A stimulating collection of one hundred problems, complete with instructive solutions, on numbers, equations, polygons, polyhedra and many other topics. Extremely challenging for anyone with a fair knowledge of mathematics up to calculus. Includes an additional 13 problems without solutions.

This is a book of entertaining problems that can be solved through the use of algebra, problems with intriguing plots to excite the readers curiosity, amusing excursions into the history of mathematics, unexpected uses that algebra is put to in everyday affairs, and more. Algebra Can Be Fun has brought hundreds of thousands of youngsters into the fold of mathematics and its wonders. It is written in the form of lively sketches that discuss the multifarious (and exciting!) applications of algebra to the world about us. Here we encounter equations, logarithms, roots, progressions, the ancient and famous Diophantine analysis and much more. The examples are pictorial, vivid, often witty and bring out the essence of the matter at hand. There are numerous excursions into history and the history of algebra too. No one who has read this book will ever regard mathematics again in a dull light" Reviewers regard it as one of the finest examples of popular science writing.

The heart of mathematics is its elegance; the way it all fits together. Unfortunately, its beauty often eludes the vast majority of people who are intimidated by fear of the difficulty of numbers. Mathematical Elegance remedies this. Using hundreds of examples, the author presents a view of the mathematical landscape that is both accessible and fascinating. At a time of concern that American youth are bored by math, there is renewed interest in improving math skills. Mathematical Elegance stimulates students, along with those already experienced in the discipline, to explore some of the unexpected pleasures of quantitative thinking. Invoking mathematical proofs famous for their simplicity and brainteasers that are fun and illuminating, the author leaves readers feeling exuberant--as well as convinced that their IQs have been raised by ten points. A host of anecdotes about well-known mathematicians humanize and provide new insights into their lofty subjects. Recalling such classic works as Lewis Carroll's Introduction to Logic and A Mathematician Reads the Newspaper by John Allen Paulos, Mathematical Elegance will energize and delight a wide audience, ranging from intellectually curious students to the enthusiastic general reader.

Introduction to Matrix Analysis is a comprehensive guide to the study of matrices, written by renowned mathematician Richard Bellman. The book covers all the fundamental concepts of matrix theory, including matrix algebra, determinants, eigenvalues and eigenvectors, and linear transformations. The text is designed to be accessible to students with a basic understanding of linear algebra, and includes numerous examples and exercises to reinforce key concepts. In addition, the book also explores advanced topics such as singular value decomposition, positive definite matrices, and the spectral theorem. With its clear and concise presentation, Introduction to Matrix Analysis is an essential resource for anyone interested in the study of matrices and their applications in mathematics, science, and engineering.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

Abraham Adrian Albert (1905-72) was an American mathematician primarily known for his groundbreaking work on algebra. In this book, which was originally published in 1938, Albert provides a detailed exposition of 'modern abstract algebra', taking into account numerous discoveries in the field during the preceding ten years. A glossary is included. This is a highly informative book that will be of value to anyone with an interest in the development of algebra and the history of mathematics.

Arnold, V.I.; Ordinary Differential Equations, 3rd edition by Valdimir I. Arnold

Aerodynamics by Theodore Von Karman is a classic textbook that provides a comprehensive introduction to the principles of aerodynamics. The book covers the fundamental concepts of fluid dynamics, including the behavior of gases and liquids, the equations of motion, and the principles of conservation of mass, momentum, and energy. It also explores the physics of aerodynamic forces, such as lift and drag, and the role of viscosity and turbulence in the flow of fluids. The book includes detailed discussions of various aerodynamic phenomena, such as boundary layers, shock waves, and vortices, and their impact on aircraft design and performance. It also covers the design and analysis of airfoils, wings, and other aerodynamic components, as well as the principles of aircraft stability and control. Written by one of the most renowned figures in the field of aerodynamics, this book is an essential resource for students and professionals in the aerospace industry, as well as anyone interested in the science of flight. With its clear explanations, extensive illustrations, and practical examples, Aerodynamics is a valuable reference for anyone seeking a deeper understanding of the principles that govern the behavior of fluids in motion.Selected Topics In The Light Of Their Historical Development.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

"Circularity" is the story of a Janus-face conceptual structure, that on the one hand led to deep scientific discoveries, and on the other hand is used to trick the mind into believing the impossible. Alongside mathematical revolutions that eventually led to the invention of the computer, the book describes ancient paradoxes that arise from circular thinking. Another aspect of Circularity, its ability to entertain, leads to a surprising insight on the time old question " What is humor."

