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This note covers the following topics: Set theory, Group theory, Ring theory, Isomorphism theorems, Burnsides formula, Field theory and Galois theory, Module theory, Commutative algebra, Linear algebra via module theory, Homological algebra, Representation theory.
Author s : Romyar Sharif This book aims to give an introduction to using GAP with material appropriate for an undergraduate abstract algebra course.
It does not even attempt to give an introduction to abstract algebra, there are many excellent books which do this.
Topics covered includes: The GGAP user interface, Rings, Groups, Linear Algebra, Fields and Galois Theory, Number Theory.
Author s : Alexander Hulpke This note covers the following topics: Hochschild cohomology and group actions, Differential Weil Descent and Differentially Large Fields, Minimum positive entropy of complex Enriques surface automorphisms, Nilpotent structures and collapsing Ricci-flat metrics on K3 surfaces, Superstring Field Theory, Superforms and Supergeometry, Picard groups for tropical toric schemes, Complex multiplication and Brauer groups of K3 surfaces.
Author s : arXiv.
Author s : Audun Holme This is a basic note in algebraic topology, it introduce the notion of fundamental groups, covering spaces, methods for computing fundamental groups using Seifert Van Kampen theorem and some applications such as the BrouwerÂ’s fixed point theorem, Borsuk Ulam theorem, fundamental theorem of algebra.
Author s : Prof.
Srinivasan This note covers the following topics: Important examples of topological spaces, Constructions, Homotopy and homotopy equivalence, CW -complexes and homotopy, Fundamental group, Covering spaces, Higher homotopy groups, Fiber bundles, Suspension Theorem and Whitehead product, Homotopy groups of CW -complexes, Homology groups, Homology groups of CW -complexes, Homology with coefficients and cohomology groups, Cap product and the Poincare duality, Elementary obstruction theory.
Author s : Boris Botvinnik This note describes the following topics: Normed Linear Spaces and Banach Spaces, Hilbert Spaces, Spectral Theory and Compact Operators, Distributions, The Fourier Transform, Sobolev Spaces, Boundary Value Problems, Differential Calculus in Banach Spaces and the Calculus of Variations.
Author s : Todd Arbogast and Jerry L.
Bona This book explains the following topics: Linear Equations, Matrices, Linear Programming, Mathematics of Finance, Sets and Counting, Probability, Markov Chains, Game Theory.
Author s : Rupinder Sekhon This note explains the following topics: Classical arithmetic geometry, The Convergence Theorem, The link with the classical AGM sequence, Point counting on elliptic curves, A theta structure induced by Frobenius.
Author s : Robert Carls This note covers the following topics: Rational points on varieties, Heights, Arakelov Geometry, Abelian Varieties, The Brauer-Manin Obstruction, Birational Geomery, Statistics of Rational Points, Zeta functions.
Author s : Caucher Birkar and Tony Feng This note covers the following topics: Symbolic Expressions, Transcription of Verbal Information into Symbolic Language, Linear Equations in One Variable, Linear Equations in Two Variables and Their Graphs, Simultaneous Linear Equations, Functions and Their Graphs, Linear functions and proportional reasoning, Linear Inequalities and Their Graphs, Exponents, Quadratic Functions and Their Graphs, The Quadratic Formula and Application.
Author s : H.
Wu This is a set of lecture notes on please click for source school algebra written for middle school teachers.
Topics covered includes: Symbolic Expressions, Transcription of Verbal Information into Symbolic Language, Linear Equations in One Variable, Linear Equations in Two Variables and Their Graphs, Simultaneous Linear Equations, Functions and Their Graphs, Linear functions and proportional reasoning, Linear Inequalities and Their Graphs, Exponents, Quadratic Functions and Their Graphs, The Quadratic Formula and Applications.
