1 SUMS Springer Undergraduate Mathematics Series
斯普林格大学本科数学系列（SUMS）是为全球数学和科学专业的本科生设计的系列。 从核心基础材料到最后一年的主题，SUMS书籍采用新颖和现代的方法。 文字说明有大量的例子，问题和完善的解决方案，尤其是普遍存在的困难领域。 这些实用而简洁的教科书是针对一两个学期的课程而设计的，但是自学式方法使其成为独立使用的理想选择。
【代数】
- Matrix Groups
- Codes
- Introduction to Lie Algebras
- Metric Spaces
【数论】
- Elementary Number Theory
【分析】
- Analytic Methods for Partial Differential Equations
- Calculus of one Variable
- Linear Functional Analysis
【几何】
- Applied Geometry for Computer Graphics and CAD
- Elementary Differential Geometry
- Dyperbolic Geometry
- Worlds out of Nothing
【拓扑】
【计算】
【统计】
- General Relativity
【概率】
- Basic Stochastic Process
- Measure, Integral and Probability
【组合】
- A First Course in Discrette Mathematics
【其他】
- Game Theory
- Sturm-Lioouville Theory and its applications
2 Undergraduate Texts in Mathematics
数学本科课程介绍了数学的各个子领域。 这些教科书通常针对美国大学的大学三年级和四年级的数学学生，通常为学生和教师提供有关材料的新观点。 即使对于本科课程的标准主题，这些书中的大多数也提供了新颖的方法和见解。 作为有效的教学工具，这些书包括引导读者了解主题的内在联系的动机，展示概念的具体体现的示例以及在各种难度下测试和增强理解的练习。
【代数】
- A concrete Introduction to Higher Algebra
- A Field Guide to Algebra
- An Introduction to Mathematical Cryptography
- An Introduction to wavelets through linear algebra
- Applied Linear algebra and Matrix analysis
- Groups and Symmetry
- A concrete introduction to algebraic Curves
- Glimpses of Algebra and Geometry
- Finite-Dimensional Vector Spaces
- Ideals, Varieties, and Algorithms
- Integers, polynomials, and rings
- Introduction to Boolean Algebras
- Introduction to CryptoGraphy
- The Joy of Sets
- Undergraduate Algebra
- Linear Algebra Done Right
- Naive Lie Theory
- Notes on Set Theory
- The Laplace Transfrom: Theory and Applications
- Rational Points on Elliptic Curves
- linearity symmetry and prediction in the Hydrogen Atom
- Elemments of number theory
- The Fundamental theorem of algebra
【数论】
- Introduction to Analytic Number Theory
- Elementary Number Theory
- Exercise in Number Theory
【分析】
- A Course in Calculus and Real Analysis
- A First Course in Calculus
- Understanding analysis
- Analysis by its history
- Complex Analysis
- The Lebesguestielgjes Integral
- Difference Equations
- An Introduction to Difference Equations
- Practical Analysis in one variable
- Inside Calculus
- Introduction to Calculus and classsical Analysis
- Elementary Stability and bifurcation Theory
- Calculus I II III
- Problems and Solutions for undergranduate analysis
- Basic elements of real analysis
- Real Mathematical Analysis
- Beginning Functional Analysis
- Second Year Calculus
- A Brief on Tensor Analysis
- Students Guide to Calculus
- Mathematical Methods of Classical Mechanics
- Fourier Series
- Differential Analysis on Complex Manifolds
【几何】
- Elementary Topics in Differential Geometry
- Geometry Euclid and beyond
- Measure Topology and Fractal Geometry
- The Four Pollars of Geometry
- Variational Problems in Geometry
- Modern Graph Theory
【拓扑】
- Basic Topology
- Topological and uniform spaces
- Topology of Surfaces
- Topology
【计算】
- Computing the Continuous Discretely
【概率】
- Elementary Probability Theory
- Discrete Probability
- The Pleasures of Probability
- Exercises in Probability
- Advanced Probalility II
【组合】
- Combinatorics and Graph Theory
- Discrete Mathematics
- Mathematical Masterpieces
- Mathematics : A Concise History and Philosophy
【其他】
- Mathematical Logic
- Reading, Writing, and Proving
3 PBM problem books in mathematics
是Springer出版社以数学习题为主的一系列书籍
内容深刻全面，结果新颖实用，方法精巧简洁，习题丰富多样
值得大家参考
【代数】
- A Sequence of Problems on SemiGroups
- Functional Equations and How to Solve Them
- Problems and Theorems in clssical Set Theory
- Pells Equation
- Exercises in Classical Ring Theory
- An Introduction to Hilbert Space and Quantum Logic
【数论】
- Unsolved Problems in Number Theory
- Exercises in Number Theory
- Fermats Last Theorem
【分析】
- Limits, Series, and Fractional Part Integrals
