Mathematics eBooks

Mathematics Books

This section contains free e-books and guides on Mathematics, some of the resources in this section can be viewed online and some of them can be downloaded.

Recently Added Books

Abstract Algebra Theory and Applications

This PDF covers the following topics related to Abstract Algebra : The Integers, Groups, Cyclic Groups, Permutation Groups, Cosets and Lagrange’s Theorem, Matrix Groups and Symmetry, Isomorphisms, Homomorphisms, The Structure of Groups, Group Actions, Vector Spaces.

s442 Pages

Abstract Algebra by Santiago Canez

This PDF covers the following topics related to Abstract Algebra : Introduction to Groups, Integers mod n , Dihedral Groups, Symmetric Groups, Homomorphisms, Group Actions, Some Subgroups, Cyclic Groups, Generating Sets, Zorn’s Lemma, Normal Subgroups, Cosets and Quotients, Lagrange’s Theorem, First Isomorphism Theorem, More Isomorphism Theorems, Simple and Solvable Groups, Alternating Groups, Orbit-Stabilizer Theorem, More on Permutations, Class Equation, Conjugacy in Sn, Simplicity of An, Sylow Theorems, More on Sylow, Applications of Sylow, Semidirect Products, Classifying Groups, More Classifications, Finitely Generated Abelian, Back to Free Groups.

s103 Pages

Computational Algebraic Geometry by Wolfram Decker

This PDF book covers the following topics related to Algebraic Geometry : General Remarks on Computer Algebra Systems, The Geometry–Algebra Dictionary, Affine Algebraic Geometry, Ideals in Polynomial Rings, Affine Algebraic Sets, Hilbert’s Nullstellensatz, Irreducible Algebraic Sets, Removing Algebraic Sets, Polynomial Maps, The Geometry of Elimination, Noether Normalization and Dimension, Local Studies, Projective Algebraic Geometry, The Projective Space, Projective Algebraic Sets, Affine Charts and the Projective Closure, The Hilbert Polynomial, Computing, Standard Bases and Singular, Applications, Ideal Membership, Elimination, Radical Membership, Ideal Intersections, Ideal Quotients, Kernel of a Ring Map, Integrality Criterion, Noether Normalization, Subalgebra Membership, Homogenization, Dimension and the Hilbert Function, Primary Decomposition and Radicals, Buchberger’s Algorithm and Field Extensions, Sudoku, A Problem in Group Theory Solved by Computer Algebra, Finite Groups and Thompson’s Theorem, Characterization of Finite Solvable Groups.

s133 Pages

Algebraic Geometry I Lecture Notes Roman Bezrukavnikov

The contents of this book include: Course Introduction, Zariski topology, Affine Varieties, Projective Varieties, Noether Normalization, Grassmannians, Finite and Affine Morphisms, More on Finite Morphisms and Irreducible Varieties, Function Field, Dominant Maps, Product of Varieties, Separateness, Sheaf Functors and Quasi-coherent Sheaves, Quasi-coherent and Coherent Sheaves, Invertible Sheaves, (Quasi)coherent sheaves on Projective Spaces, Divisors and the Picard Group, Bezout’s Theorem, Abel-Jacobi Map, Elliptic Curves, KSmoothness, Canonical Bundles, the Adjunction Formulaahler Differentials, Cotangent Bundles of Grassmannians, Bertini’s Theorem, Coherent Sheves on Curves, Derived Functors, Existence of Sheaf Cohomology, Birkhoff-Grothendieck, Riemann-Roch, Serre Duality, Proof of Serre Duality.

s63 Pages

Lectures on Algebraic Topology by Haynes Miller

This PDF Lectures covers the following topics related to Algebraic Topology : Singular homology, Introduction: singular simplices and chains, Homology, Categories, functors, and natural transformations, Basic homotopy theory, The homotopy theory of CW complexes, Vector bundles and principal bundles, Spectral sequences and Serre classes, Characteristic classes, Steenrod operations, and cobordism.

s307 Pages

Algebraic Topology A Comprehensive Introduction

This book explains the following topics: Introduction, Fundamental group, Classification of compact surfaces, Covering spaces, Homology, Basics of Cohomology, Cup Product in Cohomology, Poincaré Duality, Basics of Homotopy Theory, Spectral Sequences. Applications, Fiber bundles, Classifying spaces, Applications, Vector Bundles, Characteristic classes, Cobordism, Applications.

