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A Wrangler's shortlist
Complex Algebraic Curves (London Mathematical Society Student Texts)
"Covers around half of the 3rd year Riemann surfaces course. Lots of nice illustrations of algebraic curves."
Linear Analysis (Cambridge Mathematical Textbooks)
"Covers all of the 3rd year Linear Analysis course. Some very hard exercises."
REAL & COMPLEX ANALYSIS 3E (5P) (Int'l Ed) (McGraw-Hill International Editions: Mathematics Series)
"Useful for 3rd year Riemann surfaces and Linear (Functional) Analysis"
Problems in Algebraic Number Theory (Graduate Texts in Mathematics)
"Good for Number Fields and the Number Theory C course."
Probability with Martingales (Cambridge Mathematical Textbooks)
"Probabilistic approach to Probability and Measure. Martingales are the correct approach to many of the theorems in the course."
Algebraic Geometry (Graduate Texts in Mathematics)
"The bible for algebraic geometry. Soon to be an undergraduate course."
A Course in Galois Theory
"Far greater coverage than Stewart though more difficult to read."
General Relativity: An Introduction for Physicists
"Much more easy going than most general relativity books and with similar content in terms of differential geometry."
A Classical Introduction to Modern Number Theory: v. 84 (Graduate Texts in Mathematics)
"Excellent coverage of 3rd year number theory."
Linear Representations of Finite Groups: v. 42 (Graduate Texts in Mathematics)
"Most likely the best choice for Representation theory. Fulton and Harris is a little advanced for undergrad's."
"Nice easy going book with plenty of illustrative examples that really makes Quantum Mechanics easy. Not written for mathematicians but has the content."
Partial Differential Equations (Graduate Studies in Mathematics)
"Decent book for PDEs. See also Rudin's Real and Complex Analysis."
A Hilbert Space Problem Book (Graduate Texts in Mathematics)
"Complements Linear Analysis and Hilbert Spaces (now defunct) courses"
Probability and Random Processes
"A good choice for Applied probability"
Options, Futures and Other Derivatives
"Default book for Stochastic financial models. Solutions book also available."
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