- A Problem book in Real Analysis
- Principles of Partial Differential Equations
- Contests in Higher Mathematics
- Problems in Real and Comples Analysis
- Exercises in Integration
- Probelm book for First Year Calculus
- Theorems and Problems in Functional Analysis
- Introduction to Oprator Theory
- p-adic Numbers p-adic Analysis and Zeta-Functions
【几何】
- Analysis and algebra on differentiable Manjifolds
- Linear Geometry
- A Course in Differential Geometry
- Algebraic Geometry
- Combinatorics with emphasis on the theory of graphs
- Introduction to Knot Theory
【拓扑】
- A Cp-Theory Problem Book
- Geometric Topology in Dimensions 2 and 3
- Algebraic Topologiy
【概率】
- Problems in Probability
- 40 Puzzles and Problems in Pjrobability and Mathematical Statistics
- Probability Theory
【其他】
- The IMO Compendium
- Berkeley Problems in Mathematics
- Problem-Solving Strategies
- Problem-Solving through problems
- General Relativity for Mathematicians
- A Course in Mathematical Logic
4 GTM Graduate Texts in Mathematics
Graduate Texts in Mathematics(GTM)是Springer出版的一个数学基础系列书籍,包括了数学分析、高等代数、复变分析、概率论、随机过程等的数学教材。
4.1【代数】
- Introduction to Axiomatic Set Theory
- Topological Vector Spaces
- A Course in Homological Algebra
- Categories for the Working Mathematician
- A Course in Arithmetic
- Axiomatic Set Theory
- Introduction to Lie Algebrtas and Representation Theory
- A course in simple Homotopy Theory
- Rings and Catregories of Modules
- Stable Mappings and Their Singularities
- The Structure of Fields
- Measure Theory
- Fibre Bundles
- Linear Algebraic Groups
- An Algebraic Introduction to Mathematical Logic
- Linear Algebra
- Algebraic Theories
- Commutative Algebra
- Lectures in Abstract Algebra Basic Comcepts
- Several Complex Variables and Branach Algebras
- Linear Topological Spaces
- An Invitation to C-Algebras
- Linear Representations of Finite Groups
- Rings of Continuous Functions
- Cyclotomic Fields
- Elements of Homotopy Theory
- Fundamentals of the Theory of Groups
- Introduction to Affine Group Schemes
- Local Fields
- Linear Operators in Hilbert Spaces
- Singular Homology Theory
- Algebra
- Basic Theory of Algebraic Group and Lie Algebras
- A course in Iniversal Algebra
- An Introdunction to Ergodic Theory
- A Course in the theory of groups
- Introduction to Cyclotomic Fields
- Introduction to Coding Theory
- Cohomology of Groups
- Associative Algebras
- Introduction to Algebraic and Abelian Functions
- The Geometry of Discrete Groups
- Foundations of Differentiable Manifolds and Lie Groups
- Introduction to Elliptic Curves and Modular Forms
- Representations of Compact Lie Groups
- Finite Reflection Groups
- Harmonic Analysis on Semigroups
- Galois Theory
- Lie groups
- SL2(R)
- The Arithmetic of Elliptic Curves
- Applications of Lie Groups to Differential Equations
- Elliptic Curves
- Elliptic Functions
- A Course in Number Theory and Cryptography
- Algebraic Groups and Class Fields
- Weakly differentiable Functions
- Cyclotomic Fields
- Linear Algebraic Groups
- Representation Theory
- A First Course in Noncummutative Rings
- Coding and Information Theory
- Advanced Linear Algebra
- Algebra
- Topics in Banach Space Theory
- Grobner Bases
- Measure Theory
- Noncommutative Algebra
- Algebraic K- Theory
- An Introduction to the theory of Groups
- Commutative Algebra
- Advanced Topic in the Arithmetic of Elliptic Curves
- An Introduction to Analysis
- Quantum Groups
- Classical Descriptive Set Theory
- Field Theory
- Groups and Representations
- Permutation Groups
- Field and Galois Theory
- Matrix Analysis
- Branach Algebra Techniques in operator Theory
- Moduli of Curves
- Lectures on Modules and Rings
- Basic Homological Algebra
- Theory of Bergman Spaces
- The Symmetric Group
- Galois Theory
- Rational Homotopy Theory
