市大で利用可能な数学の電子ブックガイド
大阪市立大学 理学部
古澤 昌秋

数学科

May 11, 2018
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はじめに
数学教室は限られた予算からやりくりしながら，eBook=電子ブックの充実に力を入れてきました．市大で利用可能な電子ブックは，
大阪市立大学学術情報総合センター電子リソース検索から検索できます．また，市大で利用可能な電子ブック パッケージの一覧は，
電子ブックパッケージ一覧にあります．Springer eBook Collections, AMS eBooks, Cambridge Books
Online - Mathematics の 3 つ（の一部）が利用可能な数学のパッケージです．
電子ブックは，PDF ファイル（または ePub ファイル）によって提供される
ので，それをダウンロードすれば，コンピューター，タブレット，スマート・
フォンで読めます．もちろんプリント・アウトも出来ます．電子ブックは，
OCU net に学内から，または学外から VPN によって接続することによって，
ダウンロードできます．なお，利用は個人の研究・教育・学習に限られており，複製や改変，再配布，転売，そのほか著作権の侵害にあたる行為は固く禁じられているので注意して下さい．
利用可能な電子ブックの殆どは英語で書かれています．最初は少し戸惑うかもしれませんが，数学で使われる英語の語彙は限られているので，慣れてくれば語学的な困難は感じなくなると思います．一般的に英語の本（特に教科書レベルの本）は，日本語の本よりも数学的な説明が丁寧なので，英語の本の方が分かりやすい場合も多いです．学部生の早い段階で，例えば，解1析や線形代数の日本語の教科書で学習した内容が英語の本ではどのように説明されているか眺めてみる，といったようなことから始めてみると良いかもしれません．英語の数学の本は，自分で購入しようとすると，数千円から 1万円以上のものが殆どです．経済的な観点からも，在学中に利用してみることをおすすめします．
とは言ううものの，市大において利用可能な電子ブックの数は大変多く，どれから眺めてみるか迷ってしまうかもしれません，以下に，大まかに分野
分けしながら，利用可能な電子ブックの一部をリスト・アップしてみました．
まず，これらを足がかりにして，気軽に電子ブックに接してみて下さい．なお，以下はあくまで電子ブックとして市大において利用可能なものであり，それぞれの分野においてベストと思われる本，というわけではありません．
電子ブックになっていない本，及び市大において電子ブックとしては利用可
能ではないが冊子体として利用可能な本で，優れた本は沢山あります．興味のある特定の分野を，本格的な専門書を精読して勉強したいと思ったときは，どんな本を読んだら良いのか，専門が近いと思われる先生に是非相談するよ
うにしましょう．

1

授業の参考書

まず，授業の参考になりそうな電子ブックを科目ごとにリスト・アップしま
した．授業を受けるのに直接的に参考になるものだけでなく，授業の内容をずっと発展させていったらどうなるのかに興味のある人のために，大学院レベルの本も沢山含まれています．一つの科目に複数の本があります．その中から，自分の好みや関心に合うものを見つけて下さい．本の順番には，意味はありません．
一回生科目，代数系科目，幾何系科目，解析系科目，の順番です．

一回生科目
解析 I

• Peter Lax, Maria Shea Terrell: Calculus With ApplicationsPeter Lax は，2005 年にアーベル賞を受賞した解析学の大家です．
• Peter R. Mercer: More Calculus of a Single Variable• Steen Pedersen: From Calculus to Analysis2解析 II• Peter Lax, Maria Shea Terrell: Multivariable Calculus With Applications• Jerry Shurman: Calculus and Analysis in Euclidean Space• James J. Callahan: Advanced Calculus - A Geometric View
• Harold M. Edwards: Advanced Calculus - A Diﬀerential Forms Approach• Antonio Galbis, Manuel Maestre: Vector Analysis Versus Vector Calculus
解析 I・II の進んだ内容については，解析系科目の解析学 I・II のところも参照してください．
数学要論 A• John Stillwell: The Real Numbers - An Introduction to Set Theory andAnalysis• Abhijit Dasgupta: Set Theory - With an Introduction to Real Point
Sets• Yiannis Moschovakis: Notes on Set Theory• Péter Komjáth, Vilmos Totik: Problems and Theorems in Classical Set
Theory
数学要論 B
解析系科目の解析学 I, II のところを参照してください．
線形代数 I, II• Sheldon Axler: Linear Algebra Done Right• Peter Petersen: Linear Algebra• James B. Carrell: Groups, Matrices, and Vector Spaces - A Group
Theoretic Approach to Linear Algebra

