一些有趣的数学文献

代数

Joseph H. Silverman - Abstract Algebra: An Integrated Approach
Martin Isaacs - Algebra A Graduate Course
Louis Halle Rowen - Graduate algebra
Saunders Mac Lane - Sheaves in Geometry and Logic: A First Introduction to Topos Theory
Michel Broué - From Rings and Modules to Hopf Algebras: One Flew Over the Algebraist's Nest

群论

Serre - Finite Group
J.S. Milne - Group Theory
H.S.M. Coxeter, W.O.J. Moser - Generators and Relations for Discrete Groups
John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss - The symmetries of things
> 对称性与群论，前半部分分为面向普通人的几何物体的对称性概念、更进一步的关于有色物体对称性和轨道流形的讨论以及关于许多有限群和二维晶体群，后半部分关于许多空间群变换群和四维物体对称性等等

Roger C. Lyndon , Paul E. Schupp - Combinatorial Group Theory

表示论

J.-P. Serre - Linear Representation of Finite Group
Fulton, Harris - Representation Theory A First Course
Pavel Etingof - Introduction to Representation Theory
Barry Simon - Representations of Finite and Compact Groups
> 分析学家视角的表示论

Charles W. Curtis - Pioneers of Representation Theory Frobenius, Burnside, Schur, and Brauer
Walter Feit - The Representation Theory of Finite Groups
> 老书

Hermann Weyl - The Classical Groups : Their Invariants and Representations

交换代数/同调代数

Michael F. Atiyah, I.G. MacDonald - Introduction To Commutative Algebra
David Eisenbud - Commutative Algebra with a View Toward Algebraic Geometry
Masayoshi Nagata - Local Rings
> 有很多反例

Bourbaki - Commutative Algebra
Hideyuki Matsumura - Commutative Algebra
Sergei I. Gelfand, Yuri I. Manin - Methods of Homological Algebra
Charles A. Weibel - An Introduction to Homological Algebra
Alexandre Grothendieck - Some Aspects of Homological Algebra
Saunders Mac Lane - Homology
J.-P. Serre - Local Fields
J.-P. Serre - Local Algebra
Masaki Kashiwara, Pierre Schapira - Categories and Sheaves
P. J. Hilton, U. Stammbach - A course in homological algebra

代数几何

Michael Artin - Algebraic Geometry: Notes on a Course
Shafarevich - Basic Algebraic Geometry I/II
Griffiths, Harris - Principles of Algebraic Geometry
Griffiths - 代数曲线
William Fulton - Algebraic Curves, An Introduction to Algebraic Geometry
> 非常友善，学过基本的抽代就行

Ravi Vakil - The Rising Sea Foundations of Algebraic Geometry
Oscar Zariski - Algebraic Surfaces
> The second edition of the book under review appeared in 1971 enriched by updating appendices one for each chapter, which were written by S.S. Abhyankar, J. Lipman, and D. Mumford. These ten appendices gave outlines of the developments of algebraic surface theory during the period from 1935 to 1970, connecting in this way Zariski's original classic text to the methods and results of abstract modern algebraic geometry. The present edition is an unchanged reprint of the second edition from 1971.

David Eisenbud, Joe Harris - The Geometry of Schemes
J.-P. Serre - FAC (代数性凝聚层)
Peter Scholze - Algebraic Geometry (Notes)
Grothendieck - Pursuit Stacks https://thescrivener.github.io/PursuingStacks/ / https://arxiv.org/pdf/2111.01000.pdf
A. Beilinson, V. Drinfeld - Opers (Paper, arxiv)
Araceli Bonifant, John Milnor - Group Actions, Divisors, and Plane Curves (arxiv)
Araceli Bonifant, John Milnor - On Real and Complex Cubic Curves (arxiv)
Peter Scholze - Perfectoid Spaces A survey (arxiv)
Fundamental algebraic geometry: Grothendieck’s FGA explained
David Cox, John Little, Donal O’ Shea - Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
Claire Voisin - Hodge Theory and Complex Algebraic Geometry I

范畴论/泛代数

MacLane - Category Theory for Working Mathematicians
Emily Riehl - Category theory in context
George M. Bergman - An invitation to General Algebra and Universal Constructions