s318 Pages

Applied Mathematics by CBSE

This PDF Lecture covers the following topics related to Applied Mathematics : Number Theory, Prime Number Ratio, Proportion and Logarithms, Interpretatlysis of Data, Commercial Mathematics, Set Theory Unit 6: Relation and Function, Algebra Complex Number, Sequence and Series, Permutations and Combinations, Trigonometry.

s148 Pages

Introduction to Applied Mathematics

This PDF Lecture covers the following topics related to Applied Mathematics : Introduction - What is Applied Mathematics, Dimensional Analysis and Scaling, Asymptotic analysis, Perturbation Methods, Asymptotic Expansion of Integrals, Functional Analysis - A Crash Course, Calculus of Variations, Orthogonal Expansions, Sturm Liouville Problem.

s90 Pages

Arithmetic and Algebraic Geometry

This PDF Lectures covers the following topics related to Arithmetic and Algebraic Geometry : Rings, Spectra, Affine Varieties, Projective Varieties, Regularity, Curves.

s74 Pages

Arithmetic Geometry by Prof Szpiro

This PDF Lectures covers the following topics related to Arithmetic Geometry : Operations with modules, Schemes and projective schemes, Rings of dimension one, The compactified Picard group of an order of a number field, Different, discriminant and conductor, The classic theorems of the algebraic number theory, Heights of rational points on a scheme over a number field.

s87 Pages

Basic Concepts of Algebra

This PDF Lectures covers the following topics related to Basic Concepts of Algebra : The Real-Number System, Integer Exponents, Scientific Notation, and Order of Operations, Addition, Subtraction, and Multiplication of Polynomials, Factoring, Rational Expressions, Radical Notation and Rational Exponents, The Basics of Equation Solving.

s1058 Pages

Elementary Algebra 2e

This PDF Lectures covers the following topics related to Elementary Algebra : Foundations, Solving Linear Equations and Inequalities, Math Models, Graphs, Systems of Linear Equations, Polynomials, Factoring, Rational Expressions and Equations, Roots and Radicals, Quadratic Equations.

s1340 Pages

Contemporary Mathematics by Donna Kirk

This PDF book covers the following topics related to Contemporary Mathematics :Sets, Logic, Real Number Systems and Number Theory, Number Representation and Calculation, Algebra, Money Management, Probability, Statistics, Metric Measurement, Geometry, Voting and Apportionment, Graph Theory, Math and Art.

s1575 Pages

Elementary Mathematics by William Chen

This page covers the following topics related to Elementary Mathematics : Basic Algebra, Introduction to Matrices, Trigonometry, Indices and Logarithms, Polynomial Equations, Inequalities and Absolute Values, Progressions, Elementary Counting Techniques, Complex Numbers, Functions and Lines, Introduction to Differentiation, Further Techniques of Differentiation, Applications of Differentiation, Introduction to Integration.

sNA Pages

Calculus Volume 1 by Edwin Herman

This PDF book covers the following topics related to Calculus : Functions and Graphs, Limits, Derivatives, Applications of Derivatives, Integration, Applications of Integration.

s875 Pages

Multivariable Calculus Worksheets

This PDF book covers the following topics related to Multivariable Calculus : Curves Defined by Parametric Equations, Tangents, Areas, Arc Lengths, and Surface Areas, Polar Coordinates, Vectors, Dot Products, Cross Products, Lines and Planes, Quadric Surfaces, Vector Functions and Space Curves, Cross Products and Projections, Functions of Several Variables, Limits and Continuity, Partial Derivatives, Tangent Planes and Differentials, The Chain Rule, Directional Derivatives and the Gradient Vector, Maximum and Minimum Values, Lagrange Multipliers, Double Integrals over Rectangles, Double Integrals over General Regions, Double Integrals in Polar Coordinates, Applications of Double Integrals, Surface Area, Triple Integrals in Cartesian, Spherical, and Cylindrical Coordinates, Change of Variable in Multiple Integrals, Gravitational Potential Energy, Vector Fields, Line Integrals, etc.

s74 Pages

Category Theory in Context by Emily Riehl

This PDF book covers the following topics related to Category Theory : Categories, Functors, Natural Transformations, Universal Properties, Representability, and the Yoneda Lemma, Limits and Colimits, Adjunctions, Monads and their Algebras, All Concepts are Kan Extensions.

