Each chapter references historicalsources on real analysis while also providing proof-orientedexercises and examples that facilitate the development ofcomputational skills. In addition, an extensive bibliographyprovides additional resources on the topic.
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Introduction to Real Analysis: An Educational Approach isan ideal book for upper- undergraduate and graduate-level realanalysis courses in the areas of mathematics and education. It isalso a valuable reference for educators in the field of appliedmathematics. KGaA - Betreiber - www.
All rights reserved. Versand In den Warenkorb. Weitere Versionen. The text opens with three 'lessons' that i get the reader thinking about numbers and definitions, ii encourage the reader to work out the details of computations and algebraic manipulations given in the text, and iii give some philosophical insights into solving problems. After that, rather than just giving the reader results of analysis, Part I raises questions on numbers building on the opening lesson and series. Only after another interlude on Fourier series does the text focus more on finding answers to the problems. The construction of real numbers is left to the end, at which point the student has more appreciation for thinking about what numbers are.
An aspect of the book that I particularly appreciate is how much thought the authors have given to initiating ideas that they come back to later--such as the theme of understading what a number is, which opens the first lesson of the text and also rounds out the text in the concluding material.
Besides a normal index. The index might lack complete comprehesiveness I didn't find 'Snell's Law' there , but that does not really matter since one can search in a. The text, being very enjoyable to work through and leaving it the reader to complete proofs, would seem to work very well with but not only with a flipped classroom style of teaching.
MATHS - Real Analysis | Course Outlines
Something that is usually underdeveloped in mathematics education is letting students discover interesting problems; this text makes some progress towards doing that by telling the tale of how interesting problems in analysis were come upon. From Number to Cantor's Theorem, this book brings you on a journey of the development of mathematical analysis. Several important stops along the way include Taylor Series, the Bolazano-Weierstrass Theorem, and Cauchy Sequences, I cannot think of any notable omissions along the road.
The approach the authors take is essentially timeless, in that it brings us to modern analysis. I imagine fifty years from now we could still look at this book as a very good exposition of how we got to where we are in twentieth century mathematics, and that will still be quite relevant for our moderately advanced undergraduates and casual mathematically curious students. There are times when the prosaic nature of the narrative is a little strained, but the intention is to make the text more accessible. It is not a serious detraction, nor does it significantly get in the way of the text's movement.
In the final analysis, it is a pleasure to read and the text moves logically. Very strong. The authors have a genuine interest in the story they weave and keep the tale together throughout the text. The text builds naturally through the history of mathematical analysis, so modularity is not itself a strong objective. With that said, you can reasonable go to any section and learn from it, but this text intentionally and appropriately is intended to be taken more as a sequential whole than in unrelated parts. Robbin, Dietmar A. Erdman Calculus and Linear Algebra.
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