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Complex Analysis (Graduate Texts in Mathematics, 103) 4th Edition

by Serge Lang (Author)
4.5 4.5 out of 5 stars 41 ratings
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The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. The first half, more or less, can be used for a one-semester course addressed to undergraduates. The second half can be used for a second semester, at either level. Somewhat more material has been included than can be covered at leisure in one or two terms, to give opportunities for the instructor to exercise individual taste, and to lead the course in whatever directions strikes the instructor's fancy at the time as well as extra read­ ing material for students on their own. A large number of routine exer­ cises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recommend to anyone to look through them. More recent texts have emphasized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex analysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues.
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  1. ISBN-10
    0387985921
  2. ISBN-13
    978-0387985923
  3. Edition
    4th
  4. Publisher
    Springer
  5. Publication date
    December 7, 1998
  6. Part of series
    Graduate Texts in Mathematics
  7. Language
    English
  8. Dimensions
    6.5 x 1.3 x 9.3 inches
  9. Print length
    503 pages
  10. See all details
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Editorial Reviews

Review

"The very understandable style of explanation, which is typical for this author, makes the book valuable for both students and teachers."
EMS Newsletter, Vol. 37, Sept. 2000

Fourth Edition

S. Lang

Complex Analysis

"A highly recommendable book for a two semester course on complex analysis."

―ZENTRALBLATTMATH

Product details

  • Publisher ‏ : ‎ Springer; 4th edition (December 7, 1998)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 503 pages
  • ISBN-10 ‏ : ‎ 0387985921
  • ISBN-13 ‏ : ‎ 978-0387985923
  • Item Weight ‏ : ‎ 2.03 pounds
  • Dimensions ‏ : ‎ 6.5 x 1.3 x 9.3 inches
  • Customer Reviews:
    4.5 4.5 out of 5 stars 41 ratings

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  1. Serge Lang

    Serge Lang

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  2. Serge A. Lang

    Serge A. Lang

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    Serge Lang (French: [lɑ̃ɡ]; May 19, 1927 – September 12, 2005) was a French-born American mathematician. He is known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He was a member of the Bourbaki group.

    Lang was born in Paris in 1927, and moved with his family to California as a teenager, where he graduated in 1943 from Beverly Hills High School. He subsequently graduated from the California Institute of Technology in 1946, and received a doctorate from Princeton University in 1951. He held faculty positions at the University of Chicago and Columbia University (from 1955, leaving in 1971 in a dispute). At the time of his death he was professor emeritus of mathematics at Yale University.

    Bio from Wikipedia, the free encyclopedia. Photo by Bogdan Oporowski at English Wikipedia (Transferred from en.wikipedia to Commons.) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons.

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Customer reviews

4.5 out of 5 stars
4.5 out of 5
41 global ratings

Top reviews from the United States

Frank Cannonito
5.0 out of 5 stars Excellent tutorial on Complex Analysis
Reviewed in the United States on May 23, 2013
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Prior to Lang's book under review several excellent texts existed but none of them, in my opinion, possessed, what I have come to understand about Lang's books, the combination of rich pedagogical skill coupled with an excellent understanding about what research topics are - as of the writing of the book - currently important. I think Lang, whom I knew and had correspondence about this matter with, wrote to educate the next generation of mathematicians. So his books are not compendiums of everything that is known but rather guide books into the research frontiers. This book was a delight for me to read and reconnect with a subject, admittedly not my area of research while a professor at the University of California, Irvine, that I always found especially beautiful. Lang goes to gerat lengths to actually teach the subject in a detailed and leisurely way. Of course, given the series in which the book appears the reader is expected to make some effort as the material is not spoon-fed, but readers who make the effort will find themselves richly rewarded with a deep knowledge of parts of the theory of complex analysis.
22 people found this helpful
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Crackle
5.0 out of 5 stars Of course, this is the best
Reviewed in the United States on December 5, 2020
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A well written treatment by the OG, what more can be said? Good reference to have and nice emphasis on analytic ideas and principles.
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Jason
5.0 out of 5 stars good and fast
Reviewed in the United States on July 25, 2018
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good and fast
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dadof5
4.0 out of 5 stars A very good text
Reviewed in the United States on March 13, 2010
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Lang's Complex Analysis is an very good text for anyone wanting to move beyond introductory complex analysis.
3 people found this helpful
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Paulson
5.0 out of 5 stars Five Stars
Reviewed in the United States on September 29, 2014
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good
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exp{ix}
5.0 out of 5 stars Excellent Text for Grad Math Student
Reviewed in the United States on January 24, 2011
This book is the best book on Complex Analysis that I have seen in a long time. It is well written and the proofs in the book are layed out nicely. I especially appriciate the section on conformal mapping. Complex Analysis is one of the most beautiful branches of mathematics which deserves a lot of attention. Lang has done a great job in his exposition of the subject. I highly recommend this book to any professor planning to teach this subject. It is important that the student have at least an undergraduate course in Real Analysis.

