 | Complex Algebraic Curves (London Mathematical Society Student Texts) by Frances Kirwan
Buy new: £28.49 / Used from: £25.18 Covers around half of the 3rd year Riemann surfaces course. Lots of nice illustrations of algebraic curves.
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 | Linear Analysis (Cambridge Mathematical Textbooks) by Bila Bollobás
Buy used from: £9.92 Covers all of the 3rd year Linear Analysis course. Some very hard exercises.
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 | REAL & COMPLEX ANALYSIS 3E (5P: Mathematics Series (McGraw-Hill International Editions: Mathematics Series) by Walter Rudin
Buy new: £32.78 / Used from: £25.00 Useful for 3rd year Riemann surfaces and Linear (Functional) Analysis
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 | Problems in Algebraic Number Theory (Graduate Texts in Mathematics) by M. Ram Murty
Buy new: £43.69 / Used from: £15.52 Good for Number Fields and the Number Theory C course.
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 | Probability with Martingales (Cambridge Mathematical Textbooks) by David Williams
Buy new: £23.08 / Used from: £20.00 Probabilistic approach to Probability and Measure. Martingales are the correct approach to many of the theorems in the course.
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 | Algebraic Topology by Allen Hatcher
Buy new: £17.88 / Used from: £16.75 'Nuff said
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 | Algebraic Geometry (Graduate Texts in Mathematics) by Robin Hartshorne
Buy new: £45.37 / Used from: £27.00 The bible for algebraic geometry. Soon to be an undergraduate course.
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 | A Course in Galois Theory by D. J. H. Garling
Buy new: £20.99 / Used from: £8.08 Far greater coverage than Stewart though more difficult to read.
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 | General Relativity: An Introduction for Physicists by M. P. Hobson
Buy new: £33.80 / Used from: £33.41 Much more easy going than most general relativity books and with similar content in terms of differential geometry.
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 | A Classical Introduction to Modern Number Theory: v. 84 (Graduate Texts in Mathematics) by Kenneth Ireland
Buy new: £43.99 / Used from: £30.71 Excellent coverage of 3rd year number theory.
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 | Linear Representations of Finite Groups: v. 42 (Graduate Texts in Mathematics) by Jean-Pierre Serre
Buy used from: £25.64 Most likely the best choice for Representation theory. Fulton and Harris is a little advanced for undergrad's.
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 | Quantum Physics by Stephen Gasiorowicz
Buy new: £39.79 / Used from: £38.50 Nice easy going book with plenty of illustrative examples that really makes Quantum Mechanics easy. Not written for mathematicians but has the content.
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 | Partial Differential Equations (Graduate Studies in Mathematics) by Lawrence C. Evans
Buy new: £56.00 / Used from: £45.00 Decent book for PDEs. See also Rudin's Real and Complex Analysis.
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 | A Hilbert Space Problem Book (Graduate Texts in Mathematics) by P.R. Halmos
Buy new: £41.79 / Used from: £33.07 Complements Linear Analysis and Hilbert Spaces (now defunct) courses
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 | Probability and Random Processes by Geoffrey Grimmett
Buy new: £30.03 / Used from: £29.00 A good choice for Applied probability
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 | Options, Futures and Other Derivatives by John C. Hull
Buy used from: £35.00 Default book for Stochastic financial models. Solutions book also available.
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