Five recent book reviews
The book is a collection of problems from elementary mathematics. It can be of substantial help in work with gifted secondary school students. On the other hand, it also contains problems on determinants, special sequences, functional equations, primitive functions, difference and differential equations, so that it will be useful for work with students of basic courses on analysis and algebra. The collection is divided into 24 groups. Over 100 problems are presented with solutions, and another 150 are accompanied by hints and clear ideas how to proceed on the way to a solution. Using included material, the author leads readers from active problem solving to exploration of methods to obtain new problems and to an active use of the gained inventive skills. The book is based on the author’s personal long lasting cooperation with the Romanian journal Gazeta Matematica.
This little book is the third revised edition of a textbook targeted at university students who have passed calculus courses and are entering the world of pure mathematics. The core of the text is a detailed explanation of basic mathematical concepts and notions, such as sets (up to concepts of denumerability and uncountability), operations on them, functions and relations. Also, mathematical notation is analyzed. There are parts written as an essay (What is mathematics and what does it do for us?) and short historical remarks - these should give a motivation rather than a complete account of the topic. The text is accompanied by a lot of exercises. The style is very narrative, sometimes too much, with the aim to motivate and persuade at every step. Therefore the book should even find interested high-school students among its readers.
The book is a compilation of problems with solutions, which have appeared on the written examinations in Berkeley since 1977. The 3rd edition has been updated and includes the exams up to the fall 2003 term. (Reviews of previous editions have appeared in this Newsletter, Issues 30 and 43.)
This remarkable book is the revised translation of the German edition published in 1996. On almost 1300 pages, Eberhard Zeidler offers a fascinating panoramic overview of mathematics, ranging from elementary results to advanced and sophisticated parts of contemporary mathematics. The book is a beautiful illustration of the fact that mathematics is much more than a dry collection of formulas, definitions, theorems and manipulation with symbols. The historical background of results and theories is explained in many places throughout the book and an emphasis to significant applications is given. The introductory chapter is a 200-page reference book on basic mathematical notions usually required by students, scientists and other practitioners. The following three chapters are devoted to analysis (375 pages), algebra (125 pages) and geometry (150 pages). A short chapter on logic and set theory follows this. The last three chapters are devoted to the following fields of applications of mathematics: calculus of variations and optimization, stochastic calculus, numerical mathematics and scientific computing. The eight chapters are divided into 62 sections and 367 subsections. More than 20 pages at the end of the book are devoted to a detailed sketch of the history of mathematics. Throughout the book, there are many tables, illustrations and indications on software systems making it possible to carry out many routine jobs in mathematics on a standard PC. Also, a rich bibliography is included.
In order to show that the book is by no means a dry collection of mathematical facts, a selection (necessarily limited) of several subtitles can be offered: the perihelion motion of Mercury, fast computers and the death of the sun, mathematics and computers – a revolution in mathematics, rigorous justifications of the Cartan differential calculus and its applications, vector analysis and physical fields, conservation laws in mechanics, applications of ODE’s to electrical circuits or chemical reactions, the two body problem, laws of Kepler, shock waves and the conditions for entropy of Lax, the Hamilton-Jacobi equations, applications to geometric optics, electrostatics and Green’s functions, applications to quantum mechanics, dynamics of gases, sound waves, applications to hydromechanics, number theory and coding theory, A. Weil and Fermat’s last theorem, the Dirac equation and relativistic electrons, spin geometry and fermions, the necessity of proofs in the age of computers, wavelets, data compression and adaptivity, etc. The book is aimed at a wide readership: students of mathematics, engineering, natural sciences, and economy, practitioners who work in these fields, school and university teachers. No doubt professional mathematicians will also find the book very useful. This fascinating book can be strongly recommended to anybody who applies mathematics or simply wants to understand important concepts and results from both classical and modern mathematics.
This remarkable book collects some interesting creative writing of 21 authors (young poets, writers, artists, mathematicians, geologists and philosophers). At the end, the editors add short biographical notes of the contributors. The contributions are in the form of short stories, poems, essays, dramas, fictions, nonfictions and play excerpts. Each of them has a strong mathematical or scientific content. One of the main aims of the book is to show the beauty of mathematics and the sciences and to reveal some areas where art, science and mathematics come together. Another aim is to present creativity of mathematicians and theoretical scientists and to illustrate their works, results and ideas. The book gives many opportunities to think about and discuss scientific works, their difficulties and their roles in our society, to learn why some people do science, to encourage young students into science, and to criticise the current situation and system. The book can be recommended to readers interested in science and literature.