Ref: The Road to Reality: a complete guide to the laws of the universe, (Vintage, 2005) by Roger Penrose [Chap. 7: Complex-number calculus and Chap. 8: Riemann surfaces and complex mappings]
I'm searching for an easily readable and understandable book (or resource of any kind; but preferably textbook with many worked-out problems and solutions and problem sets) to learn complex analysis and basics of Riemann surfaces – and applications to theoretical physics. (Particularly: material geared towards / written with undergraduate-level physics / theoretical physics students in view).
Any suggestions?
My math background: I have a working knowledge of single- and multivariable calculus, linear algebra, and differential equations; also some rudimentary real analysis.
Best Answer
I don't think you'll be able to read a book on Riemann surfaces before you study complex analysis. Once you've finished learning the rudiments of complex analysis, I recommend Rick Miranda's book "Algebraic Curves and Riemann Surfaces". It probably is the gentlest introduction I know.