Analysis I: Convergence, Elementary functions (Universitext) by Roger Godement (2004-01-22) by (PDF)

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⭐Godement is a noted French mathematician who “personalizes” his approach to mathematical analysis. In both Volumes I & II the formal expository style so common to mathematical texts containing advanced material is for the most part absent. Generally the author organizes his discussions in a section around a related group of ideas and mathematical structures, such as an introduction to set theory, and attempts to give a self-contained account of the topics he chooses to cover. The style is informal, but the author does address key points in depth and with enough rigour that the reader who expects to grasp the material will have to be comfortable with mathematics as taught in a 2nd year honors course or 3rd year course of analysis taken by a math or science major at the undergraduate collegiate level. The author will often introduce historical asides or personal views which generally are an entertaining complement to the material under discussion. At its best the author’s approach results in inspiring and insightful reading, while at its worst it can seem disjointed and rambling. Fortunately, the positives far outweigh the negatives in most sections. “Entertaining” is not generally used to describe mathematical exposition on topics at this level, but Godement’s idiosyncractic style makes it seem appropriate. Volume I covers a variety of topics that would be included in the typical “Introductory Real Analysis” course while Volume II covers a variety of more advanced mathematical analysis topics that would be covered in courses like “Complex Analysis” or “Theory of Integration”. Unfortunately, the other two volumes in this series of books have never been translated into English from their original French versions(Godement is a Professor of Mathematics at the University of Paris).Who should consider these books ? They certainly would be worthwhile additions to any math teacher’s library who is looking for ideas and insight on how to make advanced concepts related to analysis more accessible to their students. Any collegiate-level student who feels mathematical analysis is likely to be a core part of their curriculum and has an interest in reading a novel treatment of material he’s likely encountered or will encounter in his course work will also find the books rewarding. Finally, anyone who has graduated with a math/science degree and wants to re-visit mathematical analysis topics presented in a “stimulating” context different from that of standard textbooks may also find Godement’s approach of interest. These books can’t really be used as undergraduate course textbooks though due to the lack of exercises at the end of sections and clearly delineated examples in the text – the emphasis is on revisiting key ideas and concepts of mathematical analysis from the personal perspective of an accomplished mathematician.

⭐Not suitable for self-study. Maybe of interest to those who want to know more about Roger Godemont’s way of thinkig. The book is quirky. with idiosyncratic asides, some about the history, and others more like personal rants on politics. In the end the mathematical exposition is terse since so much verbiage is tangential. I regret having bought this book.

⭐In every generation, the French school of mathematics delivers very great quality and insight. Godement has been a creditable contributor in many ways and is certainly a part of the core contribution of his generation. A reviewer has a poor view of the book, but I think that it is not just allowable but at least, to an extent, helpful if a great mathematician allows the student a more informal look into the workings of his mind as it relates to important subject matter. Very serious students of analysis will not want to miss this.

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Free Download Analysis I: Convergence, Elementary functions (Universitext) by Roger Godement (2004-01-22) in PDF format
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Analysis I: Convergence, Elementary functions (Universitext) by Roger Godement (2004-01-22) PDF Free Download
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