数论

Hardy, Wright - An Introduction to the Theory of Numbers
Gauss - Disquisitiones Arithmeticae
Dirichlet, Dedekind - Lectures on Number Theory
J.-P. Serre - A Course in Arithmetic
P. Erdos, Suranyi - Topics in the Theory of Numbers
华罗庚 - 数论导引
Joseph H. Silverman - A Friendly Introduction to Number Theory
Z. I. Borevich, I. R. Shafarevich - Number Theory
Allen Hatcher - Topology of Numbers
> This is an introduction to elementary number theory from a geometric point of view, in contrast to the usual strictly algebraic approach. A large part of the book is devoted to studying quadratic forms in two variables with integer coefficients, a very classical topic going back to Fermat, Euler, Lagrange, Legendre, and Gauss, but from a perspective that emphasizes Conway's much more recent notion of the topograph of a quadratic form. The book has been published by the AMS in 2022 as a paperback, ISBN 978-1-4704-5611-5. See the AMS webpage for the book.

John Horton Conway - The Sensual (Quadratic) Form
Yuri I. Manin, Alexei A. Panchishkin - Introduction to Modern Number Theory Fundamental Problems, Ideas and Theories

代数数论

J.-P. Serre - Local Fields
David Cox - Primes of the Form x² + ny²
Barry Mazur - On the passage from local to global in number theory (Paper, arxiv)
Ben Green - Algebraic Number Theory (2020, Notes, with sheets)
André Weil - Basic Number Theory
Emil Artin - Algebraic Numbers and Algebraic Functions
T.Y. Lam - Introduction to Quadratic Forms over Fields
Helmut Hasse - Number Theory
J.-P. Serre - Algebraic Groups and Class Fields
Franz Lemmermeyer - Quadratic Number Fields
> 串烧数学史

Pierre Samuel - Algebraic Number Theory
加藤和也, 黑川信重, 斋藤毅 - 数论I: Fermat的梦想和类域论

解析数论

Gerald Tenenbaum - Introduction to Analytic and Probabilistic Number Theory (解析和概率数论导引)
Henryk Iwaniec, Emmanuel Kowalski - Analytic Number Theory
Barry Mazur - Prime Numbers and the Riemann Hypothesis
H. L. Montgomery, R. C. Vaughan - Mulplicative Number Theory Ⅰ: Classical Theory

模形式

Zagier - The 1-2-3 of modular forms
Goro Shimura - Modular Forms
Goro Shimura - Elementary Dirichlet Series and Modular Forms

拓扑/几何

Nicolas Bourbaki - Elements of Mathematics General Topology
Steven G. Krantz - A Guide to Topology
Ronald Brown - Topology and groupoids
> With Exposition of part of Chapter 6

John L. Kelley - General Topology
Jacques Dixmier - General Topology
肖盖 - 拓扑学教程
汪林 - 拓扑空间与线性拓扑空间中的反例
C. McMullen - Topology (Notes)
O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov - Elementary Topology: Problem Textbook
> 包含对General Topology的详细介绍和对Algebraic Topology的介绍

John H. Conway, Peter G. Doyle, Jane Gilman, William P. Thurston - Geometry and the Imagination in Minneapolis (arxiv 1804.03055)
> 关于"Geometry and the Imagination"的讨论班的部分记录和补充文本
> 关于 The Shape of Space by Jeff Weeks 与 Introduction to Geometry by Coxeter，也推荐Flatland by Abbott 和 What is Mathematics by Courant and Robbins

Raoul Harry Bott - Differential Forms in Algebraic Topology
> 代数拓扑与微分拓扑

Glen Bredon - Topology and Geometry
> 代数拓扑与微分拓扑

Miles Reid, Balázs Szendrői - Geometry and Topology

David Hilbert, S. Cohn-Vossen - Geometry and the Imagination
Jeffrey R.Weeks - The Shape of Space
> 直观

Pavel Alexandroff - Elementary Concepts of Topology

K. Parthasarathy - Topology: An Invitation
> 结合数学史的入门教材

H. Edelsbrunner, J. L. Harer - Computational Topology: An Introduction
> 计算拓扑学

H.S.M. Coxeter - Introduction to Geometry
Marcel Berger - Geometry Revealed: A Jacob's Ladder to Modern Higher Geometry
> 古典与现代几何，几何学史

B. A. Dubrovin, A. T. Fomenko, S. P. Novikov - Modern Geometry - Methods and Applications. Part I/II/III
> 各种现代几何

A. Mishchenko, A. Fomenko - A Course of Differential Geometry and Topology
> 包括但不限于黎曼几何和同调理论

Miles Reid, Balazs Szendroi - Geometry and Topology
S.P. Novikov, A.T. Fomenko - Basic Elements of Differential Geometry and Topology
S. Ramanan - Global Calculus
> Analysis, topology and algebra brought new power to geometry, revolutionizing the way geometers and physicists look at conceptual problems. Some of the key ingredients in this interplay are sheaves, cohomology, Lie groups, connections and differential operators. In Global Calculus, the appropriate formalism for these topics is laid out with numerous examples and applications by one of the experts in differential and algebraic geometry.

