Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations--as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal relevance that explores the great variety of applications and importance of symmetry.

    QFT is the only physics theory that makes sense and that dispels or resolves the paradoxes of relativity and quantum mechanics that have confused and mystified so many people.

    Linear Equations; Vector Spaces; Linear Transformations; Polynomials; Determinants; Elementary canonical Forms; Rational and Jordan Forms; Inner Product Spaces; Operators on Inner Product Spaces; Bilinear Forms For all readers interested in linear algebra.

    Dozens of examples in innumeracy show us how it affects not only personal economics and travel plans, but explains mis-chosen mates, inappropriate drug-testing, and the allure of pseudo-science.

    Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't be solved. For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.

    The calculus is not a hard subject and I prove this through an easy to read and obvious approach spanning only 100 pages. I have written this book with the following type of student in mind; the non-traditional student returning to college after a long break, a notoriously weak student in math who just needs to get past calculus to obtain a degree, and the garage tinkerer who wishes to understand a little more about the technical subjects. This book is meant to address the many fundamental thought-blocks that keep the average 'mathaphobe' (or just an interested person who doesn't have the time to enroll in a course) from excelling in mathematics in a clear and concise manner. It is my sincerest hope that this book helps you with your needs.Show more Show less

    The material is arranged chronologically beginning with archaic origins and covers Egyptian, Mesopotamian, Greek, Chinese, Indian, Arabic and European contributions done to the nineteenth century and present day. There are revised references and bibliographies and revised and expanded chapters on the nineteeth and twentieth centuries.

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    The Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included.Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises.

    This book marks the first substantial and authoritative effort to close this gap. Colin Camerer, one of the field's leading figures, uses psychological principles and hundreds of experiments to develop mathematical theories of reciprocity, limited strategizing, and learning, which help predict what real people and companies do in strategic situations. Unifying a wealth of information from ongoing studies in strategic behavior, he takes the experimental science of behavioral economics a major step forward. He does so in lucid, friendly prose.Behavioral game theory has three ingredients that come clearly into focus in this book: mathematical theories of how moral obligation and vengeance affect the way people bargain and trust each other; a theory of how limits in the brain constrain the number of steps of I think he thinks . . . reasoning people naturally do; and a theory of how people learn from experience to make better strategic decisions. Strategic interactions that can be explained by behavioral game theory include bargaining, games of bluffing as in sports and poker, strikes, how conventions help coordinate a joint activity, price competition and patent races, and building up reputations for trustworthiness or ruthlessness in business or life.While there are many books on standard game theory that address the way ideally rational actors operate, Behavioral Game Theory stands alone in blending experimental evidence and psychology in a mathematical theory of normal strategic behavior. It is must reading for anyone who seeks a more complete understanding of strategic thinking, from professional economists to scholars and students of economics, management studies, psychology, political science, anthropology, and biology.

    Who invented zero? Why are there 60 seconds in a minute? Can a butterfly's wings really cause a storm on the far side of the world? In 50 concise essays, Professor Tony Crilly explains the mathematical concepts that allow use to understand and shape the world around us.

    The God series fully reveals what Pythagoras meant. Mathematics - built from numbers - is not an abstraction but is ontological: it actually exists. Numbers are real things. Specifically, they are the frequencies of energy waves. (Moreover, energy waves are simply sinusoidal waves: sines and cosines, meaning that the study of energy is the study of sinusoids). There are infinite energy waves, hence infinite numbers. No numbers are privileged over any others, so negative and imaginary numbers are as ontologically important as real numbers (upon which science is exclusively based).Real numbers correspond to space and imaginary numbers to time. Negative numbers are "antimatter": a mirror image universe.The two most powerful numbers of all - and the ultimate basis of Illuminist thinking - are zero and infinity, which are harnessed together ontologically (opposite sides of the same coin, so to speak). The existence of zero and infinity is vehemently denied by the ideology of scientific materialism. In Illuminism, these two numbers not only exist, they are the "God" numbers: the origin of all other numbers. Zero and infinity comprise the Big Bang Singularity itself from which an infinitely large universe emerged: "everything" literally came from "nothing".Moreover, zero is also the "monad" of Leibniz (an Illuminati Grand Master). It is therefore the number of THE SOUL, and it has INFINITE capacity. Being dimensionless - a mathematical point - the soul is outside the dimensional, material domain of space and time, hence the soul is indestructible, immortal and cannot be detected by any conventional scientific experiment.What we are describing are the necessary, analytic, eternal truths of mathematics - they have no connection with Abrahamic religious faith. There is NO Creator God but, astoundingly, each soul is capable of being promoted to God status, just as the pawn in chess can become the most important chess piece, the Queen, if it reaches the other side of the battlefield (the board). In Illuminism, if you reach gnosis - enlightenment - you become God.Mathematics is literally everything. Unlike science, mathematics offers certainty: 100% true and incontestable knowledge. Mathematics unifies science, religion and metaphysics. Mathematics is the true Grand Unified Theory of Everything that science pursues so futilely. Science can never deliver truth and certainty because it is inherently a succession of provisional theories, any of which can be overturned at any time by new experimental data. Science is based on ideas of validation and falsification. Mathematics is based on absolute analytic and unarguable certainty. No experiment can ever contradict a mathematical truth.Mathematics is the ONLY answer to everything. Mathematics is the ONLY subject inherently about eternal, Platonic truth. As soon as existence is understood to be nothing but ontological mathematics, all questions are ipso facto answered.The God series, starting with The God Game, reveals the astonishing power of ontological mathematics to account for everything, including things such as free will, irrationalism, emotion, consciousness and qualia, which seem to have no connection with mathematics.Read the God series and you will become a convert to the world's only rational religion - Illuminism, the Pythagorean religion of mathematics that infallibly explains all things and guarantees everyone a soul that is not only eternal but also has the capacity to make of each of us a true God.Isn't it time to become Illuminated?

    The book is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology.Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous asides, ranging from limericks and tall stories to cartoons and decorative drawings.

    Human beings have long been both fascinated and appalled by randomness. On the one hand, we love the thrill of a surprise party, the unpredictability of a budding romance, or the freedom of not knowing what tomorrow will bring. We are inexplicably delighted by strange coincidences and striking similarities. But we also hate uncertainty's dark side. From cancer to SARS, diseases strike with no apparent pattern. Terrorists attack, airplanes crash, bridges collapse, and we never know if we'll be that one in a million statistic. We are all constantly faced with situations and choices that involve randomness and uncertainty. A basic understanding of the rules of probability theory, applied to real-life circumstances, can help us to make sense of these situations, to avoid unnecessary fear, to seize the opportunities that randomness presents to us, and to actually enjoy the uncertainties we face. The reality is that when it comes to randomness, you can run, but you can't hide. So many aspects of our lives are governed by events that are simply not in our control. In this entertaining yet sophisticated look at the world of probabilities, author Jeffrey Rosenthal--an improbably talented math professor--explains the mechanics of randomness and teaches us how to develop an informed perspective on probability.

    It emphasizes forms suitable for students and researchers whose interest lies in solving equations rather than in general theory. Solutions to odd-numbered problems appear at the end. 1957 edition.