I completed a year of Complex Analysis back in graduate school and had the misfortune of using Alfors book which is a terrible book. I had to purchase a supplementary book by Speigal to understand the basics. I wish I had got a hold of Langs book then.
14 people found this helpful
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Jordan Bell
3.0 out of 5 stars Not bad, but here are some better books on complex analysis
Reviewed in the United States on July 1, 2014
Lang's book isn't bad. I used it a lot in the last year of my undergraduate degree when I was learning about modular forms, as a reference for complex analysis. But there are better books on complex analysis. Instead of proving that "if a sequence of holomorphic functions on a domain converges uniformly on every compact subset of the domain to a particular function then that function is holomorphic", a more systematic way of talking about this is to give a topology to the vector space of continuous functions on the domain with the topology induced by a family of seminorms corresponding to the compact sets, and to show that the holomorphic functions are a closed subspace. This is an instance of a Fréchet space, and Montel's theorem can then be given a clean statement: a subset of this Fréchet space is compact if and only if it is closed and bounded (namely, the space has the Heine-Borel property). This point of view is taken in Chapter V of Cartan's "Elementary Theory of Analytic Functions of One or Several Complex Variables".

If one is willing to take the whole dose of medicine, I think that the connected presentation of measure theory and complex analysis in Rudin's "Real and Complex Analysis" would be the best way to learn complex analysis. One would need a decent background in analysis before trying this, but would not need to know anything about holomorphic functions beforehand.

Both of the books that I have recommended so far are at a higher level than Lang. A book that I think is more approachable is Stein and Shakarchi's "Complex Analysis". Finally, if you are looking for other books on complex analysis, try Conway's "Functions of One Complex Variable". I haven't read this but I have spent time with his "A Course in Functional Analysis", which I find clear.
7 people found this helpful
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chicken head cut off
5.0 out of 5 stars sweet dude
Reviewed in the United States on December 20, 2004
I dont like lang's algebra, ugrad linear algebra, or diff/riemannian manifolds books all that much, but i LOVED this one.

I think an undergrad with calculus and patience can read it.

there are characteristic lang-style things like research-oriented material, and he actually has examples. He covers topics towards the end of the book which arent common elsewhere, so i've never put it down. I am not a mathematician and I like this book. It's in one of my standard 8 books that I dont leave home without (4 physics 4 math)
17 people found this helpful
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Mason Legere
5.0 out of 5 stars Overall very good. Note that answers are not included at the ...
Reviewed in Canada on January 5, 2018
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Use this book in conjunction with another text. Difficult to learn from fully without reference to other sources. Overall very good. Note that answers are not included at the back of the book, making it a pain to track down if you are fully understanding something.
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Davide Morgante
5.0 out of 5 stars Ottimo libro
Reviewed in Italy on March 5, 2018
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Non credo ci sia molto da dire, il libro è molto specialistico. Chiaro e ben fatto, la manifattura è ottima
2 people found this helpful
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Arpan S.
5.0 out of 5 stars Worth choosing.
Reviewed in India on January 15, 2017
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A tremendous text with rigourous treatment from initial class type to terminal in undergraduate/postgraduate course in complex analysis.
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Praecipua
1.0 out of 5 stars Great text but the quality of printing is crappy.
Reviewed in Italy on September 27, 2022
Verified Purchase
Springer is not that great publisher it usually was 20 years ago.

Great mathematics text but crappy printing. Pages are glued not
bond to the cover and the paper texture is like hygienic paper.

You can compare in my pictures the paper and printing quality of my
old copy of GTM 94 vs. the new GTM 103 I just bought.

The cover is made of thick printed cardboard covered with a thin layer
of plastic. The older covers where covered with a layer of good quality
canvas before printed so they were very strong.

I am wondering to go with the pirate copies as there is not to much
difference once printed with my laser printer, hum still I can say my
in-house printing quality is much better!

Definitively, I will never buy any book from Springer now on.
Customer image
Praecipua
1.0 out of 5 stars Great text but the quality of printing is crappy.
Reviewed in Italy on September 27, 2022
Springer is not that great publisher it usually was 20 years ago.

Great mathematics text but crappy printing. Pages are glued not
bond to the cover and the paper texture is like hygienic paper.

You can compare in my pictures the paper and printing quality of my
old copy of GTM 94 vs. the new GTM 103 I just bought.

The cover is made of thick printed cardboard covered with a thin layer
of plastic. The older covers where covered with a layer of good quality
canvas before printed so they were very strong.

I am wondering to go with the pirate copies as there is not to much
difference once printed with my laser printer, hum still I can say my
in-house printing quality is much better!

Definitively, I will never buy any book from Springer now on.
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Sairam Kaliraj
4.0 out of 5 stars Excellent book!
Reviewed in India on February 15, 2019
Verified Purchase
This book is very good for learning complex analysis, which contains several interesting exercises as well.
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