Ramanan has chosen an uncommon but natural path through the subject. In this almost completely self-contained account, these topics are developed from scratch. The basics of Fourier transforms, Sobolev theory and interior regularity are proved at the same time as symbol calculus, culminating in beautiful results in global analysis, real and complex. Many new perspectives on traditional and modern questions of differential analysis and geometry are the hallmarks of the book.

The book is suitable for a first year graduate course on global analysis.

李群李代数

Terence Tao - Hilbert's Fifth Problem and Related Topics
J.-P. Serre - Lie Algebras and Lie Groups
Nathan Jacobson - Lie Algebras
> 胡乱分类

微分几何

John Willard Milnor - Topology from the Differentiable Viewpoint
Lars Hörmander - Advanced Differential Calculus
Heinz Hopf - Differential Geometry in the Large
James Morrow、Kunihiko Kodaira - Complex Manifolds
Taubes - Differential Geometry
Charles W. Misner, Kip S. Thorne, John Archibald Wheeler - Gravitation
> 微分几何和广相

Peter Dombrowski - 150 Years After Gauss’ “Disquisitiones generales circa superficies curvas”
> Gauss与微分几何的诞生

Manfredo Perdigão do Carmo - Differential Forms and Applications
> 小书

Frank W. Warner - Foundations of Differentiable Manifolds and Lie Groups

Anatole Katok, Vaughn Climenhaga - Lectures on Surfaces
Tristan Needham - Visual Differential Geometry and Forms-A Mathematical Drama in Five Acts

陈省身 - Lectures on Differential Grometry
丘成桐 - 微分几何讲义
Surveys in Differential Geometry (好多卷)
Sigurdur Helgason - Differential Geometry, Lie Groups, and Symmetric Spaces
Wilhelm Klingenberg - a course in differential geometry
De Rham - Differentiable Manifolds

黎曼面

Simon Donaldson - Riemann Surfaces
Hermann Weyl - The Concept of a Riemann Surface
Jürgen Jost - Compact Riemann Surfaces
Lars Ahlfors - Riemann Surfaces

黎曼几何

Lars Hörmander - Riemann Geometry
Peter Peterson - Riemannian Geometry
Marcel Berger - A Panoramic View of Riemannian Geometry
> 参考、欣赏、兴趣，质量有待评估

Manfredo Perdigão do Carmo - Riemannian Geometry
Jürgen Jost - Riemannian Geometry and Geometric Analysis
Nail H. Ibragimov - Tensors and Riemannian Geometry
> 非常多物理，质量有待评估

David Dai-Wai Bao, Shiing-Shen Chern, Zhongmin Shen - An introduction to Riemann-Finsler geometry
Wilhelm P. A. Klingenberg - Riemann Geometry

低维几何

W. Thurston - Three-Dimensional Geometry and Topology
Marvin J. Greenberg - Euclidean and Non-Euclidean Geometries: Development and History

代数拓扑

Allen Hatcher - Algebraic Topology
> With extra chapter Chapter 5. Spectral Sequences and some extra exercises
> Revisions and Additions
> Corrections and Corrections to Algebraic Topology

Daniel Quillen - Homotopical Algebra
J. F. Adams - Algebraic Topology
> 很多数学史文献

William Fulton - Algebraic Topology: A First Course
Michael Atiyah - K-theory
J. P. May - A Concise Course in Algebraic Topology
Tammo tom Dieck - Algebraic Topology
> May的加细

J. P. May, K. Ponto - More Concise Algebraic Topology
Anatoly Fomenko, Dmitry Fuchs - Homotopical Topology
Samuel Eilenberg, Norman Steenrod - Foundations of Algebraic Topology
Friedl - Algebraic Topology I-V
> 用来查的巨型字典

复几何

Mark Green, Phillip Griffiths and Matt Kerr - Hodge Theory, Complex Geometry, and Representation Theory

微分拓扑

John Willard Milnor - Topology from the Differentiable Viewpoint
John Milnor - Differential Topology Forty-six Years Later
> In the 1965 Hedrick Lectures,1 I described the state of differential topology, a field that was then young but growing very rapidly. During the intervening years, many problems in differential and geometric topology that had seemed totally impossible have been solved, often using drastically new tools. The following is a brief survey, describing some of the highlights of these many developments.

