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Collects six short illustrated volumes covering topics in mathematics, physics, chemistry, biology, evolution, and astronomy.
Offering undergraduates a solid mathematical background (and functioning equally well for independent study), this rewarding, beautifully illustrated text covers geometry and matrices, vector algebra, analytic geometry, functions, and differential and integral calculus. 1961 edition.
Mathematics is as much a part of our humanity as music and art. And it is our mathematics that might be understandable, even familiar, to a distant race and might provide the basis for mutual communication. This book discusses, in a conversational way, the role of mathematics in the search for extraterrestrial intelligence. The author explores the science behind that search, its history, and the many questions associated with it, including those regarding the nature of language and the philosophical/psychological motivation behind this search.
Professor Michael Edgeworth McIntyre is an eminent scientist who has also had a part-time career as a musician. From a lifetime's thinking, he offers this extraordinary synthesis exposing the deepest connections between science, music, and mathematics, while avoiding equations and technical jargon. He begins with perception psychology and the dichotomization instinct and then takes us through biological evolution, human language, and acausality illusions all the way to the climate crisis and the weaponization of the social media, and beyond that into the deepest parts of theoretical physics — demonstrating our unconscious mathematical abilities.He also has an important message of hope for the future. Contrary to popular belief, biological evolution has given us not only the nastiest, but also the most compassionate and cooperative parts of human nature. This insight comes from recognizing that biological evolution is more than a simple competition between selfish genes. Rather, he suggests, in some ways it is more like turbulent fluid flow, a complex process spanning a vast range of timescales.Professor McIntyre is a Fellow of the Royal Society of London (FRS) and has worked on problems as diverse as the Sun's magnetic interior, the Antarctic ozone hole, jet streams in the atmosphere, and the psychophysics of violin sound. He has long been interested in how different branches of science can better communicate with each other and with the public, harnessing aspects of neuroscience and psychology that point toward the deep 'lucidity principles' that underlie skilful communication.
Whether you are stumped by the "commutative law" in algebra or a whiz at multiplying three-digit numbers in your head, this book opens the door to the wonders of mathematical imagining. By using simple language and intriguing illustrations drawn by her husband, Hugh, Lillian Lieber presents subtle mathematical concepts in an easy-to-understand way. Over sixty years after its release, this whimsical exploration of how to think in a mathematical mood will continue to delight math-lovers of all ages. Barry Mazur's new introduction is a tribute to the Liebers' influence on generations of mathematicians.
This book identifies the organizing concepts of physical and biological phenomena by an analysis of the foundations of mathematics and physics. Our aim is to propose a dialog between different conceptual universes and thus to provide a unification of phenomena. The role of “order” and symmetries in the foundations of mathematics is linked to the main invariants and principles, among them the geodesic principle (a consequence of symmetries), which govern and confer unity to various physical theories. Moreover, an attempt is made to understand causal structures, a central element of physical intelligibility, in terms of both symmetries and symmetry breakings. A distinction between the principles of (conceptual) construction and of proofs, both in physics and in mathematics, guides most of the work.The importance of mathematical tools is also highlighted to clarify differences in the models for physics and biology that are proposed by continuous and discrete mathematics, such as computational simulations.Since biology is particularly complex and not as well understood at a theoretical level, we propose a “unification by concepts” which in any case should precede mathematization. This constitutes an outline for unification also based on highlighting conceptual differences, complex points of passage and technical irreducibilities of one field to another. Indeed, we suppose here a very common monist point of view, namely the view that living objects are “big bags of molecules”. The main question though is to understand which “theory” can help better understand these bags of molecules. They are, indeed, rather “singular”, from the physical point of view. Technically, we express this singularity through the concept of “extended criticality”, which provides a logical extension of the critical transitions that are known in physics. The presentation is mostly kept at an informal and conceptual level./a
This book offers an engaging and comprehensive introduction to scientific theories and the evolution of science and mathematics through the centuries. It discusses the history of scientific thought and ideas and the intricate dynamic between new scientific discoveries, scientists, culture and societies. Through stories and historical accounts, the volume illustrates the human engagement and preoccupation with science and the interpretation of natural phenomena. It highlights key scientific breakthroughs from the ancient to later ages, giving us accounts of the work of ancient Greek and Indian mathematicians and astronomers, as well as of the work of modern scientists like Descartes, Newton, Planck, Mendel and many more. The author also discusses the vast advancements which have been made in the exploration of space, matter and genetics and their relevance in the advancement of the scientific tradition. He provides great insights into the process of scientific experimentation and the relationship between science and mathematics. He also shares amusing anecdotes of scientists and their interactions with the world around them. Detailed and accessible, this book will be of great interest to students and researchers of science, mathematics, the philosophy of science, science and technology studies and history. It will also be useful for general readers who are interested in the history of scientific discoveries and ideas.
