"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.

Most mathematicians, when asked about the nature and meaning of mathematics, vacillate between the two unrealistic poles of Platonism and formalism. By looking carefully at what mathematicians really do when they are doing mathematics, Reuben Hersh offers an escape from this trap. This book of selected articles and essays provides an honest, coherent, and clearly understandable account of mathematicians' proof as it really is, and of the existence and reality of mathematical entities. It follows in the footsteps of Poincare, Hadamard, and Polya. The pragmatism of John Dewey is a better fit for mathematical practice than the dominant ""analytic philosophy''. Dialogue, satire, and fantasy enliven the philosophical and methodological analysis. Reuben Hersh has written extensively on mathematics, often from the point of view of a philosopher of science. His book with Philip Davis, The Mathematical Experience, won the National Book Award in science.

This book analyzes the different ways mathematics is applicable in the physical sciences, and presents a startling thesis--the success of mathematical physics appears to assign the human mind a special place in the cosmos. Mark Steiner distinguishes among the semantic problems that arise from the use of mathematics in logical deduction; the metaphysical problems that arise from the alleged gap between mathematical objects and the physical world; the descriptive problems that arise from the use of mathematics to describe nature; and the epistemological problems that arise from the use of mathematics to discover those very descriptions. The epistemological problems lead to the thesis about the mind. It is frequently claimed that the universe is indifferent to human goals and values, and therefore, Locke and Peirce, for example, doubted science's ability to discover the laws governing the humanly unobservable. Steiner argues that, on the contrary, these laws were discovered, using manmade mathematical analogies, resulting in an anthropocentric picture of the universe as "user friendly" to human cognition--a challenge to the entrenched dogma of naturalism.

Using Technology for Problem Solving in Middle and High School Mathematics: Investigations Using Scientific and Graphing Calculators, Spreadsheets, and The Geometer's Sketchpad © Firmly rooted in the NCTM Principles and Standards, Using Technology for Problem Solving in Middle and High School Mathematics examines why technology is essential to today's mathematics classroom, and illustrates how using technology can encourage and enhance your students' study and understanding of mathematics. Inquiry-based, this book provides both a five-step model and 23 sample investigations that demonstrate how to help students become better problem solvers through the use of four types of instructional technology: the scientific calculator, the graphing calculator, spreadsheet software, and The Geometer's Sketchpad © software. Here's what reviewers say about this book: "The five-step model provided here is excellent, giving teachers a rich mathematical perspective to draw upon. This process moves students from inductive explorations to deductive justifications of the results, which is aligned with current theories on how students best learn." Dr. Robert M. Horton, Clemson University "I like the organization of the investigations; they include a nice variety of topics and tend to avoid the 'already known' examples. The level of technology used moves from simple to more complex, and the reader is exposed to potentially new uses of the technology beyond commonly used (novice) features." Dr. Linda Bolte, Eastern Washington University "I really like the idea of the research summaries. In all cases, I think bringing mathematics research into the practice arena is extremely useful and productive." Dr. Janet Bowers, San Diego State University

Solution of Equations and Systems of Equations, Second Edition deals with the Laguerre iteration, interpolating polynomials, method of steepest descent, and the theory of divided differences. The book reviews the formula for confluent divided differences, Newton's interpolation formula, general interpolation problems, and the triangular schemes for computing divided differences. The text explains the method of False Position (Regula Falsi) and cites examples of computation using the Regula Falsi. The book discusses iterations by monotonic iterating functions and analyzes the connection of the Regula Falsi with the theory of iteration. The text also explains the idea of the Newton-Raphson method and compares it with the Regula Falsi. The book also cites asymptotic behavior of errors in the Regula Falsi iteration, as well as the theorem on the error of the Taylor approximation to the root. The method of steepest descent or gradient method proposed by Cauchy ensures "global convergence" in very general conditions. This book is suitable for mathematicians, students, and professor of calculus, and advanced mathematics.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

1959, probably a First Edition but not stated, no other date present, stated First Printing, red cloth hardcover with black lettering on the spine, 482 pages with Index, illustrated with diagrams, measures about 8 7/8 inches X 6 1/8 inches.

This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images. At one of the first international mathematical congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the nineteenth century as a legacy for the twentieth century). In spite of the simplicity and importance of this problem (including its numerous applications), it remains unsolved to this day (although, as you will now see, many remarkable results have been discovered).

A classic treatment of cross-spaces from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.

One of the great achievements of contemporary mathematics is the new understanding of four dimensions. Michael Freedman and Frank Quinn have been the principals in the geometric and topological development of this subject, proving the Poincar and Annulus conjectures respectively. Recognition for this work includes the award of the Fields Medal of the International Congress of Mathematicians to Freedman in 1986. In Topology of 4-Manifolds these authors have collaborated to give a complete and accessible account of the current state of knowledge in this field. The basic material has been considerably simplified from the original publications, and should be accessible to most graduate students. The advanced material goes well beyond the literature; nearly one-third of the book is new. This work is indispensable for any topologist whose work includes four dimensions. It is a valuable reference for geometers and physicists who need an awareness of the topological side of the field.Originally published in 1990.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

A volume containing original essays from quite diverse fields in mathematics is something of a rarity, especially if renowned scientists show the width of their discipline to the reader. This book is just such a rarity - a veritable gem. It was written to celebrate the 50th anniversary of the mathematical research institute at Oberwolfach. The articles span a range of topics from general reflections on the place of mathematics in contemporary culture to essays dealing with aspects of algebra, analysis, geometry, coding theory, scientific computing and topology. All essays are interrelated, proving the old rule that you can divide and still conquer. A book in which every mathematician or scientist interested in mathematics will find something to take their fancy.

This book was first published in 1942 for distribution to American soldiers during WWII. The title character, T.C. Mits is an acronym for The Celebrated Man In The Street. Like many Americans who fought in the war, everyman Mits has a limited education. The point of this book is to provide that everyman with a series of short lessons in mathematics. The presentation is unique, heavily illustrated with line drawings, and all text is presented as free verse.