Author s : Avinash Sathaye This note covers the following topics: Numbers, functions, and sequences, Limit and continuity, Differentiation, Maxima, minima and curve sketching, Approximations, Integration, Logarithmic and exponential functions, Applications of Integration, Series of numbers and functions, Limit and continuity of scalar fields, Differentiation of scalar fields, Maxima and minima for scalar fields, Multiple Integration, Vector fields, StokesÂ’ theorem and applications.
Author s : NPTEL In Additive Number Theory we study subsets of integers and their behavior under addition.
Topics covered includes:Lower Bound on Sumset, Erdos conjecture on arithmetic progressions, Szemeredi theorem, Algorithm to find Large set with 3-term AP, Condition for a set not having 3-term AP, Cardinality of set with no 3-term AP, Improved Size of A, Sum Free Sets and Prime number theorem.
Author s : R.
Balasubramanian The note is intended as a one and a half term course in calculus for students who have studied calculus in high school.
It is intended to be self contained, so that it is possible to follow it without any background in calculus, for the adventurous.
Author s : Daniel Kleitman This note covers following topics of Integral and Differential Calculus: Differential Calculus: rates of change, speed, slope of a graph, minimum and maximum of functions, Derivatives measure instantaneous changes, Integral Calculus: Integrals measure the accumulation of some quantity, the total distance an object has travelled, area under a curve, volume of a region.
Author s : Gerald Hoehn The book is aimed primarily at the beginning graduate student.
It gives the de nition of this notion, goes through the various associated gadgetry such as functors, natural transformations, limits and colimits, and then explains adjunctions.
just click for source s : Harold Simmons This note covers the following topics related to Category Theory: Categories, Functors and Natural Transformations, subcategories, Full and Faithful Functors, Equivalences, Comma Categories and Slice Categories, Yoneda Lemma, Grothendieck universes, Limits and Colimits, Adjoint Functors, Adjoint Functor Theorems, Monads, Elementary Toposes, Cartesian Closed Categories, Logic of Ra slots free and Sheaves.
Author s : Thomas Streicher 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.
Author s : Lawrence C.
Evans and Maciej Zworski This note explains the following topics: linearly related sequences of difference derivatives of discrete orthogonal polynomials, identity for zeros of Bessel functions, Close-to-convexity of some special functions and their derivatives, Monotonicity properties of some Dini functions, Classification of Systems of Linear Second-Order Ordinary Differential Equations, functions of Hausdorff moment sequences, Van der Corput inequalities for Bessel functions.
Author s : arXiv.
Topics covered includes: What is Enumerative Combinatorics, Sieve Methods, Partially Ordered Sets, Rational Generating Functions, Graph Theory Terminology Author s : Richard P.
Stanley This lecture note covers the following topics: What is Combinatorics, Permutations and Combinations, Inclusion-Exclusion-Principle and Mobius Inversion, Generating Functions, Partitions, Partially Ordered Sets and Designs.
Author s : Torsten Ueckerdt Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.
Basic commutative algebra will be explained in this document.
Author s : Columbia University This book is a clear, concise, and efficient textbook, aimed at beginners, with a good selection of topics.
Topics covered includes: Rings and Ideals, Radicals, Filtered Direct Limits, Cayley–Hamilton Theorem, Localization of Rings and Modules, Krull–Cohen–Seidenberg Theory, Rings and Ideals, Direct Limits, Filtered direct limit.
Author s : Allen Altman and Steven Kleiman This book has plenty of figures, plenty of examples, copious commentary, and even in-text exercises for the students.
But, since it is not a formal textbook, it does not have exercise sets.
It does not have a Glossary or a Table of Notation.
Topics covered includes: The Complex Plane, Complex Line Integrals, Applications of the Cauchy Theory, Isolated Singularities and Laurent Series, The Argument Principle, The Geometric Theory of Holomorphic Functions, Harmonic Functions, Infinite Series and Products, Analytic Continuation.
Author s : Steven G.