3

代数系科目
代数学 I• Steven Roman: Advanced Linear Algebra• Igor R. Shafarevich, Alexey O. Remizov: Linear Algebra and Geometry
代数学 II, III, IV• Anthony W. Knapp: Basic Algebra• Anthony W. Knapp: Advanced Algebra
上記の二冊で代数のまとまった一通りのコースになっています．

• I. Martin Isaacs: Algebra: A Graduate Course
時々，使われている記号が独特ですが，あざやかな証明の多い，優れた本だと思います．

• Joseph J. Rotman: Advanced Modern Algebra, Third Edition, Part 1• Pierre Antoine Grillet: Abstract Algebra• E. B. Vinberg: A Course in Algebra• I. Martin Isaacs: Finite Group Theory• H. E. Rose: A Course on Finite Groups• Robert A. Wilson: The Finite Simple Groups• John M. Howie: Fields and Galois Theory• Steven H. Weintraub: Galois Theory• Igor R. Shafarevich: Basic Notions of Algebra• T. Y. Lam: Exercises in Modules and Rings

4

幾何系科目
位相数学 I, II• Volker Runde: A Taste of Topology• Vilmos Komornik: Topology, Calculus and Approximation• John B. Conway: A Course in Point Set Topology
位相幾何学 I, II• Steven H. Weintraub: Fundamentals of Algebraic Topology• Marco Manetti: Topology• John M. Lee: Introduction to Topological Manifolds• Mahima Ranjan Adhikari: Basic Algebraic Topology and its Applications• Martin Arkowitz: Introduction to Homotopy Theory
曲線と曲面の幾何学• Sebastián Montiel, Antonio Ros: Curves and Surfaces, Second Edition• Marco Abate, Francesca Tovena: Curves and Surfaces• Kristopher Tapp: Diﬀerential Geometry of Curves and Surfaces• Victor A. Toponogov: Diﬀerential Geometry of Curves and Surfaces A Concise Guide• Francis Borceux: A Diﬀerential Approach to Geometry - Geometric
Trilogy III• Andrew Pressley: Elementary Diﬀerential Geometry
微分幾何学 I, II• Loring W. Tu: An Introduction to Manifolds• Loring W. Tu: Diﬀerential Geometry5• Pedro M. GadeaJaime, Muñoz Masqué, Ihor V. Mykytyuk: Analysis
and Algebra on Diﬀerentiable Manifolds - A Workbook for Students
and Teachers• Rajnikant Sinha: Smooth Manifolds• Gerardo F. Torres del Castillo: Diﬀerentiable Manifolds - A Theoretical
Physics Approach• Thierry Aubin: A Course in Diﬀerential Geometry• Jacques Lafontaine: An Introduction to Diﬀerential Manifolds• Torsten Wedhorn: Manifolds, Sheaves, and Cohomology• Peter Petersen: Riemannian Geometry• Isaac Chavel: Riemannian Geometry - A Modern Introduction• Andrew McInerney: First Steps in Diﬀerential Geometry - Riemannian,Contact, Symplectic• Leonor Godinho, José Natário: An Introduction to Riemannian Geometry - With Applications to Mechanics and Relativity• Jürgen Jost: Riemannian Geometry and Geometric Analysis• Mikhail Gromov: Metric Structures for Riemannian and Non-RiemannianSpaces• Liviu Nicolaescu: An Invitation to Morse Theory• Simon Brendle: Ricci Flow and the Sphere Theorem• Gary R. Jensen, Emilio Musso, Lorenzo Nicolodi: Surfaces in ClassicalGeometries - A Treatment by Moving Frames• Steven G. Krantz, Harold R. Parks: The Implicit Function Theorem History, Theory, and Applications

6解析系科目
最初に，1 人の著者が統一的に書いた解析学の教科書を紹介します．

• Barry Simon: A Comprehensive Course in Analysis– Part 1. Real Analysis 【解析学 III, 解析学 IV，確率・統計概論】– Part 2A. Basic Complex Analysis 【複素解析 I, II】– Part 2B. Advanced Complex Analysis– Part 3. Harmonic Analysis– Part 4. Operator Theory 【解析学 IV】• Roger Godement: Analysis– II: Diﬀerential and Integral Calculus, Fourier Series, Holomorphic
Functions 【解析学 I, 複素解析 I】– III: Analytic and Diﬀerential Functions, Manifolds and RiemannSurfaces 【解析学 II】– IV: Integration and Spectral Theory, Harmonic Analysis, the Garden of Modular Delights 【解析学 III, IV】
残念ながら，Analysis I は市大では利用できません．

