My graduate books selection

Here is my selection of graduate books, mostly geared towards mathematical statistics and machine learning. Most of them are not suitable as an introduction to the subject, with the exception perhaps of those labeled "undergraduate". Also, they all require some "mathematical maturity". One of these days I might add some reviews.

Linear algebra

• Gilbert Strang, Linear Algebra and Its Applications, Brooks Cole, 2005
• P.R. Halmos, Finite-Dimensional Vector Spaces, Springer
• Steven Roman, Advanced Linear Algebra, Springer, 2007
• Jonathan S. Golan, The Linear Algebra a Beginning Graduate Student Ought to Know, Springer, 2007

Matrix algebra

• David A. Harville, Matrix Algebra From a Statistician's Perspective, Springer, 2008

Algebra

• Charles Pinter, A Book of Abstract Algebra, McGraw-Hill, 2003 (The Dover edition is much cheaper)
• David S. Dummit, Richard M. Foote, Abstract Algebra, Wiley, 2003
• Michael Artin, Algebra, Prentice Hall
• Serge Lang, Algebra, Springer, 2002
• Thomas W. Hungerford, Algebra, Springer 1980
• I. N. Herstein, Topics in Algebra, Wiley, 1975

Calculus and undergraduate analysis

• John and Barbara Hubbard, Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, Matrix Editions, 2010
• Stephen Abbott, Understanding Analysis, Springer, 2001
• Walter Rudin, Principles of Mathematical Analysis, McGraw-Hill, 1976
• Charles Chapman Pugh, Real Mathematical Analysis, Springer, 2010

Real Analysis and Functional Analysis

• Halsey Royden, Patrick Fitzpatrick, Real Analysis, Prentice Hall, 2007
• Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, Wiley, 1999
• Walter Rudin, Real and Complex Analysis, McGraw-Hill, 1986
• Walter Rudin, Functional Analysis, McGraw-Hill, 1991

Complex Analysis

• Tristan Needham, Visual Complex Analysis, Oxford University Press, 1999
• Lars Ahlfors, Complex Analysis, McGraw-Hill, 1979
• Elias M. Stein, Rami Shakarchi, Complex Analysis, Princeton University Press, 2003
• John B. Conway, Functions of One Complex Variable, Vol. 1 and 2, Springer, 1995
• Theodore W. Gamelin, Complex Analysis, Springer, 2001

Topology

• Bert Mendelson, Introduction to Topology, Dover, 1990
• John M. Lee, Introduction to Topological Manifolds, Springer, 2000
• James Munkres, Topology, Prentice Hall, 2000
• Edwin H. Spanier, Algebraic Topology, Springer, 1994
• Allen Hatcher, Algebraic Topology, Cambridge University Press, 2001
• Glen E. Bredon, Topology and Geometry, Springer, 2009
• Raoul Bott, Loring W. Tu, Differential Forms in Algebraic Topology, Springer, 2009

Differential geometry

• William M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, Academic Press, 2002
• John M. Lee, Introduction to Smooth Manifolds, Springer, 2002
• John M. Lee, Riemannian Manifolds: An Introduction to Curvature, Springer, 1997
• Manfredo P. Carmo, Riemannian Geometry, Birkhäuser Boston 1992

Graph theory

• John Harris, Jeffry L. Hirst, Michael Mossinghoff, Combinatorics and Graph Theory, Springer, 2008
• Adrian Bondy, U.S.R. Murty, Graph Theory, Springer, 2007
• Reinhard Diestel, Graph Theory, Springer, 2006
• Bela Bollobas, Modern Graph Theory, Springer, 1998

Measure Theory and Probability

Elementary probability (undergraduate level), without measure theory:

• Paul G. Hoel, Sidney C. Port, Charles J. Stone, Introduction to Probability Theory, Brooks Cole, 1972
• Sheldon M. Ross, Introduction to Probability Models, Academic Press, 2009

Introductory graduate, using measure theory:

• Marek Capinski, Measure, Integral and Probability, Springer, 2004
• Jeffrey Rosenthal, First Look at Rigorous Probability Theory, World Scientific, 2006
• Sidney Resnick, A Probability Path, Birkhäuser Boston, 1999
• Jean Jacod, Probability Essentials, Springer, 2002
• David M. Bressoud, A Radical Approach to Lebesgue's Theory of Integration, Cambridge University Press, 2008

Graduate level:

• R. M. Dudley, Real Analysis and Probability, Cambridge University Press, 2002
• Kai Lai Chung, A Course in Probability Theory, Academic Press, 2000
• Elias M. Stein, Rami Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces, Princeton University Press, 2005
• Patrick Billingsley, Probability and Measure, Wiley-Interscience, 1995
• David Williams, Probability with Martingales, Cambridge University Press, 1991
• Albert N. Shiryaev, Probability, Springer, 1995
• Daniel W. Stroock, Probability Theory, an Analytic View, Cambridge University Press, 2000
• Rick Durrett, Probability: Theory and Examples, Cambridge University Press, 2010