Krantz The book is intended as a text, appropriate for use by advanced undergraduates or graduate students who have taken a course in introductory real analysis, or as it is often called, advanced calculus.
No background in complex variables is assumed, thus making the text suitable for those encountering the subject for the first time.
The Elementary Theory, General Cauchy TheoremApplications of the Cauchy Theory, Families of Analytic Functions, Factorization of Analytic Functions and The Prime Number Theorem.
Author s : R.
Novinger This note covers the following topics: Holomorphic functions, Contour integrals and primitives, The theorems of Cauchy, Applications of CauchyÂ’s integral formula, Argument.
Logarithm, Powers, Zeros and isolated singularities, The calculus of residues, The maximum modulus principle, Mobius transformations.
Author s : Christian Berg This text will illustrate and teach all facets of the subject in a lively manner that will speak to the needs of modern students.
It will give them a powerful toolkit for future work in the mathematical sciences, and will also point to new directions for additional learning.
Topics covered includes: The Relationship of Holomorphic and Harmonic Functions, The Cauchy Theory, Applications of the Cauchy Theory, Isolated Singularities and Laurent Series, The Argument Principle, The Geometric Theory of Holomorphic Functions, Applications That Depend on Conformal Mapping, Transform Theory.
Author s : Steven G.
Krantz This lecture note explains the following topics: This Numerical Methods for ODEs, Discretizations for ODEs, The Runge-Kutta Methods, Linear Multistep Methods, Numerical Methods for PDEs, Tools of Functional Analysis, The Ritz-Galerkin Method, FDM for Time-Dependent PDES, Finite Difference Methods for Elliptic Equations, Computational Projects.
Author s : Augusto Ferreira This note covers the following topics: Mathematical Modeling, EulerÂ’s Method, Taylor Series, Taylor Polynomials, Floating-Point Numbers, Normalized Floating-Point NumbersMATLAB.
Author s : Greg Fasshauer 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.
Author s : Miguel A.
Lerma These lectures note explains the real and complex numbers and their properties, particularly completeness; define and study limits of sequences, convergence of series, and power series.
Author s : University of Oxford The goal of this note is to contribute to the qualitative theory of differential-algebraic systems by providing new asymptotic stability criteria for a class of nonlinear, fully implicit DAEs with tractability index two.
Topics covered includes: State space analysis of differential-algebraic equations, Properly formulated DAEs with tractability index 2, The state space form, Index reduction via differentiation, Stability criteria for differential-algebraic systems, Asymptotic stability of periodic solutions, LyapunovÂ’s direct method regarding DAEs.
Author s : Michael Menrath This book covers the following topics: differential polynomial and their ideals, algebraic differential manifolds, structure of differential polynomials, systems of algebraic equations, constructive method, intersections of algebraic differential manifolds, Riquier's existence theorem for orthonomic system.
Author s : Joseph Fels Ritt 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.
Author s : Richard B.
Melrose This note covers the following topics: Introduction To PDE, Basic Tools of Analysis, Analysis of the Wave Equation in Minkowski Space, Basic Concepts in Riemannian and Lorentzian Geometry.
Author s : Sergiu Klainerman This note explains the following topics: Differentiation from first principles, Differentiating powers of x, Differentiating sines and cosines, Differentiating logs and exponentials, Using a table of derivatives, The quotient rule, The product rule, The chain rule, Parametric differentiation, Differentiation by taking logarithms, Implicit differentiation, Extending the table of derivatives, Tangents and normals, Maxima and minima.
Author s : Mathtutor This note covers the following topics: Limits and Continuity, Differentiation Rules, Applications of Differentiation, Curve Sketching, Mean Value Theorem, Antiderivatives and Differential Equations, Parametric Equations and Polar Coordinates, True Or False and Multiple Choice Problems.