C. T. C. Wall - Differential Topology
Victor Guillemin, Alan Pollack - Differential Topology
Morris W. Hirsch - Differential topology
R. C. Kirby, L. C. Siebenmann - Foundational essays on topological manifolds, smoothings and triangulations (1977, 355 p., Princeton University Press and University of Tokyo Press. V, Annals of Mathematics Studies)

低维拓扑

W. Thurston - Three-Dimensional Geometry and Topology
Vaughan F.R. Jones - The Jones Polynomial (exposition paper)

算子代数/非交换几何

不知道该怎么分类……

Operator Algebras, Quantization, and Noncommutative Geometry: A Centennial Celebration Honoring John von Neumann and Marshall H. Stone
> AMS举办的von Neumann和Stone百年诞辰庆典特别会议论文集及其它收录文章
> 关于算子代数、量子化和非交换几何

Alain Connes - Noncommutative Geometry
Kenneth R. Davidson - **C*-Algebras by Example
P. Halmos - What does the spectral theorem say?** American Mathematical Monthly, 70: 241-47.

分析

G. Wanner, E. Hairer - Analysis by its history
G.H. Hardy, J.E. Littlewood, G. Pólya - Inequalities
Lynn Harold Loomis, Shlomo Sternberg - Advanced Calculus
Elliott H. Lieb, Michael Loss - Analysis
Inequalities: Selecta of Elliott H. Lieb
> Brings together a host of inequalities otherwise scattered in the literature and hard to find

George Polya, Gabor Szegö, C.E. Billigheimer - Problems and theorems in analysis I/II
Jürgen Jost - Postmodern Analysis
Barry Simon - Real Analysis: A Comprehensive Course in Analysis, Part 1
Lars Hörmander - The Analysis of Linear Partial Differential Operators

复分析

Elias M. Stein - Complex Analysis
Tao - 246ABC Notes （Blog)
Lars Ahlfors - Complex Analysis
Kunihiko Kodaira - Complex Analysis
Henri Cartan - 解析函数论
Robert E. Greene, Steven G. Krantz - Function Theory of One Complex Variable
Barry Simon - Advanced Complex Analysis: A Comprehensive Course in Analysis, Part 2A/2B
C. L. Siegel - Topics in Complex Function Theory, Vol.1 : Elliptic Functions and Uniformization Theory

测度论

Elias M. Stein - Real Analysis
Folland - Real Analysis Modern Techniques and Their Applications
Richard Wheeden & Antoni Zygmumd - An Introduction to Real Analysis
A. N. Kolmogorov, S. V. Fomin - Elements of the Theory of Functions and Functional Analysis
汪林 - 实分析中的反例
Terence Tao - An Introduction to Measure Theory
Terence Tao - An Epsilon of Room I/II

泛函分析

Haim Brezis - Functional Analysis, Sobolev Spaces and Partial Differential Equations
Peter D. Lax - Functional Analysis
Philippe G. Ciarlet - Linear and Nonlinear Functional Analysis with Applications
A. N. Kolmogorov, S. V. Fomin - Elements of the Theory of Functions and Functional Analysis
Elias M. Stein - Functional Analysis
Lars Hörmander - Linear Functional Analysis
Frigyes Riesz, Bela Sz.-Nagy - Functional Analysis
Jürgen Jost, Xianqing Li-Jost - Calculus of Variations
Alberto Bressan - Lecture Notes on Functional Analysis: With Applications to Linear Partial Differential Equations

调和分析

Elias M. Stein, Rami Shakarchi - Fourier Analysis An Introduction
Terence Tao - Higher Order Fourier Analysis
Barry Simon - Harmonic Analysis: A Comprehensive Course in Analysis, Part 3
Lars Hörmander - Lectures on Harmonic Analysis
Hugh L. Montgomery - Early Fourier Analysis

ODE/动力系统

Vladimir I. Arnold - Ordinary Differential Equations
Morris W. Hirsch, Stephen Smale, Robert L. Devaney - Differential Equations, Dynamical Systems, and an Introduction to Chaos
L. S. Pontryagin - Ordinary Differential Equations
Ernst Hairer, Syvert Paul Nørsett, Gerhard Wanner - Solving Ordinary Differential Equations I/II