• Anthony W. Knapp– Basic Real Analysis 【解析学 I, II, III, IV, 常微分方程式】– Advanced Real Analysis 【解析学 III】
以下は科目別のリストです．
解析学 I, II
一回生科目の解析 I, II のところも参照してください．

• Stephen Abbott: Understanding Analysis• Kenneth A. Ross: Elementary Analysis - The Theory of Calculus• Richard Beals: Analysis - An Introduction• T. W. Körner: A Companion to Analysis: A Second First and First
Second Course in Analysis
7• Leszek Gasińksi Nikolaos S. Papageorgiou: Exercises in Analysis Part
1
• Leszek Gasińksi Nikolaos S. Papageorgiou: Exercises in Analysis Part
2: Nonlinear Analysis• Asuman G. Aksoy, Mohamed A. Khamsi: A Problem Book in Real
Analysis
解析学 III• Barbara MacCluer: Elementary Functional Analysis• Bryan P. Rynne, Martin A. Youngson: Linear Functional Analysis• Adam Bowers, Nigel J. Kalton: An Introductory Course in Functional
Analysis• Manfred Einsiedler, Thomas Ward: Functional Analysis, Spectral Theory, and Applications• Douglas Farenick: Fundamentals of Functional Analysis• Joseph Muscat: Functional Analysis - An Introduction to Metric Spaces,
Hilbert Spaces, and Banach Algebras• Hans Wilhelm Alt: Linear Functional Analysis - An Application-Oriented
Introduction• Balmohan V. Limaye: Linear Functional Analysis for Scientists andEngineers• S. Kesavan: Functional Analysis• Harkrishan Lal Vasudeva: Elements of Hilbert Spaces and Operator
Theory• V. S. Sunder: Operators on Hilbert Space• Rajendra Bhatia: Notes on Functional Analysis• Martin Schechter: Principles of Functional Analysis: Second Edition• John B. Conway: A Course in Abstract Analysis• John B. Conway: A Course in Operator Theory8• Alberto Bressan: Lecture Notes on Functional Analysis: With Applications to Linear Partial Diﬀerential Equations• Richard V. Kadison, John R. Ringrose: Fundamentals of the Theory
of Operator Algebras. Volume I: Elementary Theory• Richard V. Kadison, John R. Ringrose: Fundamentals of the Theory
of Operator Algebras. Volume II: Advanced Theory
解析学 IV• Donald L. Cohn: Measure Theory, Second Edition• Carlos S. Kubrusly: Essentials of Measure Theory• Michael E. Taylor: Measure Theory and Integration• Krishna B. Athreya, Soumendra N. Lahiri: Measure Theory and Probability Theory
複素解析 I, II• Rubı́ E. Rodrı́guez, Irwin Kra, Jane P. Gilman: Complex Analysis - In
the Spirit of Lipman Bers
• Joseph Bak, Donald J. Newman: Complex Analysis• Luis Barreira, Claudia Valls: Complex Analysis and Diﬀerential Equations• Rolf Busam, Eberhard Freitag: Complex Analysis
確率・統計概論• Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä,
Ludolf Erwin Meester: A Modern Introduction to Probability andStatistics - Understanding Why and How• Jay L. Devore, Kenneth N. Berk: Modern Mathematical Statistics with
Applications• Matthew A. Carlton, Jay L. Devore: Probability with Applications inEngineering, Science, and Technology• Daneil W. Stroock: Mathematics of Probability
9• John B. Walsh: Knowing the Odds: An Introduction to Probability• Davar Khoshnevisan: Probability• Wolfgang Schwarz: 40 Puzzles and Problems in Probability and Mathematical Statistics• Achim Klenke: Probability Theory - A Comprehensive Course• Terence Tao: Topics in Random Matrix Theory• Albert N. Shiryaev: Problems in Probability
常微分方程式• J. David Logan: A First Course in Diﬀerential Equations• William A. Adkins, Mark G. Davidson: Ordinary Diﬀerential Equations• David G. Schaeﬀer, John W. Cain: Ordinary Diﬀerential Equations:
Basics and Beyond• Walter G. Kelley, Allan C. Peterson: The Theory of Diﬀerential Equations Classical and Qualitative• Viorel Barbu: Diﬀerential Equations• Shair Ahmad, Antonio Ambrosetti: A Textbook on Ordinary Diﬀerential Equations• Bill Goodwine: Engineering Diﬀerential Equations - Theory and Applications• Ravi P. Agarwal, Donal O’Regan: An Introduction to Ordinary Diﬀerential Equations• Ravi P. Agarwal, Donal O’Regan: Ordinary and Partial Diﬀerential
Equations - With Special Functions, Fourier Series, and Boundary
Value Problems• A.C. King, J. Billingham, S. R. Otto: Diﬀerential Eauations - Linear,
Nonlinear, Ordinary, Partial• Martin Hermann, Masoud Saravi: A First Course in Ordinary Diﬀerential Equations - Analytical and Numerical Methods10• Belkacem Said-Houari: Diﬀerential Equations: Methods and Applications• Qingkai Kong: A Short Course in Ordinary Diﬀerential Equations• David Betounes: Diﬀerential Equations: Theory and Applications• Gerald Teschl: Ordinary Diﬀerential Equations and Dynamical Systems
偏微分方程式• Alexander Komech, Andrew Komech: Principles of Partial Diﬀerential
Equations• Gregory Eskin: Lectures on Linear Partial Diﬀerential Equations• András Vasy: Partial Diﬀerential Equations: An Accessible Route
Through Theory and Applications• Michael E. Taylor: Partial Diﬀerential Equations I: Basic Theory• Michael E. Taylor: Partial Diﬀerential Equations II: Qualitative Studies of Linear Equations• Michael E. Taylor: Partial Diﬀerential Equations III: Nonlinear Equations• Grzegorz Lukaszewicz, Piotr Kalita: Navier-Stokes Equations - An Introduction with Applications• G. P. Galdi: An Introduction to the Mathematical Theory of theNavier-Stokes Equations - Steady-State Problems• C. Foias, O. Manley, R. Rosa, R. Temam: Navier-Stokes Equations andTurbulence• Svetlin G. Georgiev: Theory of Distributions• J. J. Duistermaat, J. A. C. Kolk: Distributions - Theory and Applications• Haim Brezis: Functional analysis, Sobolev spaces and partial diﬀerential equations• Maciej Zworski: Semiclassical Analysis
11分野別リスト2

