104 Number Theory Problems: From the Training of the USA IMO Team


Titu Andreescu - 2006
    Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.

How to Count to Infinity


Marcus du Sautoy - 2020
    But this book will help you to do something that humans have only recently understood how to do: to count to regions that no animal has ever reached. By the end of this book you'll be able to count to infinity... and beyond. On our way to infinity we'll discover how the ancient Babylonians used their bodies to count to 60 (which gave us 60 minutes in the hour), how the number zero was only discovered in the 7th century by Indian mathematicians contemplating the void, why in China going into the red meant your numbers had gone negative and why numbers might be our best language for communicating with alien life.But for millennia, contemplating infinity has sent even the greatest minds into a spin. Then at the end of the nineteenth century mathematicians discovered a way to think about infinity that revealed that it is a number that we can count. Not only that. They found that there are an infinite number of infinities, some bigger than others. Just using the finite neurons in your brain and the finite pages in this book, you'll have your mind blown discovering the secret of how to count to infinity.Do something amazing and learn a new skill thanks to the Little Ways to Live a Big Life books!

Symmetry: The Ordering Principle


David G. Wade - 2006
    In this little book Welsh writer and artist David Wade paints a picture of one of the most elusive and pervasive concepts known to man.

What Is the Name of This Book?


Raymond M. Smullyan - 1978
    Raymond M. Smullyan — a celebrated mathematician, logician, magician, and author — presents a logical labyrinth of more than 200 increasingly complex problems. The puzzles delve into Gödel’s undecidability theorem and other examples of the deepest paradoxes of logic and set theory. Detailed solutions follow each puzzle.

My Brain is Open: The Mathematical Journeys of Paul Erdős


Bruce Schechter - 1998
    Hungarian-born Erdős believed that the meaning of life was to prove and conjecture. His work in the United States and all over the world has earned him the titles of the century's leading number theorist and the most prolific mathematician who ever lived. Erdős's important work has proved pivotal to the development of computer science, and his unique personality makes him an unforgettable character in the world of mathematics. Incapable of the smallest of household tasks and having no permanent home or job, he was sustained by the generosity of colleagues and by his own belief in the beauty of numbers. Witty and filled with the sort of mathematical puzzles that intrigued Erdős and continue to fascinate mathematicians today, My Brain Is Open is the story of this strange genius and a journey in his footsteps through the world of mathematics, where universal truths await discovery like hidden treasures and where brilliant proofs are poetry.

Who Is Fourier? a Mathematical Adventure


Transnational College of Lex - 1995
    This is done in a way that is not only easy to understand, but is actually fun! Professors and engineers, with high school and college students following closely, comprise the largest percentage of our readers. It is a must-have for anyone interested in music, mathematics, physics, engineering, or complex science. Dr. Yoichiro Nambu, 2008 Nobel Prize Winner in Physics, served as a senior adviser to the English version of Who is Fourier? A Mathematical Adventure.

Ludwig Wittgenstein: The Duty of Genius


Ray Monk - 1990
    Monk's life of Wittgenstein is such a one."--"The Christian Science Monitor."

Whatever Happened to Good and Evil?


Russ Shafer-Landau - 2003
    Some people, especially those who are not religious, are not sure how to substantiate this view. Whatever Happened to Good and Evil? provides a basis for exploring these doubts and ultimately defends the objectivity of ethics. Engaging and accessible, it is the first introduction to meta-ethics written especially for students and general readers with no philosophical background. Focusing on the issues at the foundation of morality, it poses such questions as: How can we know what is right and wrong? Does ethical objectivity require God? Why should I be moral? Where do moral standards come from? What is a moral value, and how can it exist in a scientific world? Do cultural diversity and persistent moral disagreement support moral skepticism? Writing in a clear and lively style and employing many examples to illustrate theoretical arguments, Russ Shafer-Landau identifies the many weaknesses in contemporary moral skepticism and devotes considerable attention to presenting, and critiquing, the most difficult objections to his view. Also included in the book are a helpful summary of all the major arguments covered, as well as a glossary of key philosophical terms. Whatever Happened to Good and Evil? is ideal for a variety of philosophy courses and compelling reading for anyone interested in ethics.

Symbolic Logic And The Game Of Logic


Lewis Carroll - 1958
    Written by the 19th-century mathematician who also gave us "Alive in Wonderland", they are among the most entertaining logical works ever written, and contain some of the most thought-provoking puzzles ever devised.

Phenomenology of Spirit


Georg Wilhelm Friedrich Hegel - 1807
    It begins with a Preface, created after the rest of the manuscript was completed, that explains the core of his method and what sets it apart from any preceding philosophy. The Introduction, written before the rest of the work, summarizes and completes Kant's ideas on skepticism by rendering it moot and encouraging idealism and self-realization. The body of the work is divided into six sections of varying length, entitled "Consciousness," "Self-Consciousness," "Reason," "Spirit," "Religion," and "Absolute Knowledge." A myriad of topics are discussed, and explained in such a harmoniously complex way that the method has been termed Hegelian dialectic. Ultimately, the work as a whole is a remarkable study of the mind's growth from its direct awareness to scientific philosophy, proving to be a difficult yet highly influential and enduring work.

Epistemology: An Anthology


Ernest SosaRichard Foley - 1999
    It is ideal as a reader for all courses in epistemology.

The Concept of Mind


Gilbert Ryle - 1949
    Ryle's linguistic analysis remaps the conceptual geography of mind, not so much solving traditional philosophical problems as dissolving them into the mere consequences of misguided language. His plain language and esstentially simple purpose place him in the traditioin of Locke, Berkeley, Mill, and Russell.

How to read and do proofs


Daniel Solow - 1982
    Shows how any proof can be understood as a sequence of techniques. Covers the full range of techniques used in proofs, such as the contrapositive, induction, and proof by contradiction. Explains how to identify which techniques are used and how they are applied in the specific problem. Illustrates how to read written proofs with many step-by-step examples. Includes new, expanded appendices related to discrete mathematics, linear algebra, modern algebra and real analysis.

Schaum's Outline of Probability and Statistics


Murray R. Spiegel - 1975
    Its big-picture, calculus-based approach makes it an especially authoriatative reference for engineering and science majors. Now thoroughly update, this second edition includes vital new coverage of order statistics, best critical regions, likelihood ratio tests, and other key topics.

Elementary Number Theory


David M. Burton - 1976
    It reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.