Author s : Veselin Jungic, Petra Menz, and Randall Pyke This note covers the following topics: Qualitative Analysis, Existence and Uniqueness of Solutions to First Order Linear IVP, Solving First Visit web page Linear Homogeneous DE, Solving First Order Linear Non Homogeneous DE: The Method of Integrating Factor, Modeling with First Order Linear Differential Equations, Additional Applications: Mixing Problems and Cooling Problems, Separable Differential Equations, Exact Differential Equations, Substitution Techniques: Bernoulli and Ricatti Equations, Applications of First Order Nonlinear Equations, One-Dimensional Dynamics, Second Order Linear Differential Equations, The General Solution of Homogeneous Equations, Existence of Many Fundamental Sets, Second Order Linear Homogeneous Equations with Constant, Coefficients, Characteristic Equations with Repeated Roots, The Method of Undetermined Coefficients, Applications of Nonhomogeneous Second Order Linear Differential Equations.
Author s : Marcel B.
Finan This note introduces students to differential equations.
Topics covered includes: Boundary value problems for heat and wave equations, eigenfunctionexpansions, Surm-Liouville theory and Fourier series, D'Alembert's solution to wave equation, characteristic, Laplace's equation, maximum principle and Bessel's functions.
Author s : Joseph M.
Mahaffy This note covers the following topics: Manifolds as subsets of Euclidean space, Abstract Manifolds, Tangent Space and the Differential, Embeddings and WhitneyÂ’s Theorem, The de Rham Theorem, Lie Theory, Differential Forms, Fiber Bundles.
Author s : Rui Loja Fernandes This note explains the following topics: From Kock–Lawvere axiom to microlinear spaces, Vector bundles,Connections, Affine space, Differential forms, Axiomatic structure of the real line, Coordinates and formal manifolds, Riemannian structure, Well-adapted topos models.
Author s : Ryszard Pawe Kostecki This note explains the following topics: The concept of a fiber bundle, Morphisms of Bundles, Vector Bundles, Principal Bundles, Bundles and Cocycles, Cohomology of Lie Algebras, Smooth G-valued Functions, Connections on Principal Bundles, Curvature and Perspectives.
Author s : Karl-Hermann Neeb This book gives a deeper account of basic ideas of differential topology than usual in introductory texts.
Also many more examples of manifolds like matrix groups and Grassmannians are worked out in detail.
Topics covered includes: Continuity, compactness and connectedness, Smooth manifolds and maps, Regular values and SardÂ’s theorem, Manifolds with boundary and orientations, Smooth homotopy and vector bundles, Intersection numbers, vector fields and Euler characteristic.
Author s : Uwe Kaiser This note explains the following topics: Sets, Sums and products, The Euclidean algorithm, Numeral systems, Counting, Proof techniques, Pascal's triangle, Recurrence sequences.
Author s : Gabor Horvath and Szabolcs Tengely This note explains the following topics: positional and modular number systems, relations and their graphs, discrete functions, set theory, propositional and predicate logic, sequences, summations, mathematical induction and proofs by contradiction.
Author s : William D Shoaff This note explains the following topics: Elliptic Integrals, Elliptic Functions, Periodicity of the Functions, LandenÂ’s Transformation, Complete Functions, Development of Elliptic Functions into Factors, Elliptic Integrals of the Second Order, Numerical Calculations.
Author s : Arthur L.
Bake Elliptic-curve cryptography is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.
Author s : Christian Wuthrich Aim of this note is to provide mathematical tools used in applications, and a certain theoretical background that would make other parts of mathematical analysis accessible to the student of physical science.
Topics covered includes: Power series and trigonometric series, Fourier integrals, Pointwise convergence of Fourier series, Summability of Fourier series, Periodic distributions and Fourier series, Metric, normed and inner product spaces, Orthogonal expansions and Fourier series, Classical orthogonal systems and series, Eigenvalue problems related to differential equations, Fourier transformation of well-behaved functions, Fourier transformation of tempered distributions, General distributions and Laplace transforms.
Author s : J.
