Geared toward college undergraduates new to the subject, this concise introduction to formal logic was written by Alice Ambrose and Morris Lazerowitz, a pair of noted scholars and prolific authors in this field. A preliminary section opens the subject under the heading of truth-functions. Two subsequent parts on quantification and classes, each subdivided into numerous brief specifics, complete the overview. Suitable for students of philosophy as well as mathematics, the three-part treatment begins with the intuitive development of the standard theory of sentential connectives (called "operators"). The theory is further developed with the assistance of truth-tables and ultimately as a logistic system. Part II explores first-order quantification theory. In addition to examining most of the familiar laws that can be expressed by monadic formulas, the text addresses polyadic principles and the theories of identity and descriptions. Part III focuses on elementary concepts of classes, from class membership and class inclusion to the algebra of classes. Each part concludes with a series of exercises.

In this fascinating look at the European scientific advances of the seventeenth and early eighteenth centuries, historian Lisa Jardine demonstrates that the pursuit of knowledge occurs not in isolation, but rather in the lively interplay and frequently cutthroat competition between creative minds. The great thinkers of that extraordinary age, including Isaac Newton, Johannes Kepler, and Christopher Wren, are shown in the context in which they lived and worked. We learn of the correspondences they kept with their equally passionate colleagues and come to understand the unique collaborative climate that fostered virtuoso discoveries in the areas of medicine, astronomy, mathematics, biology, chemistry, botany, geography, and engineering. Ingenious Pursuits brilliantly chronicles the true intellectual revolution that continues to shape our very understanding of ourselves, and of the world around us.

Leopold Infeld was one of the nine eminent scientists who, together with Albert Einstein, signed Bertrand Russell's famous letter warning that in this nuclear age, only a ban on war itself could save this planet (July, 1955). Infeld was born in the Jewish ghetto of Cracow, Poland in 1898, and this autobiography contains a vivid description of this long-since-vanished world. He was assistant to and then a scientific collaborator with Albert Einstein at the Institute for Advanced Study, Princeton, NJ (1936-1938), and this collaboration continued for twelve years while Infeld was at the University of Toronto. In 1938 he wrote a book together with Albert Einstein that became a number one bestseller, The Evolution of Physics. Infeld was lecturer and then Professor of Applied Mathematics at the University of Toronto from 1938--1950. From 1945-1950 he gave many lectures all over Canada on the elementary physics of the atom bomb, warning that Russia would soon have the bomb and urging that the short period

"Delia Welegtabit discovered two things during her childhood on a South Pacific island: her love for mathematics and a novel that isn't supposed to exist. But the elusive book proves unexpectedly dangerous. Oskar Lens, a science fiction-obsessed mobster in the midst of an existential crisis, will stop at nothing to find the novel. After Delia's husband Levi goes missing, she seeks help from Daniel Chase, a young, face-blind book dealer. The infamous novel Lode Stars was written by the infamous Eugene Charles Hartley: legendary pulp science-fiction writer and founder of the Church of the All-Seeing Eyes. In Hartley's novel, a doppelganger of Delia searches for her missing father in a strange star system. But is any of Lode Stars real? Was Hartley a cynical conman on a quest for wealth and immortality, creating a religion he did not believe in? Or was he a visionary who truly discovered the secrets of the universe?"--

The twenty-eight essays in this Handbook, all by leading experts in the field, provide the most extensive treatment of various epistemological problems, supplemented by a historical account of this field. The entries are self-contained and substantial contributions to topics such as the sources of knowledge and belief, knowledge acquisition, and truth and justification. There are extensive essays on knowledge in specific fields: the sciences, mathematics, the humanities and the social sciences, religion, and language. Special attention is paid to current discussions on evolutionary epistemology, relativism, the relation between epistemology and cognitive science, sociology of knowledge, epistemic logic, knowledge and art, and feminist epistemology.

