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During this summer break, I want to use my time to broaden my knowledge of mathematics. I am a very motivated high school student searching for some challenging material to learn, and the two subjects I had in mind are complex analysis and probability theory.

For probability theory I already choose a book, but I am struggling a bit with finding the right complex analysis textbook. I already found two textbooks which seem pretty good to me: A Friendly Approach to Complex Analysis by Sara Maad Sasane and Complex Analysis: A First Course with Applications by Zill.

As to requirements for the book:

  • The textbook must not be too broad, since I only have 6 weeks to study intensively (yes, I know it's a challenge to study most of complex analysis in 6 weeks).
  • The textbook must not require a lot of prerequisities other than knowledge of single variable calculus (not a course in proof writing) and must not be too rigourous (some pictures and intuitive explanations can come in handy).

I hope someone could give some advise as to if the books I found suit my needs, if someone has experience with those books or if someone knows a book other than the two I found which suit my needs better.

Thanks in advance.

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    $\begingroup$ personally i would advise against trying to learn complex analysis before learning ordinary analysis. I'd suggest reading Bryant's "yet another introduction to analysis." $\endgroup$
    – Mark Joshi
    Mar 8, 2015 at 0:06
  • $\begingroup$ @Mark Joshi isn't complex analysis the successor of calculus, instead of real analysis? $\endgroup$
    – Dr. Heinz Doofenshmirtz
    Mar 8, 2015 at 8:05
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    $\begingroup$ no, complex analysis is the successor of real analysis. I have list of books for wannabe be quants on my website including some on analysis: markjoshi.com/RecommendedBooks.html $\endgroup$
    – Mark Joshi
    Mar 8, 2015 at 20:06
  • $\begingroup$ I agree with @MarkJoshi Studying introductory complex analysis in 6 weeks is totally doable, but likely not if you haven't done real analysis already. Unis have prereq subjects for a reason. Probability theory requires even more real analysis and I keep finding myself looking at measure theory all the time. $\endgroup$
    – simonzack
    May 28, 2015 at 4:57

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I would give serious consideration to Needham's book:

Visual Complex Analysis

It does not demand a huge amount by way of pre-requisites, and gives a great deal of insight into what is really important in the study of complex analysis.

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  • $\begingroup$ Thank you for your answer. I already noticed that this book is one of the best. However, I think this book for far too broad (double the size of the other two books), whereas I need a book which only covers the most important stuff. $\endgroup$
    – Dr. Heinz Doofenshmirtz
    Mar 7, 2015 at 23:47
  • $\begingroup$ I think you will find that Needham really does concentrate on the most important stuff - for a serious understanding of what matters in complex analysis. Note sure that size is relevant. $\endgroup$
    – Old John
    Mar 7, 2015 at 23:49
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I recommend "Complex Analysis" by Lars Ahlfors or "Functions of One Complex Variable" by John B. Conway.

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I would recommend "Complex Variables and Applications" by Brown and Churchill.

The authors have been dead for a long time and the content of the book hasn't changed in recent new editions so you can pick up an old edition real cheap.

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  • $\begingroup$ Seconded. If the book has changed from one edition to the next, the changes are not necessarily for the better. They are up to the 9th edition now? Try to get hold of the 5th edition that was still pretty good. $\endgroup$
    – bof
    May 28, 2015 at 6:02
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I found by the far clearest text to learn Complex Analysis was "Complex Analysis" by Bak & Newman.

I found this book extremely readable and covers everything you need for a standard course in this subject. I found some books in this area quite hard going and I find it is easier to read books published at a later date usually as well.

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