このセクションでは，より専門的な本や，前のセクションの，授業の参考書という分類には入らない本を，分野別にリスト・アップしました．個人の趣味を反映して，分野が偏っていたり，分野分けがちょっと変だったりしますが，ご容赦ください．4 回生や大学院生のセミナーのテキストに使えるような本や研究の役に立ちそうな本も含まれていると思います．もちろん 3 回生
以下の皆さんも，興味のある本があったらダウンロードして読んでみてください．

一般• 岩波 数学入門辞典• Edited by Timothy Gowers: The Princeton Companion to Mathematics
上記の 2 冊は本学の EBSCOhost Ebooks 契約を通してのアクセスなので，少し余計に手間がかかりますが，ご容赦下さい．
天書の証明• Martin Aigner, Günter M. Ziegler: Proofs from THE BOOK
数学の色々な分野の定理とそのあざやかな証明が 90 個以上集められて
います．
未解決問題

• John Forbes Nash, Jr., Michael Th. Rassias: Open Problems in Mathematics
ご存知の通り，Nash は 2015 年アーベル賞受賞者かつ 1994 年ノーベル経済学賞の受賞者です．彼が編者であるこの本には，様々な未解決問
題の第一人者たちによる解説が収められています．
大学生の数学コンテスト• Răzvan Gelca, Titu Andreescu: Putnam and Beyond
Putnam Competition とは北米の大学生による数学コンテストです．
• Christopher G. Small: Functional Equations and How to Solve Them
Putnam の準備に役立つそうです．
12