Korevaar This note is an overview of some basic notions is given, especially with an eye towards somewhat fractal examples, such as infinite products of cyclic groups, p-adic numbers, and solenoids.
Topics covered includes: Fourier series, Topological groups, Commutative groups, The Fourier transform, Banach algebras, p-Adic numbers, r-Adic integers and solenoids, Compactifications and Completeness.
Author s : Stephen Semmes This book is devoted to a phenomenon of fractal sets, or simply fractals.
Topics covered includes: Sierpinski gasket, Harmonic functions on Sierpinski gasket, Applications of generalized numerical systems, Apollonian Gasket, Arithmetic properties of Apollonian gaskets, Geometric and group-theoretic approach.
Author s : A.
Kirillov Goal of this course note is primarily to develop the foundations of geometric measure theory, and covers in detail a variety of classical subjects.
A secondary goal is to demonstrate some applications and interactions with dynamics and metric number theory.
Author s : Michael Hochman This note covers the following topics: Introduction To Fractional Calculus, Fractional Integral Equations, Fractional Differential Equations and The Mittag-leffler Type Functions.
Author s : Rudolf Gorenflo and Francesco Mainardi The first chapter explains definition of fractional calculus.
The second and third chapters, look at the Riemann-Liouville definitions of the fractional integral and derivative.
The fourth chapter looks at some fractional differential equations with an emphasis on the Laplace transform of the fractional integral and derivative.
The last chapter describes application problems—a mortgage problem and a decay-growth problem.
Author s : Joseph M.
Kimeu, Western Kentucky University This note covers the following topics: Principles of Functional Analysis, The Weak and Weak Topologies, Fredholm Theory, Spectral Theory, Unbounded Operators, Semigroups of Operators.
Author s : Theo Buhler and Dietmar A.
Salamon, ETH Zurich Functional analysis plays an important role in the applied sciences as well as in mathematics itself.
These notes are intended to familiarize the student with the basic concepts, principles andmethods of functional analysis and its applications, and they are intended for senior undergraduate or beginning graduate students.
Topics covered includes: Normed and Banach spaces, Continuous maps, Differentiation, Geometry of inner product spacesCompact operators and Approximation of compact operators.
Author s : Amol Sasane This thesis is an investigation into the properties and applications of CliffordÂ’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.
Author s : Chris J.
Doran, Sidney Sussex College There are four main areas discussed in this guide is: Geometric Algebra, Projective Geometry, Multiple View Tensors and 3DReconstruction.
Author s : Christian B.
Perwass The aim of this book is to introduce hyperbolic geometry and its applications to two- and three-manifolds topology.
Topics covered includes: Hyperbolic geometry, Hyperbolic space, Hyperbolic manifolds, Thick-thin decomposition, The sphere at infinity, Surfaces, Teichmuller space, Topology of three-manifolds, Seifert manifolds, Constructions of three-manifolds, Three-manifolds, Mostow rigidity theorem, Hyperbolic Dehn filling.
Author s : Bruno Martelli This book covers the following topics: Cohomology and Euler Characteristics Of Coxeter Groups, Completions Of Stratified Ends, The Braid Structure Of Mapping Class Groups, Controlled Topological Equivalence Of Maps in The Theory Of Stratified Spaces and Approximate Fibrations, The Asymptotic Method In The Novikov Conjecture, N Exponentially Nash G Manifolds and Vector Bundles, Controlled Algebra and Topology.
Author s : Andrew Ranicki and Masayuki Yamasaki This is a great mathematics book cover the following topics: Equilateral Triangle, Perpendicular Bisector, Angle Bisector, Angle Made by Lines, The Regular Hexagon, Addition and Subtraction of Lengths, Addition and Subtraction of Angles, Perpendicular Lines, Parallel Lines and Angles, Constructing Parallel Lines, Squares and Other Parallelograms, Division of a Line Segment into Several Parts, Thales' Theorem, Making Sense of Area, The Idea of a Tiling, Euclidean and Related Tilings, Islamic Tilings.
