Mathematics books

• L.V. Ahlfors, Complex Analysis, 3rd. ed. McGraw-Hill, 1979
• F. Bates & A. Weinstein, Lectures on the Geometry of Quantization, Berkeley Mathematics Lecture Notes v.8, 1995
• O. Bratteli & D. Robinson, Operator Algebras and Quantum Statistical Mechanics, Springer, 1979 -- old, but still one of the best
• P.J. Brockwell & R.A. Davis, Time Series: Theory and Methods, 2nd ed., Springer, 1991 -- mathematical methods
• A.A. Bukhshtab, Teoriya Chisel, UchPedGiz 1960 (in Russian) -- unfortunately, no English translation
• A. Connes, Noncommutative Geometry, Academic Press, 1994 -- as Vaughan says, read and be inspired
• J.B. Conway, A Course in Functional Analysis, 2nd. ed. Springer, 1990 --Functional Analysis done right
• D.S. Dummit & R.M. Foote, Abstract Algebra, Prentice-Hall, 1991 --best introductory (and not so introductory) algebra book I know
• R. Durrett, Probability: Theory and Examples, Wadsworth & Brooks/Cole,1991 -- examples, examples, examples...
• G.B. Folland, Harmonic Analysis in Phase Space, Princeton University Press, 1989, Annals of Mathematics Studies 122 -- Mathematics done right. Yes, I know this is a strong claim
• B.R. Gelbaum, J.M.H. Olmsted, Counterexamples in Analysis, Holden-Day, 1964
• V. Guillemin & A. Pollack, Differential Topology, Prentice-Hall, 1974 -- best introductory
• H. Helson, The Spectral Theorem, Springer, 1980, LNM 1227
• C. Itzykson & J.-M. Drouffe, Statistical Field Theory I: From Brownian motion to renormalization and lattice gauge theory; II: Strong coupling, Monte Carlo methods, conformal field theory, and random systems, Cambridge University Press, 1989, Cambridge Monographs on Mathematical Physics
• S. Lang, Algebra, 3rd. ed. Addison-Wesley, 1993 --despite all its faults, still the best reference
• M.A. Lavrent'ev & B.V. Shabat, Metody Teorii Funktsiy Kompleksnogo Peremennogo, Nauka, 1965 (in Russian) -- for some reason, part I only translated into Spanish; Part II is: B.V. Shabat, Introduction to complex analysis. Part II. Functions of several variables, AMS, 1993, Translations of Mathematical Monographs, 110.
• J. Marsden & T. Ratiu, Introduction to Mechanics and Symmetry, Springer, 1994, TAM 17
• Mathematical Society of Japan, Encyclopedic Dictionary of Mathematics, 2nd. ed., MIT Press, 1993 -- going by price/bit, possibly the best book ever
• P.-A. Meyer, Quantum Probability for Probabilists, 2nd. ed., Springer, 1995, 1995, LMM 1538
• B. Øksendal, Stochastic Differential Equations, 4th. ed. Springer, 1995
• M. Reed & B. Simon, Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness, Academic Press, 1975
• J. Rice, Mathematical Statistics and Data Analysis, 2nd. ed., Duxbury Press, 1995 -- if you know 1st order Taylor expansion, this is the book for you
• W. Rudin, Real & Complex analysis, 3rd. ed. McGraw-Hill, 1987
• A.N. Shiryaev, Veroyatnost', Nauka, 1980 (in Russian) -- translated as: A.N. Shiryaev, Probability, 2nd. Ed., Springer, 1996, GTM 95
• D.W. Stroock, Probability Theory, An Analytic View, Cambridge University Press, 1993 --hard to read, but nevertheless Probability done right
• D.-V. Voiculescu, K.J. Dykema, A. Nica, Free Random Variables, AMS, 1992, CRM monograph series 1 -- best book on Free Probability
• R.L. Wheeden & A. Zygmund, Measure and Integral, An Introduction to Real Analysis, Dekker, 1977, Monographs and Textbooks in Pure and Applied Mathematics 43