s258 Pages

Categorical homotopy theory by Emily Riehl

This PDF book covers the following topics related to Category Theory : All concepts are Kan extensions, Derived functors via deformations, Basic concepts of enriched category theory, The unreasonably effective bar construction, Homotopy limits and colimits: the practice, Weighted limits and colimits, Categorical tools for homotopy limit computations, Weighted homotopy limits and colimits, Derived enrichment, Weak factorization systems in model categories, Algebraic perspectives on the small object argument, Enriched factorizations and enriched lifting properties, A brief tour of Reedy category theory,. Preliminaries on quasi-categories, Simplicial categories and homotopy coherence, Isomorphisms in quasi-categories, A sampling of 2-categorical aspects of quasi-category theory.

s292 Pages

Studies of Classical Analysis by Ting Yao Lee

This PDF book covers the following topics related to Classical Analysis : Introduction, Complex Numbers, the Theory of Convergence, Continuous Functions and Uniform Convergence, the Theory of Riemann Integration.

s116 Pages

Lectures On Semiclassical Analysis

This note explains the following topics: Symplectic geometry, Fourier transform, stationary phase, Quantization of symbols, Semiclassical defect measures, Eigenvalues and eigenfunctions, Exponential estimates for eigenfunctions, symbol calculus, Quantum ergodicity and Quantizing symplectic transformations.

s211 Pages

Combinatorics by Joy Morris

This PDF book covers the following topics related to Combinatorics : What is Combinatorics, Basic Counting Techniques, Permutations, Combinations, and the Binomial Theorem, Bijections and Combinatorial Proofs, Counting with Repetitions, Induction and Recursion, Generating Functions, Generating Functions and Recursion, Some Important Recursively-Defined Sequences, Other Basic Counting Techniques, Basics of Graph Theory, Moving through graphs,Euler and Hamilton, Graph Colouring, Planar graphs, Latin squares, Designs, More designs, Designs and Codes.

s357 Pages

Combinatorics of Centers by Sebastian Konig

This PDF book Combinatorics of Centers of 0-Hecke Algebrasin Type A covers the following topics related to Combinatorics : Introduction, Preliminaries, Coxeter groups, The symmetric group, Combinatorics, enters of 0-Hecke algebras, Elements in stair form, Equivalence classes, etc.

s59 Pages

Commutative Algebra by Allen B. Altman

This PDF book A Term of Commutative Algebra covers the following topics related to Commutative Algebra : Rings and Ideals, Prime Ideals, Radicals, Modules, Exact Sequences, Fitting Ideals, Direct Limits, Filtered direct limits, Tensor Products, Flatness, Cayley–Hamilton Theorem, Localization of Rings, Localization of Modules, Cohen–Seidenberg Theory, Noether Normalization, Jacobson Rings, Chain Condition, Noetherian Spaces, Associated Primes, Primary Decomposition, Old-primary Submodules, Length, Hilbert Functions, etc.

s434 Pages

Progress in Commutative Algebra 2

This PDF book Progress in Commutative Algebra 2 covers the following topics related to Commutative Algebra : A Guide to Closure Operations in Commutative Algebra, A Survey of Test Ideals, Finite-dimensional Vector Spaces with Frobenius Action, Finiteness and Homological Conditions in Commutative Group Rings, Regular Pullbacks, Noetherian Rings without Finite Normalization, Krull Dimension of Polynomial and Power Series Rings, The Projective Line over the Integers, On Zero Divisor Graphs, A Closer Look at Non-unique Factorization via Atomic Decay and Strong Atoms.

s328 Pages

Complex Analysis by M. Pollicott

This PDF covers the following topics related to Complex Analysis : Introduction, A few basic ideas, Analyticity, Definitions of analyticity, Integrals and Cauchy’s Theorem, Properties of analytic functions, Riemann Mapping Theorem, Behaviour of analytic functions, Harmonic functions, Singularities, Entire functions, their order and their zeros, Prime number theorem, Further Topics.

s94 Pages

Complex Analysis by Eric T. Sawyer

This PDF covers the following topics related to Complex Analysis : The Real Field, The Complex Field, Properties of holomorphic functions, The Riemann Mapping Theorem, Contour integrals and the Prime Number Theorem, The Poisson representation, Extending Riemann maps.