PDE

Vladimir I. Arnold - Lectures on Partial Differential Equations
Lawrence C. Evans - Partial Differential Equations
Jürgen Jost - Partial Differential Equations
Lars Hörmander - Seminar Notes on Pseudo-Differential Operators and Boundary Problems

组合

Richard P. Stanley - Permutations
George Pólya, Robert E. Tarjan, Donald R. Woods - Notes on Introductory Combinatorics
A. Björner, R. P. Stanley - A Combinatorial Miscellany
Terence Tao - Additive Combinatorics
Bela Bollobás - Combinatorics: Set Systems, Hypergraphs, Families of Vectors and Probabilistic Combinatorics
> Combinatorics is a book whose main theme is the study of subsets of a finite set. It gives a thorough grounding in the theories of set systems and hypergraphs, while providing an introduction to matroids, designs, combinatorial probability and Ramsey theory for infinite sets. The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures. It should be an ideal text for senior undergraduates and beginning graduates.

图论

Béla Bollobás - Graph Theory: An Introductory Course

博弈论

John Horton Conway - On numbers and games
> 超现实数与组合博弈论

数学物理

V. I. Arnol’d - Mathematical Methods of Classical Mechanics
Michael Reed, Barry Simon - Methods of Modern Mathematical Physics
Michel Talagrand - What Is a Quantum Field Theory?
John Baez, Javier P. Muniain - Gauge Fields, Knots and Gravity
> 这是一本内容广泛、极具原创性的现代电磁学、规范场和引力的介绍，其中大部分内容是用微分形式语言表达的。在其众多优秀的特点中，包括对麦克斯韦方程中霍奇二元性的作用的深刻讨论。不要忽视这本书三部分中每一部分的注释：它们包含对进一步研究的注解建议（非常像这一部分！），它们还包含迷人的历史小故事和精辟的引文。作者以友好、非正式的方式直接与读者交谈，就像对坐在他们身边的聪明朋友说话一样，而不是对着虚空讲解干巴巴的定理，这让人感到非常新鲜和有益。(当然，这也正是我在 VDGF 中试图做的！）——Needham

Shlomo Sternberg - Curvature in Mathematics and Physics
> 形式是这本书的主要语言。正如书名所示，它包含了许多有趣的数学和物理学的应用。特别是，它深入处理了以下物理课题：霍奇对偶（Hodge duality）和电磁学，施瓦兹希尔德解（Schwarzschild solution）的几何和轨道的明确计算，以及极其重要的克尔解（Kerr solution）（代表一个旋转的黑洞）的几何，尽管他在实际计算曲率 2 形式方面止步不前。但这一列表没有完全列出对所涵盖的大量材料。警告：作者将这本书描述为适合高级本科生阅读-其实不然。但是，如果你已经掌握了我的第五幕，那么你就能从这本书里学到很多东西 ——Needham

Hagen Kleinert - Path Integrals
Charles W. Misner, Kip S. Thorne, John Archibald Wheeler - Gravitation
> 微分几何和广相

John Archibald Wheeler - A Journey into Gravity and Spacetime
Anthony Zee - Einstein Gravity in a Nutshell
Jürgen Jost - Geometry and Physics
> "Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics

Pierre Deligne et al. - Quantum Fields and Strings: A Course for Mathematicians
Michael Atiyah - The Geometry and Physics of Knots
Gerald B. Folland - Quantum Field Theory: A Tourist Guide for Mathematicians

概率/统计/信息论

Kai Lai Chung - Elementary Probability Theory
Rick Durrett - Probability: Theory and Examples
Kiyosi Itô - Introduction to probability theory (伊藤清概率论)
Jean Jacod, Philip Protter - Probability Essentials
S. R. S. Varadhan - Probability Theory
Albert N. Shiryaev - Probability 1/2
Albert N. Shiryaev, Andrew Lyasoff - Problems in Probability
> 概率论习题集

George Casella, Roger L. Berger - Statistical Inference
Alfred Renyi - Probability Theory

随机过程

Kiyosi Itô - Stochastic Processes(随机过程)

信息论

Imre Csiszár, János Körne - Information Theory: Coding Theorems for Discrete Memoryless Systems
Thomas M. Cover, Joy A. Thomas - Elements of Information Theory

