1 SUMS Springer Undergraduate Mathematics Series
斯普林格大學(xué)本科數(shù)學(xué)系列（SUMS）是為全球數(shù)學(xué)和科學(xué)專業(yè)的本科生設(shè)計的系列。 從核心基礎(chǔ)材料到最后一年的主題若债，SUMS書籍采用新穎和現(xiàn)代的方法惠遏。 文字說明有大量的例子话侄，問題和完善的解決方案按声，尤其是普遍存在的困難領(lǐng)域罩缴。 這些實(shí)用而簡潔的教科書是針對一兩個學(xué)期的課程而設(shè)計的眶诈，但是自學(xué)式方法使其成為獨(dú)立使用的理想選擇衍锚。
【代數(shù)】
- Matrix Groups
- Codes
- Introduction to Lie Algebras
- Metric Spaces
【數(shù)論】
- Elementary Number Theory
【分析】
- Analytic Methods for Partial Differential Equations
- Calculus of one Variable
- Linear Functional Analysis
【幾何】
- Applied Geometry for Computer Graphics and CAD
- Elementary Differential Geometry
- Dyperbolic Geometry
- Worlds out of Nothing
【拓?fù)洹?/h2>
【計算】
【統(tǒng)計】
- General Relativity
【概率】
- Basic Stochastic Process
- Measure, Integral and Probability
【組合】
- A First Course in Discrette Mathematics
【其他】
- Game Theory
- Sturm-Lioouville Theory and its applications
2 Undergraduate Texts in Mathematics
數(shù)學(xué)本科課程介紹了數(shù)學(xué)的各個子領(lǐng)域。 這些教科書通常針對美國大學(xué)的大學(xué)三年級和四年級的數(shù)學(xué)學(xué)生奥吩，通常為學(xué)生和教師提供有關(guān)材料的新觀點(diǎn)哼蛆。 即使對于本科課程的標(biāo)準(zhǔn)主題蕊梧，這些書中的大多數(shù)也提供了新穎的方法和見解霞赫。 作為有效的教學(xué)工具，這些書包括引導(dǎo)讀者了解主題的內(nèi)在聯(lián)系的動機(jī)肥矢，展示概念的具體體現(xiàn)的示例以及在各種難度下測試和增強(qiáng)理解的練習(xí)端衰。
【代數(shù)】
- 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
【數(shù)論】
- 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
【幾何】
- 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?fù)洹?/h2>
- Basic Topology
- Topological and uniform spaces
- Topology of Surfaces
- Topology
【計算】
- Computing the Continuous Discretely
【概率】
- Elementary Probability Theory
- Discrete Probability
- The Pleasures of Probability
- Exercises in Probability
- Advanced Probalility II
【組合】
- 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出版社以數(shù)學(xué)習(xí)題為主的一系列書籍
內(nèi)容深刻全面，結(jié)果新穎實(shí)用甘改，方法精巧簡潔旅东，習(xí)題豐富多樣
值得大家參考
【代數(shù)】
- 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
【數(shù)論】
- 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
【幾何】
- 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?fù)洹?/h2>
- 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出版的一個數(shù)學(xué)基礎(chǔ)系列書籍,包括了數(shù)學(xué)分析、高等代數(shù)十艾、復(fù)變分析抵代、概率論、隨機(jī)過程等的數(shù)學(xué)教材忘嫉。
4.1【代數(shù)】
- 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 【數(shù)論】
- 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【幾何】
- 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?fù)洹?/h2>
- 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【計算】
- 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【組合】
- A Course in Enumeration
4.9【其他】
5 SMM Springer Monographs in Mathematics
該系列出版了高級專著荤牍，對數(shù)學(xué)研究領(lǐng)域中的“最新技術(shù)”進(jìn)行了很好的書寫，這些技術(shù)已經(jīng)獲得了這種療法所需的成熟度庆冕。 它們具有足夠的獨(dú)立性康吵，不僅可以讓該領(lǐng)域的專業(yè)人士接觸到，而且還具有足夠的全面性访递，可以在許多年內(nèi)保持有價值的參考晦嵌。 除了其領(lǐng)域的當(dāng)前知識狀態(tài)之外，SMM卷還應(yīng)該描述其與數(shù)學(xué)相鄰領(lǐng)域的相關(guān)性和相互作用，并為未來的研究方向提供指導(dǎo)惭载。 該系列中的各卷均精裝旱函。
【代數(shù)】
- 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
【數(shù)論】
- 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
【幾何】
- Convex Polyhedra
- Fractal Geometry Complex Dimensions and Zeta Functions
- Projective and Cayley-Klein Geometries
- Random Fields and Geometry
- The Generic Chaining
【拓?fù)洹?/h2>
- Fixed Point Theory
【計算】
- 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
【組合】
【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
7 Optimization Methods in Electromagnetic Radiation
