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Mathematician Comes of Age

Steven G. Krantz

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Description for Mathematician Comes of Age Hardcover. This book describes and analyses how a mathematics student can develop into a sophisticated and rigorous thinker. Series: Spectrum. Num Pages: 156 pages, illustrations. BIC Classification: PBK. Category: (U) Tertiary Education (US: College). Dimension: 236 x 154 x 8. Weight in Grams: 336.
This book is about the concept of mathematical maturity. The goal of a mathematics education is to transform the student into a mathematically mature individual who treats mathematical ideas analytically and can control and manipulate them effectively. At the heart of the endeavour to solidify this loosely defined but widely acknowledged concept is the privileged position of mathematics as a pure science. The book provides background, data and analysis for recognising and nurturing aspects of mathematical maturity, such as the ability to analyse and communicate abstract ideas, criticise and construct proofs, and move from intuitive to rigorous reasoning. It turns ... Read more

Product Details

Format

Hardback

Publication date

2011

Publisher

Mathematical Association of America United States

Number of pages

156

Condition

New

Series

Spectrum

Number of Pages

156

Place of Publication

Washington, United States

ISBN

9780883855782

SKU

V9780883855782

Shipping Time

Usually ships in 7 to 11 working days

Ref

99-1

About Steven G. Krantz

Steven G. Krantz is a Professor of Mathematics at Washington University, St Louis, where he has served as Chair of his department. He has previously taught at the University of California, Los Angeles, Princeton University and Penn State University, having received a PhD from Princeton in 1974. Krantz has directed numerous PhD and Masters students and is the recipient of ... Read more

Reviews for Mathematician Comes of Age

One of the most widely used yet ill-defined terms in mathematics is ""mathematical maturity."" It is used to describe everything from the background needed to understand a textbook, to succeed in a course, to explain a person's success in the field. In this book, Steven Krantz gives a more formal explanation of mathematical maturity and he succeeds in that endeavor.Not ... Read moreonly does he give an excellent explanation of what it is but he also explains how one gets there. Acquiring mathematical maturity is something developed over a long period of time by subjecting yourself to a series of partial successes, significant failures and a willingness to keep trying. While there may be a few ""Aha!"" moments in achieving high levels of mathematical skills, they never appear in isolation. A single light bulb may suddenly appear brightly lit, but only after hours, weeks and maybe years of steadily building the supporting power plant.Solid arguments can be made that one of the reasons for so much math anxiety is that actually understanding mathematics takes a great deal of internal intellectual ferment. While you may have done all the problems for a class and gotten the right answers that does not mean that you understand it. Krantz makes those points in a book that could be read in the first week in the life of a math major or much later in their career. In the first case it will help prepare them for the road ahead in college and in the second case help you either stay on the road or understand why you are there."" - Charles Ashbacher, Journal of Recreational Mathematics ""The author's intention is to investigate and make as precise as possible the notion of mathematical maturity, a phrase often heard when discussing the behavior of students who might, for example, go on to graduate work. The author, who has written cogently about his approach to teaching mathematics at the university level describes his own process of maturation as a mathematician. The style is a mixture of auto-mathography, anecdotes about colleagues, and essays and comments about various factors that contribute to, or are associated with, mathematical maturity. ...For me, the most important point, made in several different ways, is that in order for students to appreciate what it is like to think mathematically, they need to be in the presence of someone more experienced who is behaving mathematically. Students lucky enough to be taught by a mathematically mature thinker who is sensitive to what it is like to be learning to think mathematically have a real advantage over students who are subjected to a constant diet of previously digested and honed mathematics. Seeing others make mistakes, specialise, modify their conjectures, extend, generalise and abstract is much more likely to foster mathematical maturity in the novice than going without this experience. So what is mathematical maturity? Krantz lists 13 things to work on learning in order to develop maturity. The book ends with a tree of topics, partially ordered with respect to maturation of the student, and a partial etymology suggesting a basis for 'maturity' in the notion of 'ripeness.' Presumably the mathematically mature teacher offers students nutrious fruit and potent seeds for continuing the species."" - Johh H. Mason, Mathematical Review Show Less

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Mathematician Comes of Age

Steven G. Krantz

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