Hilbert Space Problem Book 1ST Edition by Paul Halmos (Author) (9.25x6.3x1.3in 365pgs Hardcover NO DJ) D VAN NOSTRAND COMPANY INC (1967)

Geared toward upper-level undergraduates and graduate students, this text explores the applications of nonstandard analysis without assuming any knowledge of mathematical logic. It develops the key techniques of nonstandard analysis at the outset from a single, powerful construction; then, beginning with a nonstandard construction of the real number system, it leads students through a nonstandard treatment of the basic topics of elementary real analysis, topological spaces, and Hilbert space. Important topics include nonstandard treatments of equicontinuity, nonmeasurable sets, and the existence of Haar measure. The focus on compact operators on a Hilbert space includes the Bernstein-Robinson theorem on invariant subspaces, which was first proved with nonstandard methods. Ever mindful of the needs of readers with little background in these subjects, the text offers a straightforward treatment that provides a strong foundation for advanced studies of analysis

First published originally in German in 1921, "Tractatus Logico-Philosophicus" is the only book-length philosophical work by Austrian philosopher Ludwig Wittgenstein published during his lifetime. Based upon notes made during his time serving in World War I, the treatise is composed of 526 numbered declarative statements that are presented without argument and were seen by Wittgenstein as being self-evident. Wittgenstein's style is succinct and sparse and his ideas are presented in a highly logical, organized, and scientific manner. Wittgenstein proposes that the solution to all major philosophical problems can be solved only with logic and a scientific analysis of language and its meaning. His idea that philosophy is not about metaphysics and mysticism, but about critical and rational thought led to a massive shift in philosophical theories after its publication. The treatise was influential with many of the "logical positivists" of the Vienna Circle, such as Rudolf Carnap and Friedrich Waismann, and to philosophers such as Bertrand Russell. Considered one of the most significant and influential philosophical works of the twentieth century, this treatise is an important read for any student of the history of language and ideas. This edition is printed on premium acid-free paper.

This book is different from other books on measure theory in that it accepts probability theory as an essential part of measure theory. This means that many examples are taken from probability; that probabilistic concepts such as independence, Markov processes, and conditional expectations are integrated into the text rather than being relegate to an appendix; that more attention is paid to the role of algebras than is customary; and that the metric defining the distance between sets as the measure of their symmetric difference is exploited more than is customary.

In these essays Heinz von Foerster discusses some of the fundamental principles that govern how we know the world and how we process the information from which we derive that knowledge. Included are path- breaking articles concerning the principles of computation in neural nets (1967), the definition of self-organizing systems (1960), the nature of cognition (1970), as well as recent expansions on these themes (e.g. "How recursive is communication," 1993). Working with Norbert Wiener, Warren McCullough, and others in the 1960s and 1970s, von Foerster was one of the founders of the science of cybernetics, which has had profound effects both on modern systems theory and on the philosophy of cognition. At the Biological Computer Laboratory at the University of Illinois he produced the first parallel computers and contributed to many other developments in the theory of computation and cognition.

Complex Variables

After completing his famous Foundations of Analysis (See AMS Chelsea Publishing, Volume 79.H for the English Edition and AMS Chelsea Publishing, Volume 141 for the German Edition, Grundlagen der Analysis), Landau turned his attention to this book on calculus. The approach is that of an unrepentant analyst, with an emphasis on functions rather than on geometric or physical applications. The book is another example of Landau's formidable skill as an expositor. It is a masterpiece of rigor and clarity.