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Elementary Number Theory : Primes, Congruences, and Secrets William Stein TOC 1 Prime Numbers 1.1 Prime Factorization 1.2 The Sequence of Prime Numbers 1.3 Exercises 2 The Ring of Integers Modulo n 2.1 Congruences Modulo n 2.2 The Chinese Remainder Theorem 2.3 Quickly Computing Inverses and Huge Powers 2.4 Primality Testing 2.5 The Structure of [...]
Abstract Algebra – Theory and Applications Thomas W. Judson Stephen F. Austin State University TOC 1 Preliminaries 1.1 A Short Note on Proofs 1.2 Sets and Equivalence Relations 2 The Integers 2.1 Mathematical Induction 2.2 The Division Algorithm 3 Groups 3.1 Integer Equivalence Classes and Symmetries 3.2 De nitions and Examples 3.3 Subgroups 4 Cyclic Groups [...]
Mathematical Card Tricks, Magic Math Card Trick pdf There are many free pdf resource about mathematical card tricks : [link] 1. Why you like mathematical card tricks : – Magic Spells and Telepathy Go Well Together (A Wonderful Effect) – Complementary Card Effects Always Make a Good Impression (Two Obvious) – You Like a Challenge [...]
Mathematical and Engineering Tools Softwares, Computer Algebra System Axiom Axiom is a general purpose Computer Algebra system. It is useful for doing mathematics by computer and for research and development of mathematical algorithms. It defines a strongly typed, mathematically correct type hierarchy. It has a programming language and a built-in compiler. Axiom has been in [...]
Applied Mathematical Programming Using Algebraic Systems TOC I: INTRODUCTION 1.1 Practical Problem Analysis 1.2 Mathematical Programming Approach 1.3 Mathematical Programming in Use 1.3.1 Generating Problem Insight 1.3.2 Numerical Mathematical Programming 1.3.3 Algorithmic Development 1.4 Book Plan II: LINEAR PROGRAMMING 2.1 The Basic LP Problem 2.2 Basic LP Example 2.3 Other Forms of the LP Problem [...]
Iterative Methods for Linear and Nonlinear Equations C. T. Kelley TOC 1. Basic Concepts and Stationary Iterative Methods 1.1 Review and notation 1.2 The Banach Lemma and approximate inverses 1.3 The spectral radius 1.4 Matrix splittings and classical stationaryiterativ e methods 1.5 Exercises on stationaryiterativ e methods 2. Conjugate Gradient Iteration 2.1 Krylov methods and [...]
First Course Linear Algebra CONTENTS Chapter SLE Systems of Linear Equations WILA What is Linear Algebra? LA \Linear” + \Algebra” AA An Application SSLE Solving Systems of Linear Equations SLE Systems of Linear Equations PSS Possibilities for Solution Sets ESEO Equivalent Systems and Equation Operations RREF Reduced Row-Echelon Form MVNSE Matrix and Vector Notation for [...]
Lecture Notes on Multivariable Calculus by Jerry Shurman TOC 1 Results from One-Variable Calculus 1.1 The Real Number System 1.2 Foundational and Basic Theorems 1.3 Taylor’s Theorem Part I Multivariable Differential Calculus 2 Euclidean Space 2.1 Algebra: Vectors 2.2 Geometry: Length and Angle 2.3 Analysis: Continuous Mappings 2.4 Topology: Compact Sets and Continuity 2.5 Review [...]
Algebraic Groups, Lie Groups, and their Arithmetic Subgroups J.S. Milne TOC I Basic Theory of Affine Groups 1 Introductory overview 2 Definitions 3 Examples 4 Some basic constructions 5 Affine groups and Hopf algebras 6 Affine groups and affine group schemes 7 Group theory: subgroups and quotient groups 8 Representations of affine groups 9 Group [...]
Modern Computer Arithmetic Richard P. Brent and Paul Zimmermann TOC 1 Integer arithmetic 1.1 Representation and notations 1.2 Addition and subtraction 1.3 Multiplication 1.4 Division 1.4.1 Naive division 1.4.2 Divisor preconditioning 1.4.3 Divide and conquer division 1.4.4 Newton’s method 1.4.5 Exact division 1.4.6 Only quotient or remainder wanted 1.4.7 Division by a single word 1.4.8 [...]
Introduction to the Theory of Infinite-Dimensional Dissipative Systems TOC 1. Basic Concepts of the Theory of Infinite-Dimensional Dynamical Systems 1.1 Notion of Denamical System 1.2 Trajectories and Invariant Sets 1.3 Definition of Attractor 1.4 Dissipativity and Asymptotic Compactness 1.5 Theorems on Existence of Global Attractor 1.6 On the Structure of Global Attractor 1.7 Stability Properties [...]
Numerical Methods for Large Eigenvalue Problems TOC 1 Background in Matrix Theory and Linear Algebra 1.1 Matrices 1.2 Square Matrices and Eigenvalues 1.3 Types of Matrices 1.3.1 Matrices with Special Srtuctures 1.3.2 Special Matrices 1.4 Vector Inner Products and Norms 1.5 Matrix Norms 1.6 Subspaces 1.7 Orthogonal Vectors and Subspaces 1.8 Canonical Forms of Matrices [...]
Hilbert Space Methods for Partial Differential Equations R. E. Showalter Contents I. Elements of Hilbert Space II. Distributions and Sobolev Spaces III. Boundary Value Problems IV. First Order Evolution Equations V. Implicit Evolution Equations VI. Second Order Evolution Equations VII. Optimization and Approximation Topics VIII. Suggested Readings & Bibliography Download : link
Natural Operations in Differential Geometry Ivan Kolar, Peter W. Michor, Jan Slovak TOC I. MANIFOLDS AND LIE GROUPS 1. Differentiable manifolds 2. Submersions and immersions 3. Vector fields and flows 4. Lie groups 5. Lie subgroups and homogeneous spaces II. DIFFERENTIAL FORMS 6. Vector bundles 7. Differential forms 8. Derivations on the algebra of differential [...]
Digraphs Theory, Algorithms and Applications TOC 1. Basic Terminology, Notation and Results 1.1 Sets, Subsets, Matrices and Vectors 1.2 Digraphs, Subdigraphs, Neighbours, Degrees 1.3 Isomorphism and Basic Operations on Digraphs 1.4 Walks, Trails, Paths, Cycles and Path-Cycle Subdigraphs 1.5 Strong and Unilateral Connectivity 1.6 Undirected Graphs, Biorientations and Orientations 1.7 Mixed Graphs and Hypergraphs 1.8 [...]
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