• Edward J. Barbeau: University of Toronto Mathematics Competition(2001–2015)• Volodymyr Brayman, Alexander Kukush: Undergraduate Mathematics Competitions (1995–2016) Taras Shevchenko National University ofKyiv
数学オリンピック• Dušan Djukić, Vladimir Janković, Ivan Matić, Nikola Petrović: The
IMO Compendium - A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2009, Second Edition• Titu Andreescu, Dorin Andrica, Zuming Feng: 104 Number Theory
Problems - From the Training of the USA IMO Team
• Titu Andreescu, Zuming Feng: 103 Trigonometry Problems - From theTraining of the USA IMO Team• Antonio Caminha Muniz Neto: An Excursion through Elementary
Mathematics, Volume I - Real Numbers and Functions

数論
数論入門

• William Stein: Elementary Number Theory: Primes, Congruences, andSecrets
代数的数論• Gerald J. Janusz: Algebraic Number Fields: Second Edition• Nancy Childress: Class Field Theory• Henri Cohen: Number Theory - Volume I: Tools and Diophantine Equations• M. Ram Murty, Jody Esmonde: Problems in Algebraic Number Theory• Goro Shimura: Arithmetic of Quadratic Forms

13

• Jürgen Neukirch: Class Field Theory - The Bonn Lectures - Edited byAlexander Schmidt• Jürgen Neukirch, Alexander Schmidt, Kay Wingberg: Cohomology of
Number Fields• Yuri Ivanovic Manin, Alexei A. Panchishkin: Introduction to Modern
Number Theory - Fundamental Problems, Ideas and Theories
楕円曲線• Joseph H. Silverman, John T. Tate: Rational Points on Elliptic Curves• Joseph H. Silverman: The Arithmetic of Elliptic Curves
楕円函数• J. V. Armitage, W. F. Eberlein: Elliptic Functions
保型形式，保型表現• Goro Shimura: Modular Forms: Basics and Beyond• Goro Shimura: Elementary Dirichlet Series and Modular Forms• William Stein: Modular Forms, a Computational Approach• Fred Diamond, Jerry Shurman: A First Course in Modular Forms• Henryk Iwaniec: Topics in Classical Automorphic Forms• Henryk Iwaniec: Spectral Methods of Automorphic Forms: Second
Edition• Jan Hendrik Bruinier, Gerard van der Geer, Günter Harder, Don Zagier: The 1-2-3 of Modular Forms• Helmut Klingen: Introductory Lectures on Siegel Modular Forms• Anatoli Andrianov: Introduction to Siegel Modular Forms and Dirichlet Series• Daniel Bump: Automorphic Forms and Representations• Dorian Goldfeld: Automorphic Forms and L-functions for the GroupGL(n, R)
14• Gérard Laumon: Cohomology of Drinfeld Modular Varieties Part 1:
Geometry, Counting of Points and Local Harmonic Analysis• Gérard Laumon: Cohomology of Drinfeld Modular Varieties Part 2:
Automorphic Forms, Trace Formulas and Langlands Correspondence• C. Moeglin, J. L. Waldspurger: Spectral Decomposition of Eisenstein
Series - A Paraphrase of the Scriptures• Stephen S. Gelbart: Lectures on the Arthur-Selberg Trace Formula• Colin J. Bushnell, Guy Henniart: The Local Langlands Conjecture forGL(2)• Harish-Chandra: Admissible Invariant Distributions on Reductive padic Groups
解析的数論• H. Iwaniec: Lectures on the Riemann Zeta Function• Henri Cohen: Number Theory - Volume II: Analytic and Modern Tools• M. Ram Murty: Problems in Analytic Number Theory• Jeﬀrey Stopple: A Primer of Analytic Number Theory
ベルヌーイ数とゼータ函数• Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko: Bernoulli
Numbers and Zeta Functions
有限体• Rudolf Lidl, Harald Niederreiter: Finite Fields
有限体に関連したことが網羅的に書かれています．
暗号理論入門• Jeﬀrey Hoﬀstein, Jill Pipher, Joseph H. Silverman: An Introduction toMathematical Cryptography15代数幾何学および関連分野
可換代数• Gregor Kemper: A Course in Commutative Algebra• Ezra Miller, Bernd Sturmfels: Combinatorial Commutative Algebra• Ernst Kunz: Introduction to Commutative Algebra and Algebraic Geometry• David Eisenbud: The Geometry of Syzygies - A Second Course in Commutative Algebra and Algebraic Geometry
代数幾何• Igor R. Shafarevich: Basic Algebraic Geometry 1: Varieties in Projective Space• Igor R. Shafarevich: Basic Algebraic Geometry 2: Schemes and Complex Manifolds• Daniel Perrin: Algebraic Geometry - An Introduction• Brendan Hassett: Introduction to Algebraic Geometry• Audun Holme: A Royal Road to Algebraic Geometry• David Cox, John Little, Donal O Shea: Ideals, Varieties, and Algorithms - An Introduction to Computational Algebraic Geometry andCommutative Algebra• David Cox, John Little, Donal O Shea: Using Algebraic Geometry• David Mumford: The Red Book of Varieties and Schemes - Second,Expanded Edition. Includes Michigan Lectures (1974) on Curves andtheir Jacobians• Ulrich Görtz, Torsten Wedhorn: Algebraic Geometry I - Schemes With
Examples and Exercises• Günter Harder: Lectures on Algebraic Geometry I: Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces• Günter Harder: Lectures on Algebraic Geometry II: Basic Concepts,
Coherent Cohomology, Curves and their Jacobians
16• Steven Dale Cutkosky: Resolution of Singularities• Janos Kollár, Shigefumi Mori: Birational Geometry of Algebraic Varieties• Igor Dolgachev: Lectures on Invariant Theory• V. Lakshmibai, Justin Brown: The Grassmannian Variety - Geometricand Representation-Theoretic Aspects
代数曲線• C. Herbert Clemens: A Scrap Book of Complex Curve Theory: Second
Edition• Ernst Kunz: Introduction to Plane Algebraic Curves• Egbert Brieskorn, Horst Knörrer: Plane Algebraic Curves• Patrick Popescu-Pampu: What is the Genus?
• Enrico Arbarello, Maurizio Cornalba, Phillip A. Griﬃths: Geometryof Algebraic Curves - Volume II with a contribution by Joseph Daniel
Harrisホモロジー代数，代数的 K 理論