"This Third Edition includes basic modern tools of computational mathematics for boundary value problems and also provides the foundational mathematical material necssary to understand and use the tools. Central to the text is a down-to-earth approach that shows readers how to use differential and integral equations when tackling significant problems in the physical sciences, engineering, and applied mathematics, and the book maintains a careful balance between sound mathematics and meaningful applications. A new co-author, Michael J. Holst, has been added to this new edition, and together he and Ivar Stakgold incorporate recent developments that have altered the field of applied mathematics, particularly in the areas of approximation methods and theory including best linear approximation in linear spaces; interpolation of functions in Sobolev Spaces; spectral, finite volume, and finite difference methods; techniques of nonlinear approximation; and Petrov-Galerkin and Galerkin methods for linear equations. Additional topics have been added including weak derivatives and Sobolev Spaces, linear functionals, energy methods and A Priori estimates, fixed-point techniques, and critical and super-critical exponent problems. The authors have revised the complete book to ensure that the notation throughout remained consistent and clear as well as adding new and updated references. Discussions on modeling, Fourier analysis, fixed-point theorems, inverse problems, asymptotics, and nonlinear methods have also been updated"--

"Evelyn Fox Keller trained as a theoretical physicist at a time when women didn't "do physics." Unable to find a supportive advisor, she moved into the new field of molecular biology just getting off the ground. After receiving her doctorate, she returned to physics but then took another swerve, joining a small interdisciplinary effort to develop mathematical models of biological systems. This work led to her appointment to a special position as Professor of Mathematics and Humanities at Northeastern University. When second-wave feminism arrived in the 1960s, it changed the lives of everyone in its path. It certainly changed Keller's, leading her beyond the borders of science altogether. Eventually she began to think of herself as a dual citizen of the proverbial two cultures―science and humanities. The trajectory was hardly straightforward, nor was it conducive to building a conventional career, or even getting a job. Now in hindsight, after an illustrious career and having published fourteen books, Keller reflects on her life, influences, successes and struggles along her trailblazing path as a scientist and feminist." -- From publisher's website

"A delightful book."— New York Times "I have studied with pleasure [this] new book…Beautiful examples…Illuminating. I am convinced that [Lieber's] original enterprise will get the recognition it so richly deserves."—Albert Einstein "The Liebers have written an ingenious, entertaining, and illuminating book."— Saturday Review of Literature "The book should be 'required reading' especially for non-mathematicians." —E.T. Bell, author of The Development of Mathematics First published in 1942, this whimsical exploration of how to think in a mathematical mood continues to delight math-lovers of all ages. Do you know that two times two is not always four; that the sum of the angles in a triangle does not always equal 180°; that sometimes it is possible to draw two parallel lines through the same point? In The Education of T. C. MITS , Lillian Lieber opens the door to the wonder of mathematical thinking and its application to everyday life. Lieber uses simple language and fanciful illustrations drawn by her husband, Hugh, to present fundamental mathematical concepts with a deft touch. The new foreword by Harvard University mathematics professor Barry Mazur is a tribute to the Liebers' influence on generations of mathematicians.

1. Vectors and matrices.- 2. Functions.- 3. Differentiation.- 4. More about differentiation.- 5. Applications to motion.- 6. Integration.- 7. Line and surface integrals.- 8. Divergence and Stokes' Theorems and conservation laws.- 9. Partial differential equations.- Answers to selected problems.- Index.

The aim of this book is to explain in simple language what we know and what we do not know about information and entropy two of the most frequently discussed topics in recent literature and whether they are relevant to life and the entire universe. Entropy is commonly interpreted as a measure of disorder. This interpretation has caused a great amount of "disorder" in the literature. One of the aims of this book is to put some "order" in this "disorder." The book explains with minimum amount of mathematics what information theory is and how it is related to thermodynamic entropy. Then it critically examines the application of these concepts to the question of "What is life?" and whether or not they can be applied to the entire universe.