Author s : Rich Cochrane and Andrew McGettigan This is an introductory note in generalized geometry, with a special emphasis on Dirac geometry, as developed by Courant, Weinstein, and Severa, as well as generalized complex geometry, as introduced by Hitchin.
Dirac geometry is based on the idea of unifying the geometry of a Poisson structure with that of a closed 2-form, whereas generalized complex geometry unifies complex and symplectic geometry.
Author s : Prof.
Marco Gualtieri The intension of this note is to introduce the subject of graph theory to computer science students in a thorough way.
This note will cover all elementary concepts such as coloring, covering, hamiltonicity, planarity, connectivity and so on, it will also introduce the students to some advanced concepts.
Author s : NPTEL This note covers the read more topics: Immersion and embedding of 2-regular digraphs, Flows in bidirected graphs, Average degree of graph powers, Classical graph properties and graph parameters and their definability in SOL, Algebraic and model-theoretic methods in constraint satisfaction, Coloring random and planted graphs: thresholds, structure of solutions and algorithmic hardness.
Author s : Andrew Goodall This note covers the following topics: Notation for sets and functions, Basic group theory, The Symmetric Group, Group actions, Linear groups, Affine Groups, Projective Groups, Finite linear groups, Abelian Groups, Sylow Theorems and Applications, Solvable and nilpotent groups, p-groups, a second look, Presentations of Groups, Building new groups from old.
Author s : Mark Reeder The goal of this book is to present several central topics in geometric group theory, primarily related to the large www free book centre com geometry of infinite groups and spaces on which such groups act, and to illustrate them with fundamental theorems such as GromovÂ’s Theorem on groups of polynomial growth.
Topics covered includes: Geometry and Topology, Metric spaces, Differential geometry, Www free book centre com Space, Groups and their actions, Median spaces and spaces with measured walls, Finitely generated and finitely presented groups, Coarse geometry, Coarse topology, Geometric aspects of solvable groups, GromovÂ’s Theorem, Amenability and paradoxical decomposition, Proof of StallingsÂ’ Theorem using harmonic functions.
Author s : Cornelia Drutu and Michael Kapovich Https://fancomics.ru/book/us-b1-visa-slot-booking-in-hyderabad.html note explains the following topics: The Fourier Transform and Tempered Distributions, Interpolation of Operators, The Maximal Function and Calderon-Zygmund Decomposition, Singular Integrals, Riesz Transforms and Spherical Harmonics, The Littlewood-Paley g-function and Multipliers, Sobolev Spaces.
Author s : Chengchun Hao This textbook presents more than any professor can cover in class.
The first part of the note emphasizes Fourier series, since so many aspects of harmonic analysis arise already in that classical context.
Topics covered includes: Fourier series, Fourier coefficients, Fourier integrals,Fourier transforms, Hilbert and Riesz transforms, Fourier series and integrals, Band limited functions, Band limited functions, Periodization and Poisson summation.
Author s : Richard S.
Laugesen This note explains the following topics: Group Theory, SylowÂ’s Theorem, Field and Galois Theory, Elementary Factorization Theory, Dedekind Domains, Module Theory, Ring Structure Theory, Tensor Products.
Author s : David Surowski This book is intended as a sequel to our Elementary Algebra for Schools.
The first few chapters are devoted to a fuller discussion of Ratio, Proportion, Variation, and the Progressions, and then introduced theorems with examples.
Author s : Henry Sinclair Hall, Samuel Ratcliff Knight The purpose of this book, is to acquaint the student with mathematical language and mathematical life by means of a number of historically important mathematical vignettes.
This book will also serve to help the prospective school teacher to become inured in some of the important ideas of mathematics—both classical and modern.
Author s : Steven G.
Krantz This is the classic resource on the history of math providing a deeper understanding of the subject and how it has impacted our culture, all in one essential volume.
