私が推薦する本

最も基本的で私が好きなものに限っています。

リストを見ればお分りの通り、多くの本は古典的なものです。

絶版になっている本は、小さいフォントで記しています。一刻も早い復刻を願っています。

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.

日本数学会（編）: 数学辞典, 第４版, 岩波書店, 2007.

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.

木下是雄： 理科系の作文技術, 中公新書, 1981.
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 (日本語訳：「スミルノフ高等数学教程」は、共立出版から今でも出版されています).
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.

吉田洋一： 函数論, 第２版, 岩波書店, 1965.
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.

高橋礼司： 新版複素解析, 東京大学出版会, 1990.
Continuous vs Discrete Math:

F. V. Atkinson: Discrete and Continuous Boundary Problems, Academic Press, 1964.
浦川肇： ラプラシアンとネットワーク, 裳華房, 1996.
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.

黒田成俊： 関数解析, 共立出版, 1980.

藤田宏・黒田成俊・伊藤清三: 関数解析, 岩波書店, 1991.
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.
藤岡敦： 具体例から学ぶ多様体, 裳華房, 2017.

坪井俊： 多様体入門, 東京大学出版会, 2005.
小林昭七： 曲線と曲面の微分幾何, 改訂版, 裳華房, 1997.

松本幸夫： 多様体の基礎, 東京大学出版会, 1988.
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.

佐竹一郎： 線型代数学, 改訂版, 裳華房, 1974.

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.

二宮信幸： ポテンシャル論, 共立出版, 1969.
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; 日本語訳：Kac統計的独立性, 数学書房, 2011).
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.

浦川肇： ラプラシアンとネットワーク, 裳華房, 1996.

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

高橋陽一郎： 漸近挙動入門—太鼓の形を聴くために, 日本評論社, 2002.

浦川肇： スペクトル幾何, 共立出版, 2015.
Spectral/Eigenvalue Problems:

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

池部晃生： 数理物理の固有値問題—離散スペクトル, 産業図書, 1976.

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.

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