- A Short Course on Spectral Theory
- Number Theory in Function Fields
- Algebra
- Matrices
- Model Theory
- An Elementray Introduction to Groups and Representations
- Lie groups
- Spaces of Holomorphic Functions in the Unit
Ball - Combinatorial Commutative Algebra
- A First Course in Modular Forms
- Combinatorics of Coxeter Groups
- Topics in Banach Space Theory
- Compack Lie Groups
- Abstract Algebra
- Topological Methods in Group Theory
- A Course in Commutative Banach Algebras
- Braid Groups
- Buildings
- The Finite Simple Groups
- Algebraic Function Fields and codes
- Symmetry Representations and Invariants
- A Course in Commutative Algebra
- Deformation Theory
- Monomial Ideals
4.2 【数论】
- Modular Functions and Dirichlet Series in Number Theory
- Multiplicative Number Theory
- Lectures on the Theory of Algebraic Numbers
- A Classical Introduction to Modern Number Theory
- Algebraic Number Theory
- Numbers
- A Course in computiational Algebraic Number Theory
- Additive Number Theory
- Analytic Number Theory
- Fourier Analysis on Number Fields
- Problems in Algebraic Number Theory
- Advanced Topics in Computational Number Theory
- One-Parameter Semigroups for Linear Evlution Equations
- Elementrary Methods in Number Theory
- An Introduction to Number Theory
- Number theory
- The Arithmetic of Dynamical Systems
- Ergodic Theory
4.3【分析】
- Functons of One Complex Variable
- Advanced Mathematical Analysis
- Lectures in Functional Analysis and Operator Theory
- Geometric Functional Analysis and its applications
- Real and Abstract Analysis
- Several Complex Variables
- A Course in Functional Analysis
- Complex Analysis
- Holomorphic Functions and Integral Representations in Several complex Variables
- Measure and Integral
- Analysis Now
- Theory of Complex Functions
- Complex Variables
- Partial Differential Equations
- Interation of Rational Functions
- Optima and Equilibria
- Real And Functional Analysis
- Functons of One Complex Variable
- Polynomials and Polunomial Inquali
- Classical Topics in Complex Function Theory
- Fundations of Real And Abstract Analysis
- Nonsmooth Analysis and Control Theory
- Numerical Analysis
- Ordinary Differential Equations
- Lectures on the Hyperreals
- Elements of Functional Analysis
- A course in p-adic analysis
- Analysis of Applied MAthematics
- Partial Differential Equations
- Fourier Analysis and its Applications
- Bounded Analytic Functions
- An Introduction to Operators on the Hardy-Hilbert Space
- Complex Analysis
- Classical Fourier Analysis
- Modern Fourier Analysis
- Distributions and Operators
- Elementary Functional Analysis
- Essentials of Integration Theory for Analysis
- Functonal Analysis calculus
- Calculus Without Derivatives
4.4【几何】
- Projective Planes
- A Hilbert Space Problem Book
- Elementray Algebraic Geometry
- Algebraic Geometry
- Lectures on Riemann Surfaces
- Sequences and Series in banach Spaces
- Modern Geometry I II
- Univalent Functions and Teichmuller Spaces
- Differential Geometry. Manifolds, curves, and Surfaces
- Tensor Geometry
- Algebraic Geometry
- Foundations of Hyperbolic Manifolds
- Lectures on Polytopes
- Algebraic Topology
- Differential and Riemannian Manifolds
- Differential Geometry
- Combinatorial Comvexity and Algebraic Geometry
- Sheaf Theory
- Riemannian Geometry
- An Introduction to Knot Theory
- Riemannian Manifolds
- Using Algebraic Geometry
- Fundamentals of Differential Geometry
- An Introduction to Riemann-Finsler Geometry
- Diophantine Geometry
- Lectures on Discrete Geometry
- From Holomorphic Functions to Complex Manifolds
- Algebraic Functions and Projective Curves
- Introduction to smooth manifolds
- Smooth Manifolds and Observables
- Metric structures in differential geometry
- The Geometry of Syzygies
- Analysis on Fock Spaces
