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My question is somewhat related to this one but is somewhat more specific. Since a lot of good mathematics is written in German, I have decided to start developing my German reading abilities. So far, my basic strategy has been to come upon some random German lecture notes in topology, analysis or algebra and together with Google translate work my way through random pages here-and-there. I think this basic approach will work for me, but I would like to be a little more methodical. I would like to add a few good German analysis texts to my library and begin working my way through those.

From the user t.b., in particular, I learned of the Analysis texts by Königsberger and since they come highly-recommended I will probably get these. I have also learned of the existence of a sequence of four texts by Storch and Wiebe:

  • Band 1: Analysis einer Veränderlichen
  • Band 2: Lineare Algebra
  • Band 3: Analysis mehrerer Varänderlicher - Integrationstheorie
  • Band 4: Analysis auf Mannigfaltigkeiten

I have been able to look at the tables of contents and they cover and tremendous amount of material; in fact, I know of no English equivalent. My question though concerns their pedagogical value; for those who are familiar with these texts, are they easy to learn from or are the basically specialist-level reference texts?

By way of comparison, for example, I find Royden's Analysis well-written and sufficiently detailed to follow. Rudin, not so much.

So if you are familiar with these texts and can comment on their pedagogical value or if you could suggest other German analysis (or algebra/topology) texts that would be good to read, I would appreciate your comments.

Martin Sleziak
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ItsNotObvious
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  • They certainly do cover a lot of material, but I'm not familiar with the books... It seems a little ambitious to me to try and work through 2k+ pages in a language you're not really reading. There should be better ways to spend your time. Spektrum Verlag (the publisher of the German version of the Scientific American) is reputable for producing quality works and accessibility to a broad audience, thus not so much so for academic mathematics beyond, say, the first two years. To give you an impression: the introductory physics book by Tipler, or Howard Anton's linear algebra appeared there. – t.b. Apr 10 '12 at 02:11
  • @t.b. Well, I have been devoting about an hour a day and plan to keep it at that level so, certainly, the end goal is not to necessarily read that many pages but when I do read in German, read from just a few sources. How I see them perhaps being used is if I'm reading (in general) on submanifolds, I might go there to read about the same material to both get another perspective and to practice German. If their pedagogical value isn't sufficient, they won't serve the former purpose. – ItsNotObvious Apr 10 '12 at 02:19
  • The amount of good mathematics written in english would dwarf the amount of good mathematics written in german. I am not trying to discourage you. It is incredible that you would consider doing this, but i do think you would get better bang for your buck investing your time reading mathematics in english. – Comic Book Guy Apr 10 '12 at 02:47
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    More importantly, there are enough good books on analysis out there. The only German book I know that has no good substitute is "Grundstrukturen der Analysis I & II" by Werner Gähler, a book that is definitely not for beginners. Basically, it is analysis for people who think Bourbaki is not general and abstract enough. – Michael Greinecker Apr 27 '12 at 22:38

3 Answers3

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Try the first in the following selection of books; it's for free. It comes with solutions to all exercises.

https://people.math.ethz.ch/~blatter/dlp.html

Christian Blatter
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I can highly recommend the book

Mass- und Integrationstheorie by Jürgen Elstrodt (Measure theory).

It is the most detailed book I know on this subject. Sometimes it is also a bit too formal, but it serves very well as a reference book (he treats $\sigma$-algebras and similar object in a very detailed manner). Furthermore, in functional analysis I would recommend

Funktionalanalysis by Dirk Werner.

It is a good source of examples and a very well written (also formal) introduction to the subject providing the fundamental definitions and theorems.

TheGeekGreek
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Measure and Integration Theory by Heinz Bauer. I have read the English translation but a friend who originally learned from it in German recommended it to me.

anktsdmcknsy
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