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Iterative Methods for Optimization TOC I Optimization of Smooth Functions 1 Basic Concepts 1.1 The Problem 1.2 Notation 1.3 Necessary Conditions 1.4 Sufficient Conditions 1.5 Quadratic Objective Functions 1.5.1 Positive Definite Hessian 1.5.2 Indefinite Hessian 1.6 Examples 1.6.1 Discrete Optimal Control 1.6.2 Parameter Identification 1.6.3 Convex Quadratics 1.7 Exercises on Basic Concepts 2 Local Convergence [...]
Proofs and Concepts – The Fundamentals of Abstract Mathematics TOC Part I. Introduction to Logic and Proofs 1. What is Logic? 1A. Assertions and deductions 1B. Two ways that deductions can go wrong 1C. Deductive validity 1D. Other logical notions 1D.1. Truth-values 1D.2. Logical truth 1D.3. Logical equivalence 1E. Logic puzzles 2. Propositional Logic 2A. [...]
A Course in Commutative Algebra TOC 0 Ring Theory Background 0.1 Prime Avoidance 0.2 Jacobson Radicals, Local Rings, and Other Miscellaneous Results 0.3 Nakayama’s Lemma 1 Primary Decomposition and Associated Primes 1.1 Primary Submodules and Ideals 1.2 Primary Decomposition 1.3 Associated Primes 1.4 Associated Primes and Localization 1.5 The Support of a Module 1.6 Artinian [...]
Notes on Differential Equations TOC 1 Introduction to Ordinary Differential Equations 1.1 The Banker’s Equation 1.2 Slope Fields 2 A Gallery of Differential Equations 3 Introduction to Partial Differential Equations 3.1 A Conservation Law 3.2 Traveling Waves 4 The Logistic Population Model 5 Separable Equations 6 Separable Partial Differential Equations 7 Existence and Uniqueness and [...]
Introduction to Tensor Calculus and Continuum Mechanics TOC PART 1: INTRODUCTION TO TENSOR CALCULUS 1.1 INDEX NOTATION 1.2 TENSOR CONCEPTS AND TRANSFORMATIONS 1.3 SPECIAL TENSORS 1.4 DERIVATIVE OF A TENSOR 1.5 DIFFERENTIAL GEOMETRY AND RELATIVITY PART 2: INTRODUCTION TO CONTINUUM MECHANICS 2.1 TENSOR NOTATION FOR VECTOR QUANTITIES 2.2 DYNAMICS 2.3 BASIC EQUATIONS OF CONTINUUM MECHANICS [...]
Predicative Arithmetic TOC 1. The impredicativity of induction 2. Logical terminology 3. The axioms of arithmetic 4. Order 5. Induction by relativization 6. Interpretability 7. Bounded Induction 8. The bounded least number principle 9. The Euclidean algorithm 10. Encoding 11. Bounded separation and minimum 12. Sets and functions 13. Exponential functions 14. Exponentiation 15. [...]
Numerical Analysis for Engineering Douglas Wilhelm Harder, M.Math., LEL TOC 0 Introduction 0.1 References 0.2 Acknowledgments 0.3 Conventions 0.4 Resourses 1 Error Analysis 1.1 Precision and Accuracy 1.2 Absolute and Relative Error 1.3 Significant Digits 2 Numeric Representation 2.1 Decimal Numbers 2.2 Binary Numbers 2.3 Decimal Floating-point Numbers 2.4 Weaknesses with Floating-point Numbers 2.5 Double-precision [...]
Convergence of Stochastic Process TOC 1. Functionals on Stochastic Process 1.1. Stochastic Process as Random Functions 2. Uniform Convergence of Empirical Measures 2.1 Uniformity and Consistency 2.2 Direct Approximation 2.3 The Combinatorial Method 2.4 Classes of Sets with Polynomial Discrimination 2.5 Classes of Functions 2.6 Rates of Convergence 3. Convergence in Distribution in Euclidean Spaces [...]
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 [...]
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