The subject-matter of this book is a historical summary of the development of mathematics, illustrated by the lives and discoveries of those to whom the progress of the science is mainly due.
It may serve as an introduction to more elaborate works on the subject, but primarily it is intended to give a short and popular account of those leading facts in the history of mathematics which many who are unwilling, or have not the time, to study it systematically may yet desire to know.
Author s : W.
Rouse Ball This course note introduces the reader to the language of categories and to present the basic notions of homological algebra, first from an elementary point of view, with the notion of derived functors, next with a more sophisticated approach, with the introduction of triangulated and derived categories.
Author s : Pierre Schapira Covered topics are: General manipulations of complexes, More on Koszul complexes, General manipulations applied to projective resolutions, Tor, Regular rings, review of Krull dimension, Regular sequences and Tor, Cohen–Macaulay rings and modules, Injective and divisible modules, Injective resolutions, A definition of Ext using injective resolutions, Duality and injective hulls, Gorenstein rings, Bass numbers.
Author s : Irena Swanson This graduate-level lecture note covers Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transform.
Author s : Prof.
Jeff Viaclovsky This note covers the following topics: Elementary Integrals, Substitution, Trigonometric integrals, Integration by parts, Trigonometric substitutions, Partial Fractions.
Author s : Mark MacLean and Andrew Rechnitzer This note covers the following topics: Vector Bundles and Bott Periodicity, K-theory Represented by Fredholm Operators, Representations of Compact Lie Groups, Equivariant K-theory.
Author s : Arun Debray This note will develop the K-theory of Banach algebras, the theory of extensions of C algebras, and the operator K-theory of Kasparov from scratch to its most advanced aspects.
Topics covered includes: Survey of Topological K-Theory, Operator K-Theory, Preliminaries, K-theory Of Crossed Products, Theory Of Extensions, KasparovÂ’s Kk-theory.
Author s : Bruce Blackadar This note focus on the so-called matrix Lie groups since this allows us to cover the most common examples of Lie groups in the most direct manner and with the minimum amount of background knowledge.
Topics covered includes: Matrix Lie groups, Topology of Lie groups, Maximal tori and centres, Lie algebras and the exponential map, Covering groups.
Author s : Alistair Savage This note covers the following topics: Fundamentals of Lie Groups, A Potpourri of Examples, Basic Structure Theorems, Complex Semisimple Lie algebras, Representation Theory, Symmetric Spaces.
Author s : Wolfgang Ziller This note covers the following topics: Linear Algebra, Matrix Algebra, Homogeneous Systems and Vector Subspaces, Basic Notions, Determinants and Eigenvalues, Diagonalization, The Exponential of a Matrix, Applications,Real Symmetric Matrices, Classification of Conics and Quadrics, Conics and the Method of Lagrange Multipliers, Normal Modes.
Author s : Leonard Evens This book is meant to provide an introduction to vectors, matrices, and least squares methods, basic topics in applied linear algebra.
Our goal is to give the beginning student, with little or no prior exposure to linear algebra, a good grounding in the basic ideas, as well as an appreciation for how they are used in many applications, including data fitting, machine learning and artificial intelligence, tomography, image processing, finance, and automatic control systems.
Topics covered includes: Vectors, Norm and distance, Clustering, Matrices, Linear equations, Matrix bonus ra free book of, Linear dynamical systems, Least squares, Multi-objective least squares, Constrained least squares.
Author s : Stephen Boyd and Lieven Vandenberghe The purpose of these notes is to introduce and study differentiable manifolds.
Topics covered includes: Manifolds in Euclidean space, Abstract manifolds, The tangent space, Topological properties of manifolds, Vector fields and Lie algebras, Tensors, Differential forms and Integration.
Author s : Henrik Schlichtkrull This book introduces the reader to the concept of smooth manifold through abstract definitions and, more importantly, through many we believe relevant examples.
