Naoki's Recommended Books

I'm listing only essential ones that I like;

I have a taste for classical styles of mathematics as you can see below;

Out-of-print books are indicated by small fonts. I truly hope that they will be republished by some publishers in the near future!

General math books, dictionaries, and tables:

T. Gower (Ed.): The Princeton Companion to Mathematics, Princeton Univ. Press, 2008.

F. W. J. Olver et al. (Eds.): NIST Handbook of Mathematical Functions, Cambridge Univ. Press, 2010.

I. S. Gradshteyn & I. M. Ryzhik: Table of Integrals, Series, and Products, 7th Ed. (A. Jeffrey & D. Zwillinger, Eds.), Academic Press, 2007.

Japan Mathematical Society: Suugaku Jiten, 4th Ed., Iwanami, 2007 (Japanese).

M. M. Deza & E. Deza: Encyclopedia of Distances, 4th Ed., Springer, 2016.

J. Havil: Gamma, Princeton Univ. Press, 2003.

M. Aigner & G. M. Ziegler: Proofs from THE BOOK, 5th Ed., Springer, 2014.

J. H. Conway & R. K. Guy: The Book of Numbers, Copernicus, 1996.

M. R. Schroeder: Number Theory in Science and Communication, 5th Ed., Springer, 2009.

P. J. Nahin: In Pursuit of Zeta-3, Princeton Univ. Press, 2021.
Books on Career Advice, Publishing, English Grammar, etc.:

I. Stewart: Letters to a Young Mathematician, Basic Books, 2007.

P. J. Feibelman: A Ph.D. Is Not Enough! A Guide to Survival in Science, 2nd Ed., Basic Books, 2011.

F. Rosei & T. Johnston: Survival Skills for Scientists, Imperial College Press, 2006.

R. M. Reis: Tomorrow's Professor: Preparing for Careers in Science and Engineering, IEEE Press, 1997.

S. G. Krantz: A Mathematician's Survival Guide: Graduate School and Early Career Development, AMS, 2003.

S. G. Krantz: The Survival of a Mathematician: From Tenure-Track to Emeritus, AMS, 2008.

R. A. Day & B. Gastel: How to Write and Publish a Scientific Paper, 7th Ed., Greenwood, 2011.

N. J. Higham: Handbook of Writing for the Mathematical Sciences, 3rd Ed., SIAM, 2019.

S. G. Krantz: A Primer of Mathematical Writing, 2nd Ed., AMS, 2017.

W. Strunk, Jr. & E. B. White: The Elements of Style, 4th Ed., Longman, 2000.

R. A. Day & N. Sakadusky: Scientific English: A Guide for Scientists and Other Professionals, 3rd Ed., Greenwood, 2011.

K. Kinoshita: Tips for Scientific Writing, Chuko Shinsho, 1981 (Japanese).
True Classics (not categorized):

K. Aki & P. G. Richards: Quantitative Seismology, 2nd Ed., Univ. Sci. Books, 2002.

E. T. Bell: Men of Mathematics, 1937, Touchstone hardcover edition, 2008.

M. Born & E. Wolf: Principles of Optics, 7th Ed., Cambridge Univ. Press, 2002.

E. A. Coddington & N. Levinson: Theory of Ordinary Differential Equations, McGraw-Hill, 1955.

R. Courant & D. Hilbert: Methods of Mathematical Physics, Vol.I-II, Wiley, 1953/1962.

H. Dym & H. P. McKean: Fourier Series & Integrals, Academic Press, 1972.

R. P. Feynman: Lectures on Physics, Vol.I-III, Commemorative Issue, Addison-Wesley, 1989.

F. R. Gantmacher: The Theory of Matrices, Vol.I-II, AMS Chelsea, 2000.

F. R. Gantmacher & M. G. Kreĭn: Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems, Revised Ed., AMS Chelsea, 2002.

P. R. Garabedian: Partial Differential Equations, AMS Chelsea, 1986.

G. H. Hardy: A Course of Pure Mathematics, Centenary Ed. (10th Ed.), Cambridge Univ. Press, 2008.

G. H. Hardy: Divergent Series, AMS Chelsea, 2nd Ed., 1991.

G. H. Hardy, J. E. Littlewood, & G. Pólya: Inequalities, 2nd Ed., Cambridge Univ. Press, 1952.

G. H. Hardy & E. M. Wright: An Introduction to the Theory of Numbers, 6th Ed., Cambridge Univ. Press, 2008.

H. Helmholtz: On the Sensations of Tone, Dover, 1954.

H. Helmholtz: Treatise on Physiological Optics, Vol.I-III, Dover Phoenix Ed., 2005.

(Sir) J. Jeans: Science & Music, Dover, 1968.