• Joseph J. Rotman: An Introduction to Homological Algebra• Charles A. Weibel: The K-Book: An Introduction to Algebraic Ktheory• Eric M. Friedlander, Daniel R. Grayson: Handbook of K-Theory

表現論および関連分野
代数群• J. S. Milne: Algebraic Groups - The Theory of Group Schemes of Finite
Type over a Field• Robert Steinberg: Lectures on Chevalley Groups
17

リー群

• Daniel Bump: Lie Groups• Roger Godement: Introduction to the Theory of Lie Groups• Claudio Procesi: Lie Groups - An Approach through Invariants andRepresentations• Joachim Hilgert, Karl-Hermann Neeb: Structure and Geometry of LieGroups• Brian C. Hall: Lie Groups, Lie Algebras, and Representations• Roe Goodman, Nolan R. Wallach: Symmetry, Representations, andInvariants• Nolan R. Wallach: Geometric Invariant Theory - Over the Real andComplex Numbers• Terence Tao: Expansion in Finite Simple Groups of Lie Type• Terence Tao: Hilbert’s Fifth Problem and Related Topics
量子群• George Lusztig: Introduction to Quantum Groups• Jean Carstein Jantzen: Lectures on Quantum Groups• Jin Hong, Seok-Jin Kang: Introduction to Quantum Groups and Crystal Bases
表現論• Ibrahim Assem, Andrzej Skowroński, Daniel Simson: Elements of theRepresentation Theory of Associative Algebras Volume 1: Techniquesof Representation Theory• Daniel Simson , Andrzej Skowroński: Elements of the Representation
Theory of Associative Algebras Volume 2: Tubes and Concealed Algebras of Euclidean type
• Daniel Simson , Andrzej Skowroński: Elements of the Representation Theory of Associative Algebras Volume 3: Representation-infinite
Tilted Algebras18• Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki: D-Modules, Perverse Sheaves, and Representation Theory• Victor Kac: Vertex algegras for beginners, Second edition• Susumu Ariki: Representations of Quantum Algebras and Combinatorics of Young Tableaux• Hiraku Nakajima: Lectures on Hilbert Schemes of Points on Surfaces• Alexander Kirillov Jr.: Quiver Representations and Quiver Varieties• James E. Humphreys: Representations of Semisimple Lie Algebras in
the BGG Category O• Neil Chriss, Victor Ginzburg: Representation Theory and Complex
Geometry
直交多項式• I. G. Macdonald: Symmetric Functions and Orthogonal Polynomials• I. G. Macdonald: Aﬃne Hecke Algebras and Orthogonal Polynomials
有限群の表現論，コンパクト群の表現論• Walter Ledermann: Introduction to Group Characters• Barry Simon: Representations of Finite and Compact Groups• Emmanuel Kowalski: An Introduction to the Representation Theory
of Groups• Yvette Kosmann-Schwarzbach: Groups and Symmetries - From Finite
Groups to Lie Groups• Michel Broué: On Characters of Finite Groups• Ilya Piatetski-Shapiro: Complex representations of GL(2, K) for finite
fields K• Cédric Bonnafé: Representations of SL2 (Fq )