After a series of light logic puzzles, the author presents a bombshell puzzle so startling that it seems incredible that there could be any solution at all! But there is indeed a solution - moreover, one that requires a chain of lesser puzzles to be solved first. The reader is thus journeyed through a maze of subsidiary problems that has all the earmarks of an entertaining detective story. Of the author's 20 published books, this is the 11th whose purpose is to lead the unwary reader into deep logical waters through seductively entertaining logic puzzles. The "deep waters" of this book is boolean algebra with such weird looking equations as 1+1=0 - a subject which today plays a vital role, not only in mathematical systems, but also in computer science and artificial intelligence.

Includes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one-parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more. Assumes prior knowledge of Naive set theory, linear algebra, point set topology, basic complex variable, and real variables. Includes an appendix on the Riesz representation theorem.

High-dimensional knot theory is the study of the embeddings of n-dimensional manifolds in (n+2)-dimensional manifolds, generalizing the traditional study of knots in the case n=1. The main theme is the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory. Many results in the research literature are thus brought into a single framework, and new results are obtained. The treatment is particularly effective in dealing with open books, which are manifolds with codimension 2 submanifolds such that the complement fibres over a circle. The book concludes with an appendix by E. Winkelnkemper on the history of open books.

A fascinating exploration of the limits of human knowledge of our planet, its history and culture, and the universe beyond, from the author of The Things that Nobody Knows There are many, many more things that nobody knows. Do animals have a sense of humor? Why do we have five fingers? How long can humans live? What did Jesus do in his youth? Which speech did Lincoln deliver at Gettysburg? Does the appendix have any use? Is there an odd perfect number? In this witty and enlightening follow-up to The Things that Nobody Know s, William Hartston takes us on a guided tour of 501 further gaps in our knowledge of cosmology, mathematics, animal behavior, medical science, music, art, and literature.

"The interpolations tying mathematics into human life and thought are brilliantly clear."— Booklist "Her presentation…is conversational and humorous, and should help to simplify some complex concepts."— Kirkus Infinity. It sounds simple…but is it? This elegant, accessible, and playful book artfully illuminates one of the most intriguing ideas in mathematics. Lillian Lieber presents an entertaining, yet thorough, explanation of the concept and cleverly connects mathematical reasoning to larger issues in society. Infinity includes a new foreword by Harvard professor Barry Mazur. "Another excellent book for the lay reader of mathematics…In explaining [infinity], the author introduces the reader to a good many other mathematical terms and concepts that seem unintelligible in a formal text but are much less formidable when presented in the author's individual and very readable style."— Library Journal "Mrs. Lieber, in this text illustrated by her husband, Hugh Gray Lieber, has tackled the formidable task of explaining infinity in simple terms, in short line, short sentence technique popularized by her in The Education of T.C. MITS ."— Chicago Sunday Tribune

Argues that the probabilities invoked in Anglo=American law do not conform to the mathematics of the classical calculus of chance but have a determinate non-POascalian structure whih is closely connected with certain other patterns of human reasoning, and notably with the strucutre of inductive reasoning in experimental science.

This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency (1979). Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention. Modal logic is concerned with the notions of necessity and possibility. What George Boolos does is to show how the concepts, techniques, and methods of modal logic shed brilliant light on the most important logical discovery of the twentieth century: the incompleteness theorems of Kurt Godel and the 'self-referential' sentences constructed in their proof. The book explores the effects of reinterpreting the notions of necessity and possibility to mean provability and consistency.

"Prime numbers are beautiful, mysterious, and beguiling mathematical objects. The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the so-called Riemann Hypothesis, which remains to be one of the most important unsolved problems in mathematics. Through the deep insights of the authors, this book introduces primes and explains the Riemann Hypothesis. Students with minimal mathematical background and scholars alike will enjoy this comprehensive discussion of primes. The first part of the book will inspire the curiosity of a general reader with an accessible explanation of the key ideas. The exposition of these ideas is generously illuminated by computational graphics that exhibit the key concepts and phenomena in enticing detail. Readers with more mathematical experience will then go deeper into the structure of primes and see how the Riemann Hypothesis relates to Fourier analysis using the vocabulary of spectra. Readers with a strong mathematical background will be able to connect these ideas to historical formulations of the Riemann Hypothesis."--Publisher description.