s121 Pages

Computational Mathematics by Oxford

This PDF book covers the following topics related to Computational Mathematics : Introduction to MATLAB, Algebraic equations and calculus, Differential equations, sums, matrices and vectors, Loops, conditionals and functions, A simple matrix function.

s56 Pages

Mathematics and Computation

This lecture note covers the following topics: Prelude: computation, undecidability and the limits of mathematical knowledge, Computational complexity 101: the basics, Problems and classes inside N P, Lower bounds, Boolean Circuits, and attacks on P vs. NP, Proof complexity, Randomness in computation, Abstract pseudo-randomness, Weak random sources and randomness extractors, Randomness in proof, Randomness in proofs, Arithmetic complexity, Interlude: Concrete interactions between Math and Computational Complexity.

s372 Pages

Sequences and series amsi

This PDF book covers the following topics related to Constants And Numerical Sequences and Series : Sequences, Series, Means, Applications to finance, The limiting sum of a geometric series, Links forward, Use of induction, Telescoping series, The harmonic series, Connection with integration, More on means, The AM–GM inequality, History and applications, An application to film and video, Fibonacci numbers, The Greeks.

s34 Pages

Notes on Infinite Sequences and Series

This book covers the following topics: Sequences, Limit Laws for Sequences, Bounded Monotonic Sequences, Infinite Series, Telescopic Series, Harmonic Series, Higher Degree Polynomial Approximations, Taylor Series and Taylor Polynomials, The Integral Test, Comparison Test for Positive-Term Series, Alternating Series and Absolute Convergence, Convergence of a Power Series and Power Series Computations.

s21 Pages

Differential Geometry by Balazs Csikos

The aim of this textbook is to give an introduction to differential geometry. Topics covered includes: Categories and Functors, Linear Algebra, Geometry, Topology, Multivariable Calculus, Ordinary Differential Equations, The Notion of a Curve, The Length of a Curve, Plane Curves, Osculating Spheres, Hypersurfaces in R n, Manifolds, Differentiation of Vector Fields and Integration of Differential Forms.

s354 Pages

Notes on Differential Algebra by Reid Dale

This PDF book covers the following topics related to Differential Algebra : Basic Differential Algebra, Derivations and Dual Numbers, Differential Ideals and Ritt Noetherianity, Characteristic Sets and the Partial Ritt-Raudenbush, Basic Differential Algebraic Geometry: Properties of the Kolchin Topology, Differentially Closed Fields, Differential Dimension Polynomials, Differential Galois Theory, Binding Groups and Internality, Pillay’s X-strongly-normal theory, Galois Theory of Linear Differential Equations, Algebraic D-Groups and Logarithmic Derivatives, Constrained Cohomology, The Galois Groupoid, Differential Algebraic Groups, Preliminaries from Model Theory.

s47 Pages

Differential and Integral Analysis by Thomas Prellberg

This PDF book covers the following topics related to Differential and Integral Analysis : Differentiation, The Mean Value Theorem, The Exponential Function, Inverse Functions, Higher Order Derivatives, Definition of the Riemann Integral, Properties of the Riemann Integral, The Fundamental Theorem of Calculus, Sequences and Series of Functions, Power Series.

s77 Pages

Differential Analysis Lecture notes by Richard B. Melrose

This note covers the following topics: Measure and Integration, Hilbert spaces and operators, Distributions, Elliptic Regularity, Coordinate invariance and manifolds, Invertibility of elliptic operators, Suspended families and the resolvent, Manifolds with boundary, Electromagnetism and Monopoles.

s243 Pages

Differential Calculus Notes For Mathematics 100 and 180

The contents include: The basics, Limits, Derivatives, Applications of derivatives, Numbers, Sets, Other important sets, Functions, Parsing formulas, Inverse functions, Another limit and computing velocity, The limit of a function, Calculating limits with limit laws, Continuity, Revisiting tangent lines, Interpretations of the derivative, Proofs of the arithmetic of derivatives, Derivatives of Exponential Functions, Derivatives of trigonometric functions, The natural logarithm, Implicit Differentiation, Inverse Trigonometric Functions, The Mean Value Theorem, Higher order derivatives, Velocity and acceleration, Related rates, Optimisation, Sketching graphs, Introduction to antiderivatives, Carbon dating, Population growth, Some examples, Further examples, The error in the Taylor polynomial approximations, Local and global maxima and minima, Finding global maxima and minima, Symmetries, A checklist for sketching, Sketching examples, Standard examples, Variations.