Argues that teachers and schools should create hybrid third spaces--neither classroom nor home--in which underserved students can merge their personal worlds with those of math and science.
"Part fiction, part overview of 'Aha!' moments in the forward march of physics, Only the Longest Threads takes readers dramatically through scientific fields such as quantum field theory, electromagnetism, relativity, quantum mechanics, and string theory. Each idea or concept is explored in an inventive chapter, each told from a different first-person narrator; the faux emails, letters, and diary entries take place from 1728 to the present day."—Boing Boing, "The Best Books for Nerds from 2014" "Science is done by real human beings, with human concerns. Only the Longest Threads tells a story that conveys the human side of science in a way that is as moving as it is accurate."—Sean Carroll, theoretical physicist at Caltech and author of The Particle at the End of the Universe Only the Longest Threads will thrill readers with its dramatic and lucid accounts of the great breakthroughs in the history of physics—classical mechanics, electromagnetism, relativity, quantum mechanics, quantum field theory, and string theory, each from the viewpoint of a (fictional) witness to the events. Tasneem Zehra Husain re-imagines the pivotal moments in the history of physics when radical new theories shifted our perception of the universe, and our place in it. Husain immerses the reader in the immediacy and excitement of the discoveries—and she guides us as we begin to understand the underlying science and to grasp the revolutionary step forward each of these milestones represents. "Tasneem Zehra Husain writes lyrically, poetically about life, love, and physics. I highly recommend this wonderful book for anyone interested in what physics, and indeed all of science, is about. She masterfully describes the most momentous moments in physics history with verve and talent."—Amir D. Aczel, bestselling author of Fermat’s Last Theorem "A delightful meditation on the development of modern physics, culminating in the discovery of the Higgs. Husain follows the thread of its creation through a dialog between a journalist and young theory student, and as seen through the eyes of witnesses."—John Huth, Donner Professor of Science, Harvard University "Well-written and cleverly constructed, this book takes us on a journey through the history of physics as a series of fictional adventures, loosely linked by another fiction, the storytellers' emails to each other. Some books are praised because 'I couldn’t put it down,' but this one merits a deeper reading, one that stops, muses on, and savors each story before going on to the next. Each one captures not only the emergence of a significant idea in physics, but also something of the characters, culture, and times surrounding that development. So take your time, pause to ponder, but persevere, you will be well rewarded!"—Helen R. Quinn, Physicist, Science Educator, and co-author of The Mystery of the Missing Antimatter, Professor Emeritus SLAC National Accelerator Laboratory "How do theoretical physicists think? Tasneem Zehra Husain knows. She knows their purpose, feels their passions, articulates their frustrations, shares their triumphs. Through the device of fiction Only the Longest Threads communicates the history of physical thought—its roots in inquisitiveness and essential disinterest in outcome—with greater clarity than any popular science text."—Michael Duff FRS, Abdus Salam Professor of Theoretical Physics, Imperial College London "An artfully constructed journey through space and time."—Freddy Cachazo, Perimeter Institute for Theoretical Physics "Husain skillfully weaves a poetic tapestry."—Joseph Mazur, author of Enlightening Symbols
Answering calls in recent reform documents to shape instruction in response to students’ ideas while integrating key concepts and scientific and/or mathematical practices, this text presents the concept of responsive teaching, synthesizes existing research, and examines implications for both research and teaching. Case studies across the curriculum from elementary school through adult education illustrate the variety of forms this approach to instruction and learning can take, what is common among them, and how teachers and students experience it. The cases include intellectual products of students’ work in responsive classrooms and address assessment methods and issues. Many of the cases are supplemented with online resources (http://www.studentsthinking.org/rtsm) including classroom video and extensive transcripts, providing readers with additional opportunities to immerse themselves in responsive classrooms and to see for themselves what these environments look and feel like.