Introduction to Classical Mathematics I: From the Quadratic Reciprocity Law to the Uniformization Theorem (Mathematics and Its Applications, 70) by Helmut Koch (PDF)

Description

6Et moi, …, si j’avait su comment en revenir, One service mathematics has rendered the human mce. It has put common sense back je n’y serais point alle.’ Jules Verne where it belongs, on the topmost shelf nCllt to the dusty canister labelled ‘discarded non­ sense’. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: ‘One service topology has rendered mathematical physics …’; ‘One service logic has rendered com­ puter science …’; ‘One service category theory has rendered mathematics …’. All arguably true. And all statements obtainable this way form part of the raison d’etre of this series.

User’s Reviews

Editorial Reviews: Review ` Recommended for all libraries, this single volume may fill many gaps in smaller collections. ‘ Science & Technology `The book is well-written, the presentation of the material is clear. … This very valuable, excellent book is recommended to researchers, students and historians of mathematics interested in the classical development of mathematics. ‘ Acta Scientiarum Mathematicarum, 56:3-4

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The aim of this book, as stated by the back cover, is very admirable: “This volume provides an illuminating overview of the classical mathematics of the 19th and first half of the 20th centuries. … Motivation, especially the original motivation, is a prime concern and so is clarity and, consequently, proofs and discussions are in terms of modern concepts and ideas.” Indeed, the selection of topics is very nice; the table of contents is well worth meditating on. But other than that this book has little new to offer. In particular, one does not see much of the alleged concern with motivation. In effect, each chapter opens with a few standard historical remarks–something like “Euler proved A, then Gauss proved B, but then Riemann proved C”–and then follows a standard textbook treatment of these theorems. Also, the typesetting is poor.

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