In this new, innovative overview textbook, the authors put special emphasis on the deep ideas of mathematics, and present the subject through lively and entertaining examples, anecdotes, challenges and illustrations, all of which are designed to excite the student's interest. The underlying ideas include topics from number theory, infinity, geometry, topology, probability and chaos theory. Throughout the text, the authors stress that mathematics is an analytical way of thinking, one that can be brought to bear on problem solving and effective thinking in any field of study.

    Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his little finger told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.

    This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.

    It resurrects from the vaults of neglect the polymath Jerome Cardano, a Milanese of the sixteenth century. Who is he? A gambler and blasphemer, inventor and chancer, plagued by demons and anxieties, astrologer to kings, emperors and popes. This stubborn and unworldly man was the son of a lawyer and a brothel keeper, but also a gifted physician and the unacknowledged discoverer of the mathematical foundations of quantum physics. That is the argument of this charming and intoxicatingly clever book, which is truly original in its style, and in the manner of the modernists embodies in its very form its theories about the world.'The Quantum Astrologer’s Handbook' is a science book with the panache of a novel, for readers of Carlo Rovelli or Umberto Eco. It is a work of and about genius.

    

    These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students. The Fifth Edition includes a more thorough and linear presentation of logic, proof types and proof writing, and mathematical reasoning. This enhanced coverage will provide students with a solid understanding of the material as it relates to their immediate field of study and other relevant subjects. The inclusion of applications and examples to key topics has been significantly addressed to add clarity to every subject. True to the Fourth Edition, the text-specific web site supplements the subject matter in meaningful ways, offering additional material for students and instructors. Discrete math is an active subject with new discoveries made every year. The continual growth and updates to the web site reflect the active nature of the topics being discussed. The book is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.

    One island, two unique societies (Norse and Inuit). Only one of these societies would succeed--the other would fail. But how? With his trademark accessibility and comprehensiveness, Diamond documents how environmental damage, climate change, loss of friendly contacts and the rise of hostile ones, and the unique political, economic, and social settings of prehistoric Greenland combine to demonstrate exactly why and how societies choose to fail or succeed. Jared Diamond's latest book, "The World Until Yesterday: What Can We Learn from Traditional Societies?," is available from Viking.

    I’m Tim. I’m a single cell in society’s body. U.S. society, to be specific.So let me explain why we’re here.As a writer and a generally thinky person, I’ve spent a lot of my life thinking about the society I live in, and societies in general. I’ve always imagined society as a kind of giant human—a living organism like each of us, only much bigger.When you’re a single cell in the body of a giant, it’s hard to understand what the giant’s doing, or why it is the way it is, because you can’t really zoom out and look at the whole thing all at once. But we do our best.The thing is, when I’ve recently tried to imagine what society might look like, I haven’t really been picturing this:Giant stick figure: "I am grown up."Based on what I see around me, in person and online, it seems like my society is actually more like this:Giant stick figure throwing a giant tantrum because their chocolate ice cream fell on the ground.Individual humans grow older as they age—but it kind of seems like the giant human I live in has been getting more childish each year that goes by.So I decided to write a blog post about this. But then something else happened.When I told people I was planning to write a post about society, and the way people are acting, and the way the media is acting, and the way the government is acting, and the way everyone else is acting, people kept saying the same thing to me.Don’t do it. Don’t touch it. Write about something else. Anything else. It’s just not worth it.They were right. With so many non-controversial topics to write about, why take on something so loaded and risk alienating a ton of readers? I listened to people’s warnings, and I thought about moving on to something else, but then I was like, “Wait what? I live inside a giant and the giant is having a six-year-old meltdown in the grocery store candy section and that’s a not-okay thing for me to talk about?”It hit me that what I really needed to write about was that—about why it’s perilous to write about society."

    But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

    Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.

    This can be used as a companion guide in the study of Creation science. This revised edition adds the background history of nine new countries. Learn the true origins of the countries and people of France, Germany, Denmark, Sweden, Ireland, Scotland, Greece, Italy, Russia, Egypt, Israel, Iraq, Iran, China, the Arabs, the Kurds, and more. Some questions answered: Who were the Pharaohs in the times of Joseph and Moses? When did the famine of Joseph occur? What Egyptian documents mention these? When did the Exodus take place? When did the kings of Egypt start being called "Pharaoh" and why? Who was the first king of a united Italy? Who was Zeus and where was he buried? Where did Shem and Ham rule and where were they buried? How large was Nimrod's invasion force that set up the Babylonian Empire, and when did this invasion occur? What is Nimrod's name in Persian documents? How can we use this information to witness to unbelievers? Brought to you by Biblefacts Ministries, Biblefacts.org

    Highly recommended for graduate-level libraries.' ChoiceThis highly successful text, which first appeared in the year 1972 and has continued to be popular ever since, has now been brought up-to-date by incorporating the remarkable developments in the field of 'phase transitions and critical phenomena' that took place over the intervening years. This has been done by adding three new chapters (comprising over 150 pages and containing over 60 homework problems) which should enhance the usefulness of the book for both students and instructors. We trust that this classic text, which has been widely acclaimed for its clean derivations and clear explanations, will continue to provide further generations of students a sound training in the methods of statistical physics.

    It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

    Provides a review of introductory noncalculus-based physics for those who do not have a strong background in mathematics.

    I also hope that it will serve as a useful reference too for the many workers engaged in one type of solid state research activity or another, who may be without formal training in the subject.