19

組合せ論

• George E. Andrews: The Theory of Partitions• Richard P. Stanley: Enumerative Combinatorics Volume 1• Richard P. Stanley: Enumerative Combinatorics Volume 2• Terence Tao, Van H. Vu : Additive Combinatorics

幾何学
トポロジー

• Jean Dieudonné: A History of Algebraic and Diﬀerential Topology,
1900–1960• Amiya Mukherjee: Diﬀerential Topology• Phillip Griﬃths, John Morgan: Rational Homotopy Theory and Differential Forms• Michèle Audin, Mihai Damian: Morse Theory and Floer Homology• Victor M. Buchstaber, Taras E. Panov: Torus Actions and Their Applications in Topology and Combinatorics
結び目理論• Seiichi Kamada: Surface-Knots in 4-Space - An Introduction• Markus Banagl, Denis Vogel: Mathematics of Knots - Theory and Application• Akio Kawauchi, Tomoko Yanagimoto: Teaching and Learning of Knot
Theory in School Mathematics• Christian Kassel, Vladimir Turaev: Braid Groups
結び目と素数• Masanori Morishita: Knots and Primes - An Introduction to Arithmetic
Topology20

双曲多様体• John G. Ratcliﬀe: Foundations of Hyperbolic Manifolds• A. Marden: Outer Circle• Michael Kapovich: Hyperbolic Manifolds and Discrete Groups
複素幾何• Donu Arapura: Algebraic Geometry over the Complex Numbers• Claire Voisin: Hodge Theory and Complex Algebraic Geometry I• Claire Voisin: Hodge Theory and Complex Algebraic Geometry II• Joseph L. Taylor: Several Complex Variables with Connections to Algebraic Geometry and Lie Groups• Raymond O. Wells Jr.: Diﬀerential Analysis on Complex Manifolds• Raymond O. Wells Jr.: Diﬀerential and Complex Geometry: Origins,
Abstractions and Embeddings• Kunihiko Kodaira: Nevanlinna Theory• Kunihiko Kodaira: Complex Manifolds and Deformation of Complex
Structures
リーマン面• Eberhard Freitag: Complex Analysis 2• Wilhelm Schlag: A Course in Complex Analysis and Riemann Surfaces• Terrence Napier, Mohan Ramachandran: An Introduction to RiemannSurfaces• Peter Buser: Geometry and Spectra of Compact Riemann Surfaces• Jürgen Jost: Compact Riemann Surfaces - An Introduction to Contemporary Mathematics• Askold Khovanskii: Galois Theory, Coverings, and Riemann Surfaces

21

解析学
フーリエ解析

• Christopher D. Sogge: Fourier Integrals in Classical Analysis• Terence Tao: Higher Order Fourier Analysis
多変数複素函数論• Paul M. Gauthier: Lectures on Several Complex Variables• Volker Scheidemann: Introduction to Complex Analysis in Several
Variables• Christine Laurent-Thiébaut: Holomorphic Function Theory in Several
Variables - An Introduction• Steven G. Krantz: Harmonic and Complex Analysis in Several Variables• Junjiro Noguchi: Analytic Function Theory of Several Variables - Elements of Oka s Coherence• Junjiro Noguchi, Jörg Winkelmann: Nevanlinna Theory in Several
Complex Variables and Diophantine Approximation• Takeo Ohsawa: L2 Approaches in Several Complex Variables - Development of Oka-Cartan Theory by L2 Estimates for the ∂¯ Operator

可積分系• Ryogo Hirota: The Direct Method in Soliton Theory

金融数学• R. J. Williams: Introduction to the Mathematics of Finance• Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko: Theory of Stochastic Processes - With Applications to
Financial Mathematics and Risk Theory22