s391 Pages

Calculus I Compact Lecture Notes by ACC Coolen

The contents include: Introduction, Proof by induction, Complex numbers, Trigonometric and hyperbolic functions, Functions, limits and differentiation, Integration, Taylor’s theorem and series, Exercises.

s135 Pages

Ordinary Differential Equations by Gabriel Nagy

This book explains the following topics: First Order Equations, Second Order Linear Equations, Reduction of Order Methods, Homogenous Constant Coefficients Equations ,Power Series Solutions, The Laplace Transform Method, Systems of Linear Differential Equations, Autonomous Systems and Stability, Boundary Value Problems.

s431 Pages

Differential Equations Jeffrey R. Chasnov

The contents of this book include: A short mathematical review, Introduction to odes, First-order odes , Second-order odes, constant coefficients, The Laplace transform, Series solutions, Systems of equations, Nonlinear differential equations, Partial differential equations.

s149 Pages

Classical Differential Geometry Peter Petersen

This book explains the following topics: General Curve Theory, Planar Curves, Space Curves, Basic Surface Theory, Curvature of Surfaces, Surface Theory, Geodesics and Metric Geometry, Riemannian Geometry, Special Coordinate Representations.

s256 Pages

Differential Geometry by Rui Loja Fernandes

This note covers the following topics: Manifolds as subsets of Euclidean space, Abstract Manifolds, Tangent Space and the Differential, Embeddings and Whitney’s Theorem, The de Rham Theorem, Lie Theory, Differential Forms, Fiber Bundles.

sNA Pages

Lectures on differential topology by Alexander Kupers

The contents include: Spheres in Euclidean space, Smooth manifolds, Submanifolds and tori, Smooth maps and their derivatives, Tangent bundles, Immersions and submersions, Quotients and coverings, Three further examples of manifolds, Partitions of unity and the weak Whitney embedding theorem, Transversality and the improved preimage theorem, Stable and generic classes of smooth maps, Transverse maps are generic, Knot theory, Orientations and integral intersection theory, Integration on manifolds, De Rham cohomology, Invariant forms in de Rham cohomology, First fundamental theorem of Morse theory, Second fundamental theorem of Morse theory, Outlook.

s279 Pages

Topology from the Differentiable Viewpoint

This PDF covers the following topics related to Differential Topology : Smooth manifolds and smooth maps, Tangent spaces and derivatives, Regular values, The fundamental theorem of algebra, The theorem of Sard and Brown, Manifolds with boundary, The Brouwer fixed point theorem, Proof of Sard's theorem, The degree modulo 2 of a mapping, Smooth homotopy and smooth isotopy, Oriented manifolds, The Brouwer degree, Vector fields and the Euler number, Framed cobordism, the Pontryagin construction, The Hopf theorem, Exercise.

s77 Pages

Digital Notes On Discrete Mathematics

This note explains the following topics related to Discrete Mathematics : Mathematical Logic, Relations, Algebraic structures, Elementary Combinatorics, Recurrence Relation, Graph Theory.

s88 Pages

Discrete Mathematics by Andrew D. Ker

This PDF covers the following topics related to Discrete Mathematics : Introduction, Sets, Functions, Counting, Relations, Sequences, Modular Arithmetic, Asymptotic Notation, Orders.

s125 Pages

Elliptic Curves by Pete L. Clark

An elliptic curve is an object defined over a ground field K. This PDF covers the following topics related to Elliptic Curves : What is an elliptic curve?, Mordell-Weil Groups, Background on Algebraic Varieties, The Riemann-Roch Express, Weierstrass Cubics, The l-adic Tate module, Elliptic Curves Over Finite Fields, The Mordell-Weil Theorem I: Overview, The Mordell-Weil Theorem II: Weak Mordell-Wei, The Mordell-Weil Theorem III: Height Functions, The Mordell-Weil Theorem IV: The Height Descent Theorem, The Mordell-Weil Theorem V: Finale, More On Heights, Diophantine Approximation, Siegel’s Theorems on Integral Points.