- Unbounded Self-adjoint operators on Hilbert Space
4.5【拓扑】
- Measure and Category
- General Topology
- Differential Topology
- Riemann Surfaces
- Classical Topology and Combinatorial Group Theory
- Differential Forms in Algebraic Topology
- An Introduction to Convex Polytopes
- An Introduction to Algebraic Topology
- A Basic Course in Algebraic Topology
- Topology and Geometry
- Homology Theory
- Graph Theory
- A Course On Borel Sets
- An Introductijon to Banach Space Theory
- Modern Graph Theory
- The Geometry of Schemes
- Introduction to Topological Manifolds
- Algebraic Graph Theory
- The Arithmetic of Hyperbolic 3-Man
- Graph Theory
4.6【计算】
- Fourier Series
- Computability
- Convex Polytopes
4.7【概率】
- Random Processes
- Principles of Random Walk
- Denumerable Markov Chains
- Probability
- Brownian Motion and Stochastic Calculus
- Integration and Probability
- An Introduction to Markov Processes
- Analysis and Probability
- Probability and Stochastics
4.8【组合】
- A Course in Enumeration
4.9【其他】
5 SMM Springer Monographs in Mathematics
该系列出版了高级专着，对数学研究领域中的“最新技术”进行了很好的书写，这些技术已经获得了这种疗法所需的成熟度。 它们具有足够的独立性，不仅可以让该领域的专业人士接触到，而且还具有足够的全面性，可以在许多年内保持有价值的参考。 除了其领域的当前知识状态之外，SMM卷还应该描述其与数学相邻领域的相关性和相互作用，并为未来的研究方向提供指导。 该系列中的各卷均精装。
【代数】
- Algebraic Cobordism
- Analysis of Toeplitz Operators
- Building
- Class Field Theory
- Complex Semisimple Lie Algebras
- Cyclotomic Fields and Zeta Values
- Complex Analysis on Infinite Dimensional Spaces
- Discrete Spectral Synthesis and its Applications
- Elementary and analytic theory of algebraic numbers
- Elementary Dirichlet Series and Modular Forms
- Find Structures of Hyperbolic Diffeomorphisms
- Finite Model Theory
- Fractals and Universal Spaces in Dimension Theory
- High-dimensional knot theory
- Ideals and Reality
- Introduction to Singularities and Deformations
- Inverse Galois Theory
- Lie Algebras and algebraic Groups
- Local Algebra
- Moduli in Modern Mapping Theory
- Perturbations of Positive Semigroups with Applications
- Set Theory
- The Higher Infinite
- Theory of Association Schemes
- Topological Invariants of Stratified Spaces
- Tree
- Twelve Sporadic Groups
- Valued Fields
- Integral Closure
【数论】
- Modular Forms
- The Development of Prime Number Theory
- The Heat Kernel and Theta Inversion on LS2(C)
【分析】
- An Introduction to Echo Analysis
- Applied Proof Theory Proof Interpretations and Their Use in Mathematics
- Asymptotic Cones and Functions in Optimization and Variational Inequalities
- Functonal Analysis in Mechanics
- Integral Closure
- Methods in Nonlinear Analysis
- Modern Methods in the Calculus of Variations : Lp Spaces
- NMonsmooth Variational Problems and Their Inequalities
- Nonstandard Analysis Axiomatically
- Self-dual Partial Differential Systems and Their Variational Principles
- Shock Wave Interactions in General Relativity
- Stratified Lie Groups and potential Theory for their Sub-Laplacians
【几何】
- Convex Polyhedra
- Fractal Geometry Complex Dimensions and Zeta Functions
- Projective and Cayley-Klein Geometries
- Random Fields and Geometry
- The Generic Chaining
【拓扑】
- Fixed Point Theory
【计算】
- Interpolation Processes
- Optimization of Elliptic Systems
- Variational and potential Methods ofr a class 0f hyperbolic Evolutionary Processes
- Vorticity ,statistical Mechanics and Monte Carlo Simulation
- Walsh Equiconvergence of Complex Interpolating Polynomials
【概率】
- Brownian Motion Obsatcles and Random Media
- Multiparameter Processes
【组合】
【其他】
- Fourier Series in Control Theory
- Interfacial Convection in Multilayer Systems
- Nevanlinnas Theory of Value Distribution
- Normal Forms and unfoldings for Local Dynamnical Systems
- Notes on Coxeter Transformations and the McKay Correspondence
- On Thom Spectra Orientablility and Cobordism
7 Optimization Methods in Electromagnetic Radiation - Reciprocity Laws
