This brief monograph by a distinguished professor is based on a mathematics course offered at the California Institute of Technology. The majority of students taking this course were advanced undergraduates and graduate students of engineering. A solid background in advanced calculus is a prerequisite. Topics include elementary and convergence theories of convolution quotients, differential equations involving operator functions, and exponential functions of operators. Tools developed in the preceding chapters are then applied to problems in partial differential equations. Solutions...
This brief monograph by a distinguished professor is based on a mathematics course offered at the California Institute of Technology. The majority of ...
Designed to help students appreciate the beauty of abstract patterns and the thrill of modeling the "real" world, this versatile, time-tested, and widely used text requires only two years of high school algebra. Suitable for a traditional one-year course in linear algebra or a more streamlined single-semester course, it can also serve for courses in finite mathematics or mathematics in the contemporary world for liberal arts students. Carefully chosen examples and exercises form the basis of this treatment, in which students solve problems related to biology (nesting habits of birds),...
Designed to help students appreciate the beauty of abstract patterns and the thrill of modeling the "real" world, this versatile, time-tested, and wid...
This groundbreaking monograph in advanced algebra addresses crossed products. Author Donald S. Passman notes that crossed products have advanced from their first occurrence in finite dimensional division algebras and central simple algebras to a closer relationship with the study of infinite group algebras, group-graded rings, and the Galois theory of noncommutative rings. Suitable for advanced undergraduates and graduate students of mathematics, the text examines crossed products and group-graded rings, delta methods and semiprime rings, the symmetric ring of quotients, and prime ideals,...
This groundbreaking monograph in advanced algebra addresses crossed products. Author Donald S. Passman notes that crossed products have advanced from ...
This classic monograph by a mathematician affiliated with Trinity College, Cambridge, offers a brief account of the invariant theory connected with a single quadratic differential form. Suitable for advanced undergraduates and graduate students of mathematics, it avoids unnecessary analysis and offers an accessible view of the field for readers unfamiliar with the subject. A historical overview is followed by considerations of the methods of Christoffel and Lie as well as Maschke's symbolic method and explorations of geometrical and dynamical methods. The final chapter on applications,...
This classic monograph by a mathematician affiliated with Trinity College, Cambridge, offers a brief account of the invariant theory connected with a ...
This introduction to functional analysis is based on the lecture notes of Martin Davis, a distinguished professor of mathematics. The treatment demonstrates the essential unity of mathematics without assuming more background than can be expected of advanced undergraduates and graduate students majoring in mathematics. A self-contained exposition of Gelfand's proof of Wiener's theorem, this volume explores set theoretic preliminaries, normed linear spaces and algebras, functions on Banach spaces, homomorphisms on normed linear spaces, and analytic functions into a Banach space. Numerous...
This introduction to functional analysis is based on the lecture notes of Martin Davis, a distinguished professor of mathematics. The treatment demons...
The application of statistical methods in mass production make possible the most efficient use of raw materials and manufacturing processes, economical production, and the highest standards of quality for manufactured goods. In this classic volume, based on a series of ground-breaking lectures given to the Graduate School of the Department of Agriculture in 1938, Dr. Shewhart illuminated the fundamental principles and techniques basic to the efficient use of statistical method in attaining statistical control, establishing tolerance limits, presenting data, and specifying accuracy and...
The application of statistical methods in mass production make possible the most efficient use of raw materials and manufacturing processes, economica...
On October 16, 1843, Sir William Rowan Hamilton discovered quaternions and, on the very same day, presented his breakthrough to the Royal Irish Academy. Meanwhile, in a less dramatic style, a German high school teacher, Hermann Grassmann, was developing another vectorial system involving hypercomplex numbers comparable to quaternions. The creations of these two mathematicians led to other vectorial systems, most notably the system of vector analysis formulated by Josiah Willard Gibbs and Oliver Heaviside and now almost universally employed in mathematics, physics and engineering. Yet the...
On October 16, 1843, Sir William Rowan Hamilton discovered quaternions and, on the very same day, presented his breakthrough to the Royal Irish Aca...
"The book is a pleasure to read. There is no question but that it will become, and deserves to be, a widely used textbook and reference." "Bulletin of the American Mathematical Society." Character theory provides a powerful tool for proving theorems about finite groups. In addition to dealing with techniques for applying characters to "pure" group theory, a large part of this book is devoted to the properties of the characters themselves and how these properties reflect and are reflected in the structure of the group. Chapter I consists of ring theoretic preliminaries. Chapters 2 to 6...
"The book is a pleasure to read. There is no question but that it will become, and deserves to be, a widely used textbook and reference." "Bulletin of...
Suitable for a graduate course in analytic probability theory, this text requires no previous knowledge of probability and only a limited background in real analysis. In addition to providing instruction for graduate students in mathematics and mathematical statistics, the book features detailed proofs that offer direct access to the basic theorems of probability theory for mathematicians of all interests. The treatment strikes a balance between measure-theoretic aspects of probability and distribution aspects, presenting some of the basic theorems of analytic probability theory in a...
Suitable for a graduate course in analytic probability theory, this text requires no previous knowledge of probability and only a limited background i...
A thorough first course in linear algebra, this two-part treatment begins with the basic theory of vector spaces and linear maps, including dimension, determinants, eigenvalues, and eigenvectors. The second section addresses more advanced topics such as the study of canonical forms for matrices. The treatment can be tailored to satisfy the requirements of both introductory and advanced courses. Introductory courses that also serve as an initiation into formal mathematics will focus on the first six chapters. Students already schooled in matrices and linear mappings as well as...
A thorough first course in linear algebra, this two-part treatment begins with the basic theory of vector spaces and linear maps, including dimension,...