s90 Pages

Elliptic Curves by Thomas Kramer

Elliptic curves belong to the most fundamental objects in mathematics and connect many different research areas such as number theory, algebraic geometry and complex analysis. Their definition and basic properties can be stated in an elementary way: Roughly speaking, an elliptic curve is the set of solutions to a cubic equation in two variables over a field. This PDF covers the following topics related to Elliptic Curves : Analytic theory of elliptic curves, Elliptic integrals, The topology of elliptic curves, Elliptic curves as complex tori, Complex tori as elliptic curves, Geometric form of the group law, Abel’s theorem, The j-invariant, The valence formula, Geometry of elliptic curves, Affine and projective varieties, Smoothness and tangent lines, Intersection theory for plane curves, The group law on elliptic curves, Abel’s theorem and Riemann-Roch, Weierstrass normal forms, The j-invariant, Arithmetic of elliptic curves, Rational points on elliptic curves, Reduction modulo primes and torsion points, An intermezzo on group cohomology, The weak Mordell-Weil theorem, Heights and the Mordell-Weil theorem.

s77 Pages

Fourier Analysis for Beginners

This PDF book covers the following topics related to Fourier analysis : Mathematical Preliminaries, Sinusoids, Phasors, and Matrices, Fourier Analysis of Discrete Functions, The Frequency Domain, Continuous Functions, Fourier Analysis of Continuous Functions, Sampling Theory, Statistical Description of Fourier Coefficients, Hypothesis Testing for Fourier Coefficients, Directional Data Analysis, The Fourier Transform, Properties of The Fourier Transform, Signal Analysis, Fourier Optics.

s201 Pages

Fourier Series and Transforms by William Chen

This page covers the following topics related to Fourier Analysis : Introduction to Fourier Series, Algebraic Background to Fourier Series, Fourier Coefficients, Convergence of Fourier Series, Further Topics on Fourier Series, Introduction to Fourier Transforms, Further Topics on Fourier Transforms.

sNA Pages

Fractals in Probability and Analysis

This PDF book covers the following topics related to Fractals in Probability and Analysis : Minkowski and Hausdorff dimensions, Self-similarity and packing dimension, Frostman’s theory and capacity, Self-affine sets, Graphs of continuous functions, Brownian motion, Random walks, Markov chains and capacity, Besicovitch–Kakeya sets, The Traveling Salesman Theorem.

s397 Pages

Random Fractals by Peter Morters

The term fractal usually refers to sets which, in some sense, have a self-similar structure. This PDF book covers the following topics related to Random Fractals : Representing fractals by trees, Fine properties of stochastic processes, More on the planar Brownian path, etc.

s29 Pages

The Variable Order Fractional Calculus of Variations

Fractional calculus is a recent field of mathematical analysis and it is a generalization of integer differential calculus, involving derivatives and integrals of real or complex order. This PDF book covers the following topics related to Fractional Calculus : Fractional calculus, The calculus of variations, Expansion formulas for fractional derivatives, The fractional calculus of variations.

s136 Pages

Fractional Calculus Integral and Differential Equations of Fractional Order

This note covers the following topics: Introduction To Fractional Calculus, Fractional Integral Equations, Fractional Differential Equations and The Mittag-leffler Type Functions.

s56 Pages

Introduction to Functional Analysis by Daniel Daners

This PDF book covers the following topics related to Functional Analysis : The Axiom of Choice and Zorn’s Lemma, Banach Spaces, Banach algebras and the Stone-Weierstrass Theorem, Hilbert Spaces, Linear Operators, Duality, Spectral Theory.

s123 Pages

Introduction to Functional Analysis by University of Leeds

This PDF book covers the following topics related to Functional Analysis :Basics of Metric Spaces, Basics of Linear Spaces, Orthogonality, Duality of Linear Spaces, Fourier Analysis, Operators, Spectral Theory, Compactness, The spectral theorem for compact normal operators, Banach and Normed Spaces, Measure Theory, Integration, Functional Spaces, Fourier Transform, Advances of Metric Spaces.

s213 Pages

Geometric Algebra Primer by Jaap Suter

This PDF book covers the following topics related to Geometric Algebra : Introduction, Subspaces, Geometric Algebra, Tools, Applications, Conclusion.