数理逻辑

Stephen Cole Kleene - Mathematical logic
Kenneth Kunen - The Foundations of Mathematics
Kenneth Kunen - Set Theory
Yu. I. Manin - A Course in Mathematical Logic for Mathematicians
George S. Boolos, John P. Burgess - Computability and Logic (可计算性与数理逻辑)
Martin Davis - Applied Nonstandard Analysis
H. Jerome Keisler - Foundations of Infinitesimal Calculus
Thomas Jech - Set Theory
Akihiro Kanamori, Matthew Foreman, Akihiro Kanamori (eds.) - Handbook of Set Theory
Saharon Shelah - Proper & Improper Forcing
Gerald E. Sacks - higher recursion theory

计算数学/算法

Anne Greenbaum, Tim P. Chartier - Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms
Kenneth Lange - Optimization
Kenneth Lange - Algorithms from THE BOOK
Joachim von zur Gathen, Jürgen Gerhard - Modern Computer Algebra
Jeffrey Humpherys, Tyler J. Jarvis - Foundations of Applied Mathematics Volume 1: Mathematical Analysis and Volume 2: Algorithms, Approximation, Optimization
XIn-She Yang, Xing-Shi He - Mathematical Foundations of Nature-Inspired Algorithms
> The book begins with a short introduction that describes general principles of constrained and unconstrained optimization of univariate and multivariate functions. It then quickly summarizes several versions of gradient-based algorithms including the usual ones (steepest descent and conjugate gradient) as well as more advanced ones like stochastic gradient and subgradient methods.
Having set the stage with these more conventional algorithms, the authors describe a series of nature-inspired algorithms. They note that the “no-free-lunch” theorems proved in 1997 tell us that there is no best algorithm for solving all optimization problems because all algorithms are equally effective (or ineffective) when measured by average performance across all possible problems. Consequently, the authors consider nature-inspired algorithms that can be matched to specific kinds of applications. Algorithms they describe go by names such as particle swarm optimization, the bat algorithm, the firefly algorithm, and cuckoo search. Several of these algorithms are based on the idea of swarm intelligence. The aim of a swarming system is to allow the system to evolve and converge into stable states that include those with optimal performance.
The authors devote a couple of chapters to the analysis of algorithms. This has some general aspects (convergence, stability and robustness) as well as details that apply to the nature-inspired algorithms (determining and tuning of parameters and statistical characterization of performance). A final chapter describes some applications of nature-inspired algorithms that the authors have discovered. These include design optimization in engineering, image processing, vehicle routing and scheduling.
This is not a textbook and has no exercises. Most of the topics considered get very abbreviated treatments and many of the discussions of the algorithms are disappointingly sketchy. Even the algorithm analysis sections are short on detail. Critics have suggested that the elaborate metaphors of some nature-inspired algorithms have hidden their lack of novelty or effectiveness. There is just not enough detail in this book to allow any judgment in that direction.
The book is probably best suited as an inspiration for an independent project that might take one of the algorithms and fill out details of analysis and performance. The book’s level of sophistication varies, but most topics are accessible to upper level undergraduates.

数学史/传记/文集/综述

若干历史

Jean Dieudonné - A History of Algebraic and Differential Topology, 1900 - 1960
Jean Dieudonné - History of Algebraic Geometry
Jean Dieudonné - History of Functional Analysis

Bartel Leenert van der Waerden - A History of Algebra: From al-Khwārizmī to Emmy Noether

Nicolas Bourbaki - Elements of the History of Mathematics

James, I. M. ((eds.)) - History of Topology

Knoebel, A., Laubenbacher, R., Lodder, J. etc. - Mathematical Masterpieces Further Chronicles by the Explorers
> 四个主题：离散与连续；数值求解方程; 曲率和空间的概念；二次互反律

Marvin J. Greenberg - Euclidean and Non-Euclidean Geometries: Development and History
> 平面几何与双曲几何

Marcel Berger - Riemannian Geometry During the Second Half of the Twentieth Century

Peter Dombrowski - 150 Years After Gauss’ “Disquisitiones generales circa superficies curvas”
> Gauss与微分几何的诞生

David S. Richeson - Euler’s Gem
> 关于多面体欧拉公式的历史与思想

Gessel, Ira (ed.) Rota, Gian-Carlo (ed.) - Classic papers in combinatorics

Armand Borel - Essays in the History of Lie Groups and Algebraic Groups

Pesic, Peter (ed.) - Beyond geometry. Classic papers from Riemann to Einstein

Rodrigo A. Pérez - A Brief but Historic Article of Siegel
Luc Illusie, with Alexander Beilinson, Spencer Bloch, Vladimir Drinfeld, et al. - Reminiscences of Grothendieck and His School

