicians and their quirks, oddities, personal tragedies, bad behavior, descents into madness, tragic ends, and the beauty of their mathematical discoveries.

Author: Grace Lindsay
Publisher: Bloomsbury Publishing
ISBN: 1472966457
Category : Science
Languages : en
Pages : 401

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Book Description
The human brain is made up of 85 billion neurons, which are connected by over 100 trillion synapses. For more than a century, a diverse array of researchers searched for a language that could be used to capture the essence of what these neurons do and how they communicate – and how those communications create thoughts, perceptions and actions. The language they were looking for was mathematics, and we would not be able to understand the brain as we do today without it. In Models of the Mind, author and computational neuroscientist Grace Lindsay explains how mathematical models have allowed scientists to understand and describe many of the brain's processes, including decision-making, sensory processing, quantifying memory, and more. She introduces readers to the most important concepts in modern neuroscience, and highlights the tensions that arise when the abstract world of mathematical modelling collides with the messy details of biology. Each chapter of Models of the Mind focuses on mathematical tools that have been applied in a particular area of neuroscience, progressing from the simplest building block of the brain – the individual neuron – through to circuits of interacting neurons, whole brain areas and even the behaviours that brains command. In addition, Grace examines the history of the field, starting with experiments done on frog legs in the late eighteenth century and building to the large models of artificial neural networks that form the basis of modern artificial intelligence. Throughout, she reveals the value of using the elegant language of mathematics to describe the machinery of neuroscience.

Author: William Byers
Publisher: Princeton University Press
ISBN: 0691145997
Category : Mathematics
Languages : en
Pages : 424

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Book Description
To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.

Author: Michael Anthony Arbib
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description

Author: Bogumil Kaminski
Publisher: CRC Press
ISBN: 1000216675
Category : Mathematics
Languages : en
Pages : 339

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Book Description
This accessible book helps readers to see the bigger picture of advanced mathematics. The book contains carefully selected, challenging problems in an easy-to-follow, step-by-step process. Neither prior preparation nor any mathematical sophistication is required. The authors guide the reader to “train their brain” to think and express themselves in a rigorous, mathematical way, and to extract facts, analyze the problem, and identify main challenges. A firm foundation in a diverse range of topics is presented. Moreover, the authors show how to draw appropriate, true conclusions. Computer support is used to better intuition into discussed problems. The book is designed for self-study. It can be used to bridge the gap between introductory calculus/linear algebra courses and more advanced courses offered at universities. It improves the ability to read, write, and think in a rigorous, mature mathematical fashion. The reader will develop a deeper understanding in preparation to succeed in more advanced course work. Features •The authors employ a six-step process: 1.SOURCE 2.PROBLEM 3.THEORY 4.SOLUTION 5.REMARK 6.EXERCISES •An Appendix introduces programming in Julia This book is also suitable for high school students that are interested in competing in math competitions or simply for people of all ages and backgrounds who want to expand their knowledge and to challenge themselves with interesting questions.

Author: Jason Padgett
Publisher: HMH
ISBN: 0544045645
Category : Biography & Autobiography
Languages : en
Pages : 268

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Book Description
From head trauma to scientific wonder—a “deeply absorbing . . . fascinating” true story of acquired savant syndrome (Entertainment Weekly). Twelve years ago, Jason Padgett had never made it past pre-algebra. But a violent mugging forever altered the way his brain worked. It turned an ordinary math-averse student into an extraordinary young man with a unique gift to see the world as no one else does: water pours from the faucet in crystalline patterns, numbers call to mind distinct geometric shapes, and intricate fractal patterns emerge from the movement of tree branches, revealing the intrinsic mathematical designs hidden in the objects around us. As his ability to understand physics skyrocketed, the “accidental genius” developed the astonishing ability to draw the complex geometric shapes he saw everywhere. Overcoming huge setbacks and embracing his new mind, Padgett “gained a vision of the world that is as beautiful as it is challenging.” Along the way he fell in love, found joy in numbers, and spent plenty of time having his head examined (The New York Times Book Review). Illustrated with Jason’s stunning, mathematically precise artwork, his singular story reveals the wondrous potential of the human brain, and “an incredible phenomenon which points toward dormant potential—a little Rain Man perhaps—within us all” (Darold A. Treffert, MD, author of Islands of Genius: The Bountiful Mind of the Autistic, Acquired, and Sudden Savant). “A tale worthy of Ripley’s Believe It or Not! . . . This memoir sends a hopeful message to families touched by brain injury, autism, or neurological damage from strokes.” —Booklist “How extraordinary it is to contemplate the bizarre gifts that might lie within all of us.” —People