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Author s : David Farmer, Albert Schueller, and David Guichard This note covers the following topics: Vectors and the geometry of space, Directional derivatives, gradients, tangent planes, introduction to integration, Integration over non-rectangular regions, Integration in polar coordinates, applications of multiple integrals, surface area, Triple integration, Spherical coordinates, The Fundamental Theorem of Calculus for line integrals, Green's Theorem, Divergence and curl, Surface integrals of scalar functions, Tangent planes, introduction to flux, Surface download book of ra of vector fields, The Flip the game book Theorem.
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Author s : Andrew Sutherland This note covers the following topics: Primes in Arithmetic Progressions, Infinite products, Partial summation and Dirichlet series, Dirichlet characters, L 1, x and class numbers, The distribution of the primes, The prime number theorem, The functional equation, The prime number theorem for Arithmetic Progressions, SiegelÂ’s Theorem, The Polya-Vinogradov Inequality, Sums of see more primes, The Large Sieve, BombieriÂ’s Theorem.
Author s : Andreas Strombergsson This note covers the following topics: Fourier Analysis, Least Squares, Normwise Convergence, The Discrete Fourier Transform, The Fast Fourier Transform, Taylor Series, Contour integration, Laurent series, Chebyshev series, Signal smoothing and root finding, Differentiation and integration, Spectral methods, Ultraspherical spectral methods, Functional analysis, Spectrum, Infinite-dimensional linear algebra, Linear partial differential equations, Laplace's equation, Riemann–Hilbert problems, Matrix-valued Riemann–Hilbert.
Author s : Sheehan Olver This lecture note covers the following topics: Methods for Solving Nonlinear Problems, Interpolation, Approximations, Numerical Differentiation and Numerical Integration.
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Author s : Niels Richard Hansen This note explains the following topics: Rational Numbers and Rational Cuts, Irrational numbers, Dedekind's Theorem, Cantor's Theory of Irrational Numbers, Equivalence of Dedekind and Cantor's Theory, Finite, Infinite, Countable and Uncountable Sets of Real Numbers, Types of Sets with Examples, Metric Space, Various properties of open set, closure of a set.
Author s : NPTEL This note explains the following topics: Logic and Methods of Proof, Sets and FunctionsReal Numbers and their Properties, Limits and Continuity, Riemann Integration, Introduction to Metric Spaces.
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Author s : Andreas Strombergsson This continue reading covers the following topics: Differentiable Manifolds, Differential Forms, Riemannian Manifolds, Curvature, Geometric Mechanics, Relativity.
Author s : Leonor Godinho and Jose Natario On the one hand this book intends to provide an introduction to module theory and the related part of ring theory.
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Author s : Robert Wisbauer This wikibook explains ring theory.
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Author s : wikibook Goal of these notes is to introduce both some of the basic tools in the foundations of mathematics and gesture toward some interesting philosophical problems that arise out of them.
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Author s : Toby Meadows This note covers the following topics: Logic, Elementary Set Theory, Generic Sets And Forcing, Infinite Combinatorics, Pcf, Continuum Cardinals.
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Author s : Brooke Quinlan This note provides an introduction to trigonometry, an introduction to vectors, and the operations on functions.
Topics covered includes: New functions from old functions, Trigonometry in circles and triangles, trigonometric functions, vectors.
Author s : Daniel Raies This note covers the following topics: Subsets of Euclidean space, vector fields, and continuity, Differentiation in higher dimensions, Tangent spaces, normals and extrema, Multiple Integrals, Line Integrals, GreenÂ’s Theorem in the Plane, DIV, GRAD, and CURL, Change of Variables, Parametrizations, Surface Integrals, The Theorems of Stokes and Gauss.
Author s : Dinakar Ramakrishnan This note explains the following topics: Vector Algebra and Index notation, Coordinate system, Integration, Integral Theorems, Permutations and Determinants.
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