一些综述

Vladimir I. Arnold - Huygens and Barrow, Newton and Hooke
Erdős Centennial
> Erdős成就的一个survey

The Legacy of John von Neumann
> 1988会议论文集，阐述了冯·诺依曼的观念和思想及它们对当代数学的影响，以及关于冯诺依曼的若干回忆
> 算子理论、博弈论、遍历理论、科学计算和数学史相关

Camillo De Lellis - The masterpieces of John Forbes Nash Jr. (arxiv 1606.02551)
> Nash成就的一个survey

The Legacy of Bernhard Riemann After One Hundred And Fifty Years Vol I/II
> 综述文集，黎曼的工作和思想在现代的发展

The Legacy of Norbert Wiener: A Centennial Symposium
> 1994年10月，在MIT的Wiener百年诞辰研讨会上发表的演讲合集

Felix Klein - Development of Mathematics in the Nineteenth Century (数学在十九世纪的发展)

传记/个人文集

Gregory Margulis - Autobiography

Paul Halmos - I Want to Be a Mathematician
> Halmos自传

Heinz Hopf - Selected Chapters of Geometry
> This is a write-up by Hans Samelson of lectures by Hopf in a course at ETH in the summer of 1940. The four chapters are:
Euler's Formula.
Graphs.
The Four Vertex Theorem and Related Matters.
The Isoperimetric Inequality.
These total just 41 pages. There is quite a bit of overlap with notes from another course of the same title taught by Hopf at New York University in 1946 and published as the first part of volume 1000 of the Springer Lecture Notes. The 1946 course seems to have covered slightly more material, but Samelson's write-up of the earlier course is more polished and has a more pleasing appearance, being in TEX with nice electronically-drawn figures.

黎曼全集

David Hilbert - Collected works
> 分卷：Number theory/Algebra, theory of invariants, geometry/Analysis

Collected Papers of John Milnor
> 分卷：Geometry ; The Fundamental Group; Differential Topology; Homotopy, Homology and Manifolds; Algebra; Dynamical Systems (1953-2000); and Dynamical Systems (1984-2012)

Collected Works of John Tate: Parts I and II
Collected Works of William P. Thurston with Commentary
> This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff.

Selected Works of Eberhard Hopf with Commentaries
> The volume is presented in two main parts. The first section is dedicated to classical papers in analysis and fluid dynamics, and the second to ergodic theory. These works and all the others in the Selected Works carry commentaries by a stellar group of mathematicians who write of the origin of the problems, the important results that followed.

Selected Works of Phillip A. Griffiths with Commentary
> The four parts of Selected Works—Analytic Geometry, Algebraic Geometry, Variations of Hodge Structures, and Differential Systems—are organized according to the subject matter and are supplemented by Griffiths' brief, but extremely illuminating, personal reflections on the mathematical content and the times in which they were produced.

Gian-Carlo Rota - Indiscrete Thoughts
Gian-Carlo Rota - Discrete Thoughts
Gian-Carlo Rota on Combinatorics
> In this volume, the editor presents reprints of most of the fundamental papers of Gian-Carlo Rota in the classical core of cominatorics

Gian-Carlo Rota on Analysis and Probability

Felix Klein - Lectures on Mathematics (Klein数学讲座)
> 1893年芝加哥国际数学大会，F.Klein在美国西北大学作了为期两周的埃文斯顿学术报告会演讲，本书由他报告的讲义组成

Felix Klein, W. F. Sheppard, P. A. MacMahon, J. L. Mordell - Famous Problems and Other Monographs
> Klein: Famous Problems Of Elementary Geometry (初等几何的著名问题)
> Sheppard: From Determinant to Tensor
> MacMahon: Introduction to Combinatory Analysis
> Moderll: Three Lectures on Fermat's Last Theorem

Mikhail Gromov - Gromov的数学世界

Robert P. Langlands - langlands纲领和他的数学世界

John Milnor - Milnor眼中的数学和数学家

综合/数学哲学/其它

The Princeton Companion to Mathematics
The Princeton Companion to Applied Mathematics

Roger Penrose - The Road to Reality

Felix Klein - Lectures on Mathematics

Yuri I. Manin - Mathematics as Metaphor
> Manin文集

Vladimir I. Arnold - Real Algebraic Geometry

Shing-Tung Yau, Steve Nadis - The Shape of Inner Space (大宇之形)
> 科普，弦论与Calabi-Yau流形