Author: David A. Sousa
Publisher: Corwin Press
ISBN: 1452294917
Category : Education
Languages : en
Pages : 529

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Book Description
Learn how the brain processes mathematical concepts and why some students develop math anxiety! David A. Sousa discusses the cognitive mechanisms for learning mathematics and the environmental and developmental factors that contribute to mathematics difficulties. This award-winning text examines: Children’s innate number sense and how the brain develops an understanding of number relationships Rationales for modifying lessons to meet the developmental learning stages of young children, preadolescents, and adolescents How to plan lessons in PreK–12 mathematics Implications of current research for planning mathematics lessons, including discoveries about memory systems and lesson timing Methods to help elementary and secondary school teachers detect mathematics difficulties Clear connections to the NCTM standards and curriculum focal points

Author: Risto J. Ilmoniemi
Publisher: MIT Press
ISBN: 0262039826
Category : Science
Languages : en
Pages : 257

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Book Description
A unified treatment of the generation and analysis of brain-generated electromagnetic fields. In Brain Signals, Risto Ilmoniemi and Jukka Sarvas present the basic physical and mathematical principles of magnetoencephalography (MEG) and electroencephalography (EEG), describing what kind of information is available in the neuroelectromagnetic field and how the measured MEG and EEG signals can be analyzed. Unlike most previous works on these topics, which have been collections of writings by different authors using different conventions, this book presents the material in a unified manner, providing the reader with a thorough understanding of basic principles and a firm basis for analyzing data generated by MEG and EEG. The book first provides a brief introduction to brain states and the early history of EEG and MEG, describes the generation of electromagnetic fields by neuronal activity, and discusses the electromagnetic forward problem. The authors then turn to EEG and MEG analysis, offering a review of linear and matrix algebra and basic statistics needed for analysis of the data, and presenting several analysis methods: dipole fitting; the minimum norm estimate (MNE); beamforming; the multiple signal classification algorithm (MUSIC), including RAP-MUSIC with the RAP dilemma and TRAP-MUSIC, which removes the RAP dilemma; independent component analysis (ICA); and blind source separation (BSS) with joint diagonalization.

Author: Fabrizio Gabbiani
Publisher: Academic Press
ISBN: 0128019069
Category : Mathematics
Languages : en
Pages : 630

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Book Description
Mathematics for Neuroscientists, Second Edition, presents a comprehensive introduction to mathematical and computational methods used in neuroscience to describe and model neural components of the brain from ion channels to single neurons, neural networks and their relation to behavior. The book contains more than 200 figures generated using Matlab code available to the student and scholar. Mathematical concepts are introduced hand in hand with neuroscience, emphasizing the connection between experimental results and theory. - Fully revised material and corrected text - Additional chapters on extracellular potentials, motion detection and neurovascular coupling - Revised selection of exercises with solutions - More than 200 Matlab scripts reproducing the figures as well as a selection of equivalent Python scripts

Author: George Gratzer
Publisher: CRC Press
ISBN: 156881710X
Category : Mathematics
Languages : en
Pages : 255

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Book Description
Many people start the day with physical exercise but few seem to be so concerned with exercising the most human of organs-the brain. This book provides you with entertaining and challenging mental exercises for every week of the year. Whether you are a high school student eager to sharpen your brain, or someone older who would like to retain your mental agility, you will find your brain getting sharper and more agile as you solve the puzzles in this book. Read a few puzzles every week, think about them, solve them, and you will see the results. And on the way to a sharper mind, you will enjoy every step.