The Art of Proof: Basic Training for Deeper Mathematics
Presents fundamental mathematics, integers and real numbers, in a way that asks for student participation, while teaching how mathematics is done Provides students with methods and ideas they can use in future courses Primarily for: undergraduates who have studied calculus or linear algebra; mathematics teachers and teachers-in-training; scientists and social scientists who want to strengthen their command of mathematical methods Extra topics in appendices give instructor flexibility
Mary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories).
This textbook on mathematical analysis is based on many years' experience of lecturing at a higher technical college. Its aim is to train the students in active approach to mathematical exercises, as is done at a seminar.Therefore standard computational exercises are supplemented by examples and problems explaining the theory, promoting its deeper understanding and stimulating precise mathematical thinking. Some counter-examples explaining the need for certain conditions in the formulation of basic theorems are also included.
Contest Problem Book II: Annual High School Contests of the Mathematical Association of America, 1961-1965
The thesis that selective problem solving can be a vital factor in learning mathematics needs no extended defense. It is implicit in the suggestion by some curriculum experts that problems be made the central point of topical development. A good problem, like the acorn, has in it the potential for grand development.
It has been twenty years since the last edition of this classic book. Kevin Wainwright (British Columbia University and Simon Fraser University), a long time user of the text, has executed the perfect revision: he has updated examples, applications and theory without changing the elegant, precise presentation style of Alpha Chiang. Readers will find the wait was worthwhile