Shing-Tung Yau, Steve Nadis - The Gravity of Math
> 科普，引力理论与数学物理

代数结构与拓扑结构 (Structures Algébriques et Structures Topologiques)
> 不知道该放哪……

Terence Tao - Poincaré’s Legacies Part I/II
> Part I of the second-year posts focuses on ergodic theory, combinatorics, and number theory. Chapter 2 consists of lecture notes from Tao's course on topological dynamics and ergodic theory. By means of various correspondence principles, recurrence theorems about dynamical systems are used to prove some deep theorems in combinatorics and other areas of mathematics. In addition to these lectures, a variety of other topics are discussed, ranging from recent developments in additive prime number theory to expository articles on individual mathematical topics such as the law of large numbers and the Lucas–Lehmer test for Mersenne primes. Some selected comments and feedback from blog readers have also been incorporated into the articles.
> Part I of the second-year posts focuses on geometry, topology, and partial differential equations. The major part of the book consists of lecture notes from Tao's course on the Poincaré conjecture and its recent spectacular solution by Perelman. The course incorporates a review of many of the basic concepts and results needed from Riemannian geometry and, to a lesser extent, from parabolic PDE. The aim is to cover in detail the high-level features of the argument, along with selected specific components of that argument, while sketching the remaining elements, with ample references to more complete treatments. In addition to these lectures, a variety of other topics are discussed, including expository articles on topics such as gauge theory, the Kakeya needle problem, and the Black–Scholes equation. Some selected comments and feedback from blog readers have also been incorporated into the articles.
> The lectures are as self-contained as possible, focusing more on the “big picture” than on technical details.

Terence Tao - Compactness and Contradiction

V. B. Alekseev - Abel's theorem in problems and solutions based on the lectures of professor V.I. Arnold
> 不知道该放哪×2

Arthur Jaffe, Frank Quinn - Theoretical Mathematics Toward a cultural synthesis of mathematics and theoretical physics (arxiv)
Thurston - On Proof and Progress in Mathematics
Michael Atiyah et al. - Responses to "Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics'', by A. Jaffe and F. Quinn (arxiv)
Arthur Jaffe, Frank Quinn - Response to comments on “theoretical mathematics”
Michael Atiyah - Reflections on geometry and physics
Yuri I. Manin - Truth, rigour, and common sense

Kurt Gödel - What is Cantor’s Continuum Problem?

Arnold, V. (ed.); Atiyah, M. (ed.); Lax, P. (ed.); Mazur, B. (ed.) Mathematics: frontiers and perspectives

杂项

Interview with Abel Laureate 2020 Gregory Margulis
Saunders MacLane - Duality for Groups
Saunders MacLane (1948) - Groups, categories and duality Proceedings of the Nat. Acad. of Sciences of the USA 34: 263–67.
Daniel E. Loeb, Gian-Carlo Rota - Recent contributions to the calculus of finite differences a survey (arxiv 9502210)
Green B, and Tao T. 2008. The primes contain arbitrarily long arithmetic progressions. Annals of Mathematics 167: 481-547.
J. H. Conway, S. Torquato - Packing, tiling, and covering with tetrahedra
Maryna Viazovska - The sphere packing problem in dimension 8
Maryna Viazovska - On discrete Fourier uniqueness sets in Euclidean space
Samuel Eilenberg, Saunders MacLane - General Theory of Natural Equivalences
> 范畴论的起源

Samuel Eilenberg, Saunders MacLane (1945,1950) - Relations Between Homology and Homotopy Groups of Spaces I/II
Samuel Eilenberg; John C. Moore (1962) - Limits and spectral sequences ", Topology 1 (1): 1–23, doi:10.1016/0040-9383(62)90093-9, ISSN 0040-9383
Samuel Eilenberg; Norman E. Steenrod (1945) - Axiomatic approach to homology theory Proceedings of the National Academy of Sciences of the United States of America 31 (4): 117–120. doi:10.1073/pnas.31.4.117. PMID 16578143
Armand Borel, Jean-Pierre Serre (1958) - Le théorème de Riemann-Roch (The Riemann–Roch theorem)
J. Michael Steele - The Cauchy-Schwarz Master Class
V. I. Arnold - Experimental Mathematics
Roger Penrose (1955) - A generalized inverse for matrices