Stochastic processes:

• Gregory F. Lawler, Introduction to Stochastic Processes, Chapman and Hall, 2006

Stochastic integration:

• Bernt Øksendal, Stochastic Differential Equations: An Introduction with Applications, Springer, 2003
• Hui-Hsiung Kuo, Introduction to Stochastic Integration, Springer, 2005

Reference books:

• Achim Klenke, Probability Theory: A Comprehensive Course, Springer, 2007
• Olav Kallenberg, Foundations of Modern Probability, Springer, 2002

Monographs:

• Patrick Billingsley, Convergence of Probability Measures, Wiley-Interscience 1999
• Michel Ledoux, The Concentration of Measure Phenomenon, American Mathematical Society, 2005
• Devdatt P. Dubhashi, Concentration of Measure for the Analysis of Randomized Algorithms, Cambridge University Press, 2009

The probabilistic method:

• Mitzenmacher Michael, Probability and Computing: Randomized Algorithms and Probabilistic Analysis, Cambridge University Press, 2005
• Noga Alon, Joel H. Spencer, The Probabilistic Method, Wiley-Interscience, 2008

Statistics

Introductory texts (undergraduate):

• Dennis Wackerly, William Mendenhall, Richard L. Scheaffer, Mathematical Statistics with Applications, Duxbury Press, 2007

Multivariate statistical analysis:

• T. W. Anderson, An Introduction to Multivariate Statistical Analysis, Wiley-Interscience, 2003
• Richard A. Johnson, Dean W. Wichern, Applied Multivariate Statistical Analysis, Prentice Hall, 2007

Mathematical statistics:

• Erich Lehmann, Joseph P. Romano, Testing Statistical Hypotheses, Springer, 2005
• George Casella, Roger L. Berger, Statistical Inference, Duxbury Press, 2001
• Peter J. Bickel, Kjell A. Doksum, Mathematical Statistics, Prentice Hall, 2006
• Jun Shao, Mathematical Statistics, Springer, 2003
• Larry Wasserman, All of Statistics: A Concise Course in Statistical Inference, Springer, 2003
• Larry Wasserman, All of Nonparametric Statistics, Springer, 2005
• Vijay K. Rohatgi, A. K. Md. Ehsanes Saleh, An Introduction to Probability and Statistics, Wiley-Interscience, 2000
• Jayanta K. Ghosh, Mohan Delampady, Tapas Samanta, An Introduction to Bayesian Analysis: Theory and Methods, Springer, 2006

Machine Learning

Statistical Learning:

• Trevor Hastie, Robert Tibshirani, Jerome Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer, 2009
• Christopher M. Bishop, Pattern Recognition and Machine Learning, Springer, 2007
• Richard O. Duda, Peter E. Hart, David G. Stork, Pattern Classification, Wiley-Interscience, 2000
• Carl Edward Rasmussen, Christopher K. I. Williams, Gaussian Processes for Machine Learning, MIT Press, 2005
• Ethem Alpaydin, Introduction to Machine Learning, The MIT Press, 2010
• Vladimir N. Vapnik, The Nature of Statistical Learning Theory, Springer, 1999
• Daphne Koller, Nir Friedman, Probabilistic Graphical Models: Principles and Techniques, MIT Press, 2009
• Alan J. Izenman, Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning, Springer, 2008
• Bertrand Clarke, Ernest Fokoue, Hao Helen Zhang, Principles and Theory for Data Mining and Machine Learning, Springer, 2009
• Tom M. Mitchell, Machine Learning, McGraw-Hill, 1997
• Hisashi Kobayashi, Brian L. Mark, William Turin, Probability, Random Processes, and Statistical Analysis, Cambridge University Press, 2012
• David Barber, Bayesian Reasoning and Machine Learning, Cambridge University Press, 2012
• Kevin Murphy, Machine Learning: A Probabilistic Perspective, The MIT Press, 2012

SVM and kernel methods:

• Bernhard Schlkopf, Alexander J. Smola, Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond, MIT Press, 2001
• Ingo Steinwart, Andreas Christmann, Support Vector Machines, Springer, 2008
• Nello Cristianini, John Shawe-Taylor, Kernel Methods for Pattern Analysis, Cambridge University Press, 2004

Dimensionality reduction:

• John A. Lee, Michel Verleysen, Nonlinear Dimensionality Reduction, Springer, 2009
• I. T. Jolliffe, Principal Component Analysis, Springer, 2010

Monte Carlo methods:

• Christian Robert, George Casella, Monte Carlo Statistical Methods, Springer, 2004

Information theory:

• Thomas M. Cover, Joy A. Thomas, Elements of Information Theory, Wiley-Interscience, 1991
• David J. C. MacKay, Information Theory, Inference & Learning Algorithms, Cambridge University Press, 2002

Optimization theory:

• Stephen Boyd, Lieven Vandenberghe, Convex Optimization, Cambridge University Press, 2004