T. Kato: Perturbation Theory for Linear Operators, 2nd Ed., Springer, 1980.

O. Kellogg: Foundations of Potential Theory, Dover, 1954.

K. Knopp: Theory and Application of Infinite Series, 2nd English Ed., Blackie & Son, Ltd., 1951 (republished by Dover, 1990).

C. Lanczos: Applied Analysis, Prentice-Hall, 1956 (republished by Dover, 2010).

C. Lanczos: Linear Differential Operators, D. Van Nostrand, 1961 (republished by SIAM, 1996, and by Dover, 1997).

C. Lanczos: Discourse on Fourier Series, Hafner Pub. Co., 1966 (republished by SIAM, 2016).

N. S. Landkof: Foundations of Modern Potential Theory, Springer, 1972.

D. Marr: Vision, W. H. Freeman, 1982 (republished by MIT Press, 2010).

A. W. Marshall, I. Olkin, & B. C. Arnold: Inequalities: Theory of Majorization and Its Applications, 2nd Ed., Springer, 2011.

P. M. Morse & H. Feshbach: Methods of Theoretical Physics, Part I-II, Feshbach Pubs, 2005 (originally published by McGraw-Hill, 1953).
G. Pólya: Mathematics and Plausible Reasoning, Vol.I-II, Princeton Univ. Press, 1954.

J. W. S. (Lord) Rayleigh: The Theory of Sound, Vol.I-II, Dover, 1945.

W. Rudin: Real & Complex Analysis, 3rd Ed., MacGraw-Hill, 1987.

V. I. Smirnov: A Course in Higher Mathematics, Vol.I-V, Pergamon Press, 1964-65 (German and Japanese translations are still available by Verlag Harri Deutsch and Kyoritsu Shuppan, respectively).
I. Stakgold & M. J. Holst: Green's Functions and Boundary Value Problems, 3rd Ed., Wiley, 2011.

E. M. Stein: Singular Integrals & Differentiability Properties of Functions, Princeton Univ. Press, 1970.

E. M. Stein & G. L. Weiss: Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971.

E. C. Titchmarsh: The Theory of Functions, 2nd Ed., Oxford Univ. Press, 1939 (Reprinted 2002).

G. N. Watson: A Treatise on the Theory of Bessel Functions, 2nd Ed., Cambridge Univ. Press, 1944.

E. T. Whittaker & G. N. Watson: A Course of Modern Analysis, 4th Ed., Cambridge Univ. Press, 1927.

K. Yosida: Functional Analysis, 6th Ed., Springer, 1980.

Y. Yosida: Theory of Functions, 2nd Ed., Iwanami, 1965 (Japanese).
A. Zygmund: Trigonometrical Series, 2nd Ed., Chelsea, 1952.

A. Zygmund: Trigonometric Series, 3rd Ed., Cambridge Univ. Press, 2003.
Applied Analysis:

S. G. Mikhlin: Mathematical Physics, An Advanced Course, North-Holland Pub. Co., 1970.

H. Sagan: Boundary and Eigenvalue Problems in Mathematical Physics, Wiley, 1961 (republished by Dover, 1989).

F. V. Atkinson: Discrete and Continuous Boundary Problems, Academic Press, 1964.

J. L. Troutman and M. P. Bautista: Boundary Value Problems of Applied Mathematics, 2nd Ed., Dover, 2017.
Approximation Theory:

I. P. Natanson: Constructive Function Theory, Vol.I-III, Frederick Ungar, 1964-65.

L. N. Trefethen: Approximation Theory and Approximation Practice, SIAM, 2013.
Bayesian Data Analysis:

E. T. Jaynes: Probability Theory: The Logic of Science, Cambridge Univ. Press, 2003.

D. Sivia (with J. Skilling): Data Analysis: A Bayesian Tutorial, 2nd Ed., Oxford Univ. Press, 2006.
Complex Analysis:

J. E. Marsden & M. J. Hoffman: Basic Complex Analysis, 3rd Ed., 1998.

R. Takahashi: Complex Analysis, Univ. Tokyo Press, 1990 (Japanese).
Continuous vs Discrete Math:

F. V. Atkinson: Discrete and Continuous Boundary Problems, Academic Press, 1964.
H. Urakawa: Laplacian and Networks, Shokabo, 1996 (Japanese).
Data Compression & Information Theory:

T. M. Cover & J. A. Thomas: Elements of Information Theory, 2nd Ed., Wiley, 2006.
K. Sayood: Introduction to Data Compression, 5th Ed., Morgan Kaufmann, 2017.
Discrete Math/Graph Theory:

R. B. Bapat: Graphs & Matrices, 2nd Ed., Springer, 2014.

F. Chung: Spectral Graph Theory, AMS, 1997.

J. H. van Lint & R. M. Wilson: A Course in Combinatorics, 2nd Ed., Cambridge Univ. Press, 2001.

D. Cvetković, P. Rowlinson, & S. Simić: An Introduction to the Theory of Graph Spectra, Cambridge Univ. Press, 2010.

J. Matoušek: Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra, AMS, 2010.

C. H. Papadimitriou & K. Steiglitz: Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall, 1982 (republished by Dover, 1998).
Fourier/Harmonic Analysis:

G. B. Folland: Fourier Analysis & Its Applications, Brooks/Cole 1992 (republished by AMS, 2009).

T. W. Körner: Fourier Analysis, Cambridge Univ. Press, 1988.

J. S. Walker: Fourier Analysis, Oxford Univ. Press, 1988.

M. A. Pinsky: Introduction to Fourier Analysis and Wavelets, Brooks/Cole, 2002 (republished by AMS, 2009).

J. Duoandikoetxea: Fourier Analysis, AMS, 2000.

J. M. Ash: Studies in Harmonic Analysis, MAA, 1976.

S. G. Krantz: A Panorama of Harmonic Analysis, MAA, 2000.

S. G. Krantz: Explorations in Harmonic Analysis, Birkhäuser, 2009.
Functional Analysis:

N. Young: An Introduction to Hilbert Space, Cambridge Univ. Press, 1988.

P. D. Lax: Functional Analysis, Wiley, 2002.

K. Schmüdgen: Unbounded Self-adjoint Operators on Hilbert Space, Springer, 2012.

S.-T. Kuroda: Functional Analysis, Kyoritsu, 1980 (Japanese).

H. Fujita, S.-T. Kuroda, & S. Ito: Functional Analysis, Iwanami, 1991 (Japanese).
Geometry & Topology:

R. Ghrist: Elementary Applied Topology, CreateSpace Independent Publishing Platform, 2014.

H. Edelsbrunner & J. L. Harer: Computational Topology: An Introduction, AMS, 2010.

F. Morgan: Riemannian Geometry: A Beginner's Guide, 2nd Ed., A K Peters, Ltd., 1998.

W. M. Boothby: An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised 2nd Ed., Academic Press, 2003.
A. Fujioka: Manifolds through Examples, Shokabo, 2017 (Japanese).

T. Tsuboi: Introduction to Manifold Theory, Univ. Tokyo Press, 2005 (Japanese).
S. Kobayashi: Differential Geometry of Curves and Surfaces, Revised Ed., Shokabo, 1997 (Japanese).

Y. Matsumoto: Foundations of Manifolds, Univ. Tokyo Press, 1988 (Japanese).
Integral Equations:

R. Kress: Linear Integral Equations, 3rd Ed., Springer, 2014.

S. G. Mikhlin: Integral Equations, Pergamon Press, 1964.

J. A. Cochran: The Analysis of Linear Integral Equations, McGraw-Hill, 1972.
Inverse Problems:

D. Colton & R. Kress: Inverse Acoustic and EM Scattering Theory, 3rd Ed., Springer, 2013.
Lie Theory:

J. Stillwell: Naive Lie Theory, Springer, 2008.
Linear Algebra:

C. D. Meyer: Matrix Analysis and Applied Linear Algebra, SIAM, 2000.

R. A. Horn & C. R. Johnson: Matrix Analysis, Cambridge Univ. Press, 2nd Ed., 2012.

R. A. Horn & C. R. Johnson: Topics in Matrix Analysis, Cambridge Univ. Press, 1994.

I. Satake: Linear Algebra, Revised Ed., Shokabo, 1974 (Japanese).

J. Matoušek: Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra, AMS, 2010.
Numerical Analysis (general):

G. Dahlquist & Å. Björck: Numerical Methods, Prentice-Hall, 1974 (republished by Dover, 2003).

R. Kress: Numerical Analysis, Springer, 1998.

E. E. Tyrtyshnikov: A Brief Introduction to Numerical Analysis, Birkhäuser, 1997.

F. S. Acton: Real Computing Made Real, Dover, 2005.
Numerical Linear Algebra:

L. N. Trefethen & D. Bau, III: Numerical Linear Algebra, SIAM, 1997.

G. H. Golub & C. F. van Loan: Matrix Computations, 4th Ed., Johns Hopkins Univ. Press, 2013.

D. Skillicorn: Understanding Complex Datasets, Chapman & Hall, 2007.

R. S. Varga: Geršgorin and His Circles, Springer, 2004.
Numerical Integration:

P. J. Davis & P. Rabinowitz: Methods of Numerical Integration, 2nd Ed., Academic Press, 1984 (republished by Dover, 2007).
Optimal Transport:

F. Santambrogio: Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling, Birkhäuser, 2015.
Pattern Recognition/Statistical Machine Learning:

S. Watanabe: Pattern Recognition: Human & Mechanical, Wiley, 1985.

T. Hastie, R. Tibshirani, & J. Friedman: Elements of Statistical Learning, 2nd Ed., Springer, 2009.

T. Hastie, R. Tibshirani, & M. Wainwright: Statistical Learning with Sparsity: The Lasso and Generalizations, CRC Press, 2015.
PDE (Theory):

G. B. Folland: Introduction to Partial Differential Equations, 2nd Ed., Princeton Univ. Press, 1995.

F. John: Partial Differential Equations, 4th Ed, Springer, 1981.

W. Strauss: Partial Differential Equations: An Introduction, 2nd Ed., Wiley, 2008.

D. Colton: Partial Differential Equations: An Introduction, Dover, 2004.
Potential Theory:

K. L. Chung: Green, Brown, and Probability & Brownian Motion on the Line, World Scientific, 2002.

W. Strauss: Partial Differential Equations: An Introduction, 2nd Ed., Wiley, 2008.

D. Colton: Partial Differential Equations: An Introduction, Dover, 2004.

N. Ninomiya: Potential Theory, Kyoritsu, 1969 (Japanese).
Probability/Stochastic Differential Equations:

K. L. Chung: Green, Brown, and Probability & Brownian Motion on the Line, 2002.

P. G. Doyle & L. Snell: Random Walks and Electric Networks, MAA, 1984. Available online via ArXiv.

M. Kac: Statistical Independence in Probability Analysis and Number Theory, MAA, 1959 (republished by Dover, 2018; Japanese translation is also available by Suugaku Shobo).
Real Analysis:

G. B. Folland: Real Analysis, 2nd Ed., Wiley, 1999.

E. H. Lieb & M. Loss: Analysis, 2nd Ed., AMS, 2001.

P. Duren: Invitation to Classical Analysis, AMS, 2012.

K. T. Smith: Primer of Modern Analysis, Springer, 1983.
Spectral Geometry:

P. H. Bérard: Spectral Geometry: Direct and Inverse Problems, Lecture Notes in Mathematics, Springer, 1986.

S. Rosenberg: The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds, Cambridge Univ. Press, 1997.

H. Urakawa: Laplacian and Networks, Shokabo, 1996 (Japanese).

A. Grigor'yan: Heat Kernel and Analysis on Manifolds, AMS, 2009.

Y. Takahashi: Introduction to Asymptotic Behaviors, Nippon-Hyoron-sha, 2002 (Japanese).

H. Urakawa: Spectral Geometry, Kyoritsu Pub., 2015 (Japanese).
Spectral/Eigenvalue Problems:

E. B. Davies: Spectral Theory and Differential Operators, Cambridge Univ. Press, 1995.

T. Ikebe: Eigenvalue Problems in Mathematical Physics: Discrete Spectra, Sangyo Tosho, 1976 (Japanese).

W. Strauss: Partial Differential Equations: An Introduction, 2nd Ed., Wiley, 2008.

K. Schmüdgen: Unbounded Self-adjoint Operators on Hilbert Space, Springer, 2012.
Spectral Methods:

L. N. Trefethen: Spectral Methods in MATLAB, SIAM, 2000.
Time Series Analysis:

D. B. Percival & A. T. Walden: Spectral Analysis for Physical Applications, Cambridge Univ. Press, 1993.
Wavelets:

S. Jaffard, Y. Meyer, & R. D. Ryan: Wavelets: Tools for Science & Technology, SIAM, 2001.

S. Mallat: A Wavelet Tour of Signal Processing, 3rd Ed., Academic Press, 2009.
Vision Science:

D. H. Hubel: Eye, Brain, and Vision, 2nd Ed., W. H. Freeman, 1995.

B. A. Wandell: Foundations of Vision, Sinauer Assoc., 1995.

Please email me if you have any comments or questions!
Go back to Naoki's home page