الصفحة 13
الصفحة 13
A History of Abstract Algebra
This presentation provides an account of the intellectual lineage behind many of the basic concepts, results, and theories of abstract algebra.The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared unsolvable by classical means. A major theme of the approach in this book is to show how abstract algebra has arisen in attempts to solve some of these classical problems, providing context from which the reader may gain a deeper appreciation of the mathematics involved.
A first course in differential equations with modeling applications
A comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory.
A Field Guide to Algebra
Focuses on the structure of fields and is intended for a second course in abstract algebra. Besides providing proofs of the transcendance of pi and e, the book includes material on differential Galois groups and a proof of Hilbert's irreducibility theorem. The reader will hear about equations, both polynomial and differential, and about the algebraic structure of their solutions. In explaining these concepts, the author also provides comments on their historical development and leads the reader along many interesting paths. In addition, there are theorems from analysis: as stated before, the transcendence of the numbers pi and e, the fact that the complex numbers form an algebraically closed field, and also Puiseux's theorem that shows how one can parametrize the roots of polynomial equations, the coefficients of which are allowed to vary. There are exercises at the end of each chapter, varying in degree from easy to difficult. To make the book more lively, the author has incorporated pictures from the history of mathematics, including scans of mathematical stamps and pictures of mathematicians.
A Concise Introduction to Languages and Machines
This easy-to-follow text provides an accessible introduction to the key topics of formal languages and abstract machines within Computer Science.
40 Puzzles and Problems in Probability and Mathematical Statistics
"40 Puzzles and Problems in Probability and Mathematical Statistics" is intended to teach the reader to think probabilistically by solving challenging, non-standard probability problems. The motivation for this clearly written collection lies in the belief that challenging problems help to develop, and to sharpen, our probabilistic intuition much better than plain-style deductions from abstract concepts. The selected problems fall into two broad categories. Problems related to probability theory come first, followed by problems related to the application of probability to the field of mathematical statistics. All problems seek to convey a non-standard aspect or an approach which is not immediately obvious.
25 Years of Model Checking : History, Achievements, Perspectives
Model checking technology is among the foremost applications of logic to computer science and computer engineering. The model checking community has achieved many breakthroughs, bridging the gap between theoretical computer science and hardware and software engineering, and it is reaching out to new challenging areas such as system biology and hybrid systems. Model checking is extensively used in the hardware industry and has also been applied to the verification of many types of software. Model checking has been introduced into computer science and electrical engineering curricula at universities worldwide and has become a universal tool for the analysis of systems.