s66 Pages

Geometric Algebra and its Application to Mathematical Physics

This thesis is an investigation into the properties and applications of Clifford’s geometric algebra. Topics covered includes: Grassmann Algebra and Berezin Calculus, Lie Groups and Spin Groups, Spinor Algebra, Point-particle Lagrangians, Field Theory, Gravity as a Gauge Theory.

s244 Pages

Geometric Topology Rutgers

This PDF book covers the following topics related to Geometric Topology : Klee’s Trick, Manifold factors, Stable homeomorphisms and the annulus conjecture, Cellular homology, Some elementary homotopy theory, Wall’s finiteness obstruction, A weak Poincar´e Conjecture in high dimensions, Stallings’ characterization of euclidean space, Whitehead torsion, Siebenmann’s Thesis, Torus trickery 101 - local contractibility, Torus trickery 102 – the Annulus Conjecture, Homotopy structures on manifolds, etc.

s193 Pages

Geometric Topology by Dennis Sullivan

This PDF book covers the following topics related to Geometric Topology : Algebraic Constructions, Homotopy Theoretical Localization, Completions in Homotopy Theory, Spherical Fibrations, Algebraic Geometry, The Galois Group in Geometric Topology.

s250 Pages

Foundations of Geometry by David Hilbert

This PDF book covers the following topics related to Geometry : The Five Groups of Axioms, the Compatibility and Mutual Independence of the Axioms, the Theory of Proportion, the Theory of Plane Areas, Desargues’s Theorem, Pascal’s Theorem, Geometrical Constructions Based Upon the Axioms I-V.

s105 Pages

Geometry Unbound

This PDF book covers the following topics related to Geometry : Introduction, Construction of the Euclidean plane, Transformations, Tricks of the trade, Concurrence and collinearity, Circular reasoning, Triangle trivia, Quadrilaterals, Geometric inequalities, Inversive and hyperbolic geometry, Projective geometry.

s142 Pages

Graph Theory by Prof. Dr. Maria Axenovich

This PDF book covers the following topics related to Graph Theory :Preliminaries, Matchings, Connectivity, Planar graphs, Colorings, Extremal graph theory, Ramsey theory, Flows, Random graphs, Hamiltonian cycles.

s104 Pages

Graph Theory by Narsingh Deo

This PDF book covers the following topics related to Graph Theory : Introduction, Paths and Circuits, Trees and Fundamental Circuits, Cut-sets and Cut-vertices, Planar and Dual Graphs, Vector Spaces of a Graph, Matrix Representation of Graphs, Coloring, Covering, and Partitioning, Directed Graphs, Enumeration of Graphs, Graph Theoretic Algorithms and Computer, Graphs in Switching and Coding Theory, Electrical Network Analysis by Graph Theory, Graph Theory in Operations Research, Survey of Other Applications, Binet-cauchy Theorem, Nullity of a Matrix and Sylvester’s Law.

s598 Pages

Group Theory by Ferdi Aryasetiawan

This note describes the following topics: Abstract Group Theory, Theory of Group Representations, Group Theory in Quantum Mechanics, Lie Groups, Atomic Physics, The Group SU2: Isospin, The Point Groups, The Group SU3.

s140 Pages

Group Theory by Gunnar Traustason

Group Theory can be viewed as the mathematical theory that deals with symmetry, where symmetry has a very general meaning. This PDF book covers the following topics related to Group Theory : Introduction, Definitions and basic properties, Direct products and abelian groups, Composition series and solvable groups, Permutation groups and group actions, Finite groups and Sylow Theory, Semidirect products and groups of order less than 15.

s49 Pages

A Course in Harmonic Analysis by Jason Murphy

This PDF book covers the following topics related to Harmonic Analysis : Introduction, Fourier analysis, Abstract Fourier analysis, Wavelet transforms, Classical harmonic analysis, part I, Classical harmonic analysis, part II, Semiclassical and microlocal analysis, Sharp inequalities, Restriction theory and related topics, Additional topics.

s303 Pages

Explorations in Harmonic Analysis

This PDF book covers the following topics related to Harmonic Analysis : Ontology and History of Real Analysis, Advanced Ideas: The Hilbert Transform, Essentials of the Fourier Transform, Fourier Multipliers, Fractional and Singular Integrals, Several Complex Variables, Canonical Complex Integral Operators, Hardy Spaces Old and New, Introduction to the Heisenberg Group, Analysis on the Heisenberg Group.

s451 Pages