tailieunhanh - Bridge To Abstract Math Mathematical Proof And Structures

This text is directed toward the sophomore through senior levels of uni- versity mathematics, with a tilt toward the former. It presumes that the student has completed at least one semester, and preferably a full year, of calculus. The text is a product of fourteen years of experience, on the part of the author, in teaching a not-too-common course to students with a very common need. The course is taken predominantly by sophomores and juniors from various fields of concentration who. | THE RANDOM HOUSE BIRKHÃUSER MATHEMATICS SERIES BRIDGE TO ABSTRACT MATHEMATICS MATHEMATICAL PROOF AND STRUCTURES Random House. Inc. 201 East 50th Street New York. New York 10022 394-35429-X ABOUT THE TEXT Bridge to Abstract Mathematics Mathematical Proof and Structures provides the most comprehensive and accessible presentation available for the basic ideas and tools of the mathematicians craft proofc. Its goal is to prepare a variety of students for the transition from the calculus sequence to the more abstract upper-division math courses such as abstract algebra advanced calculus real analysis. The primary emphasis concerns the development of students comprehensive and critical expository skills with methods of proof. This outstanding new textbook features A broad survey of topics with great flexibility for designing a variety of courses. This includes coverage of elementary and advanced methods of proof Chapters 5 and 6 and thorough presentation of logic including its application Chapters 2-4 . Classification and presentation of proof methods according to the logical complexity of the conclusion. A wealth of worked examples many of which draw on students familiarity with mathematical ideas and experience from previous courses. A variety of exercise sets which help to develop and provide practice for the critical reasoning process. This includes critique and complete problems in exercise sets Chapters 5 and 6 to reinforce the constructive aspects of writing good proofs. ABOUT THE AUTHOR Ronald p. Morash is a Professor of Mathematics at the University of Michigan at Dearborn. He earned a . degree from Boston College and a . degree from the University of Massachusetts at Amherst Professor Morash is a former chairman of the Mathematics Department at the Dearborn campus and has a longstanding interest and commitment to undergraduate mathematics education. Professor Morash is a member of the Mathematical Association of America and the American Mathematical .