Reddit reviews Complex Analysis

Here's my rough list of textbook recommendations. There are a ton of Dover paperbacks that I didn't put on here, since they're not as widely used, but they are really great and really cheap.

Amazon search for Dover Books on mathematics

There's also this great list of undergraduate books in math that has become sort of famous: https://www.ocf.berkeley.edu/~abhishek/chicmath.htm

Pre-Calculus / Problem-Solving

• The Art of Problem Solving - Lehoczky/Ruczyk - in two volumes, both have full solutions available separately
  
  Calculus
  
  
• Calculus - Stewart - ignore the bad reviews, it's very clear and covers all of basic calculus well - it's just the book that most intro students use and as a consequence gets a bad rap
  
  
• Calculus - Spivak - this will take your understanding of calculus to the next level
  
  
• Calculus - Apostol - there are two volumes and they are very comprehensive, albeit difficult
  
  Linear Algebra
  
  
• Linear Algebra - Lay
  
  
• Linear Algebra Done Right - Axler
  
  Differential Equations
  
  
• Elementary Differential Equations - Boyce/DePrima
  
  
• Ordinary Differential Equations - Tenenbaum
  
  Number Theory
  
  
• Number Theory - Pommersheim for a change of pace and proof skills
  
  Proof-Writing
  
  
• Transition to Higher Mathematics - Dumas/McCarthy - helps to bridge the gap between "lower" and higher math
  
  Analysis
  
  
• The Way of Analysis - Strichartz
  
• Principles of Mathematical Analysis - Rudin
  
• Real and Complex Analysis - Rudin
  
  Complex Analysis
  
  
• Complex Analysis - Ahlfors
  
  Functional Analysis
  
  
• Functional Analysis - Rudin
  
  
• Introductory Functional Analysis with Applications - Kreyszig
  
  Partial Differential Equations
  
  
• Partial Differential Equations for Scientists and Engineers - Farlow
  
  Higher-dimensional Calculus and Differential Geometry
  
  
• Calculus on Manifolds - Spivak - for a modern take on multivariable calculus
  
  
• Differential Geometry - Kreyszig
  
  Abstract Algebra
  
  
• A First Course in Abstract Algebra - Fraleigh
  
• Abtract Algebra - Dummit and Foote
  
  Geometry
  
  
• The Elements - Euclid - for culture and for understanding where math has come from, plus it's still an awesome book after all these years; don't need to go through all of it
  
• Euclidean and Non-Euclidean Geometries - Greenberg
  
  Topology
  
  
• Introduction to Topology - Mendelson
  
  
• Topology - Munkres
  
  Set Theory and Logic
  
  
• Introduction to Set Theory - Hrbacek/Jech
  
  
• Elements of Set Theory - Enderton
  
  
• Mathematical Logic - Kleene
  
  
• Set Theory and the Continuum Hypothesis - Cohen
  
  Combinatorics / Discrete Math
  
  
• Combinatorics - Cameron
  
  
• Concrete Math - Graham/Knuth/Patashnik
  
  
• Discrete Math - Biggs
  
  Graph Theory
  
  
• A First Course in Graph Theory - Chartrand/Zhang
  
  P. S., if you Google search any of the topics above, you are likely to find many resources. You can find a lot of lecture notes by searching, say, "real analysis lecture notes filetype:pdf site:.edu"
  

Sure, but they're in German. I don't know if there is an English translation.

1. Königsberger: Analysis 1, Analysis 2
   
2. Forster: Analysis 2
   
3. Hildebrandt: Analysis 2
   
   I noticed that one book that I thought had ODEs didn't, which is rather akward, since that's what we're officially using in our lecture .. in which we're doing ODEs at the moment. I'm using a different book, though.
   
   Edit: I browsed through many books on amazon.co.uk, and it appears that most books don't introduce DEs of any kind. So it's definitely just my subjective experience that made me talking. :>
   
   I also stumbled upon this. I am convinced that one can woo mathematicians just by walking around with this badboy looking all suave and shit.

Pick up any decent book in complex analysis. I'd strongly recommend either Brown & Churchill or Ahlfors; the second is better if you already know some complex analysis, though.

Thanks for compiling all the links to those books. As for the two you couldn't find here are my best guesses:

Cancer

• Possibly due to his interest in radiation, he may have discovered some references of radiation as a possible link to the cause of cancer.
  
  
• A family member/coworker may have died of cancer.
  
  
• Just out of sheer curiosity.
  
  "2 Galaxies"
  
  
• This may be a reference to determining the distance between two galaxies using "red shift" (Engelbert Broda published a paper earlier in 1954 called Weiten des Weltalls: Unsere Milchstraße und ihre Nachbarn [Ranges of the universe: our Milky Way and its neighbors] about this subject)
  
  
• This may also be a reference a few observations about galaxies colliding made in 1951 and 1954, stated here:
  
  • "A decade later Spitzer & Baade (1951) extended Holmberg's work by considering the removal of interstellar gas (a process now called "stripping") in high velocity collisions, which they argued should be common in dense clusters of galaxies. The stage was set for what is argueably the seminal observational paper in this field, Baade and Minkowski's (1954) work announcing the discovery that "the radio source Cygnus A is an extragalactic object, two galaxies in actual collision."
    
    I also found links to the rest of the Course Material:
    
    Heat and Thermodynamics - Zemansky
    
    Thermodynacis, Kinetic Theory, Statistcal Mechanics - Sears
    
    Kinetic Theory of Gases - Kennard
    
    Thermodynamcis: An Advanced Treatment - Guggenheim
    
    (Couldn't Find) Electricity and Electromagnetism - Hornell
    
    Elements of the Theory of Functions
    
    Advanced Calculus
    
    Complex Analysis - Lars Alfors
    
    Introduction to Electric Fields - Rogers
    
    Electromagnetics - Krans
    
    Communication Circuits Fundamentals - Smith

Ahlfors is proof-intensive and can be used at the upper division or grad level. Great book in many ways but not always easy.

http://www.amazon.com/Complex-Analysis-Lars-Ahlfors/dp/0070006571

Ahlfors is proof-intensive and can be used in lots of ways but not always easy. http://www.amazon.com/Complex-Analysis-Lars-Ahlfors/dp/0070006571.