The student of calculus is entitled to ask what calculus is and what it can be used for. This short book provides an answer. The author starts by demonstrating that calculus provides a mathematical tool for the quantitative analysis of a wide range of dynamical phenomena and systems with variable quantities. The text then looks at the origins and intuitive sources of calculus, its fundamental methodology, and its general framework and basic structure, before examining a few typical applications. The author's style is direct and pedagogical. The new student should find that the book provides a clear and strong grounding in this important technique
Nonstandard analysis represents a fundamental change of perspective in mathematics (and sciences), comparable to the introduction of Cantor's set theory in the nineteenth century. This book is a short, readable introduction to the subject, based on the axiomatic or IST approach. The first part gives a clear, rigorous exposition of the theory; the second part consists of a number of self-contained chapters dealing with applications. As an aid to self-study, the author has included exercises at the end of each chapter, with hints as well as full solutions.
Mind Tools: The Five Levels of Mathematical Reality
Added by: Kyla | Karma: 209.07 | Self-Improvement, Maths | 3 March 2011
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Rucker - MinMind Tools connects mathematics to the world around us. Reveals mathematics' great power as an alted Tools. The Mathematics of Information
Mind Tools connects mathematics to the world around us. Reveals mathematics' great power as an alternative language for understanding things and explores such concepts as logic as a computing tool, digital versus analog processes and communication as information transmission.
Fundamentals of General Topology: Problems and Exercises
`This problem set is carefully designed; if the student goes through all the problems in the book then at the end he is familiar with almost all basic notions in general topology. In addition to this, he knows more what mathematics is about than can be expected of a student taking an ordinary course in general topology. This book is well written and will be of lasting importance to both teachers and students in general topology.' Zentralblatt für Mathematik, 568 (1986)
"A General Topology Workbook" presents elementary general topology in an unconventional way. Highly influenced by the legendary ideas of R.L. Moore, the author has taught several generations of mathematics students with these materials, proving again the usefulness and stimulation of the Moore method. The first part of the book gives a quick review of the basic definitions of the subject, interspersed with a large number of exercises, some of which are described as theorems.
