 | Local Fields: v. 67 (Graduate Texts in Mathematics) by Jean-Pierre Serre
Buy new: £49.99 / Used from: £42.08 Legend has it that your lecturer most likely learned from this book also.
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 | Representation Theory: A First Course (Graduate Texts in Mathematics) by William Fulton
Buy used from: £71.27 Quickly gets through the trivialities of finite groups and builds on undergrad. work on representations of lie groups.
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 | Basic Algebraic Geometry: Varieties in Projective Space: v. 1: Varieties in Projective Space: v. 1 by Igor R. Shafarevich
Buy used from: £46.84 First half of Algebraic geometry course
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 | Basic Algebraic Geometry: Schemes and Complex Manifolds: v. 2 by Igor R. Shafarevich
Buy new: £47.49 / Used from: £39.81 Second half
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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 The Hilbert spaces material here used to be an undergraduate course but has since faded into obscurity.
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 | Algebraic Geometry (Graduate Texts in Mathematics) by Robin Hartshorne
Buy new: £46.37 / Used from: £25.00 A little terse but more than required. Get to it!
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 | General Relativity by Wald
Buy new: £26.48 / Used from: £24.65 Often a little overly verbose and poorly presented. Has (in my opinion ) the right approach.
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 | Algebraic Topology by Allen Hatcher
Buy new: £17.88 / Used from: £16.76 You have already done half of this book, so move on to Cohomology and higher homotopy theory (incl. Bott periodicity theorem).
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 | A Brief Guide to Algebraic Number Theory (London Mathematical Society Student Texts) by H. P. F. Swinnerton-Dyer
Buy new: £22.79 / Used from: £8.00 A second book in algebraic number theory, partially building upon Murty and Esmonde
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