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Mathematics for the Physical Science TOC Chapter 1 Vector Spaces and Matrices 1.1 Vector Spaces 1.2 Schwarz Inequality and Orthogonal Sets 1.3 Linear Dependence and Independence 1.4 Linear Operators on a Vector Space 1.5 Eigenvalues and Hermitian Operators 1.6 Unitary Operators 1.7 Projection Operators 1.8 Euclidean n-space and Matrices 1.9 Matrix Algebra 1.10 The Adjoint [...]
Real Analysis : Measure and Integration TOC 1 Preliminaries 1.1 Notation and terminology 1.2 Some undergraduate mathematics 2 Families of sets 2.1 Algebras and algebras 2.2 The monotone class theorem 3 Measures 3.1 De finitions and examples 4 Construction of measures 4.1 Outer measures 4.2 Lebesgue-Stieltjes measures 4.3 Examples and related results 4.4 Nonmeasurable sets 4.5 [...]
Algebraic Number Theory TOC 1 Preliminaries from Commutative Algebra Basic definitions Ideals in products of rings Noetherian rings Noetherian modules Local rings Rings of fractions The Chinese remainder theorem Review of tensor products 2 Rings of Integers First proof that the integral elements form a ring Dedekind’s proof that the integral elements form a ring [...]
First Course in Complex Analysis TOC 1 Complex Numbers 1.0 Introduction 1.1 Definitions and Algebraic Properties 1.2 From Algebra to Geometry and Back 1.3 Geometric Properties 1.4 Elementary Topology of the Plane 1.5 Theorems from Calculus 2 Differentiation 2.1 First Steps 2.2 Differentiability and Holomorphicity 2.3 Constant Functions 2.4 The Cauchy–Riemann Equations 3 Examples of [...]
Trigonometry by Michael Coral TOC 1 Right Triangle Trigonometry 1.1 Angles 1.2 Trigonometric Functions of an Acute Angle 1.3 Applications and Solving Right Triangles 1.4 Trigonometric Functions of Any Angle 1.5 Rotations and Reflections of Angles 2 General Triangles 2.1 The Law of Sines 2.2 The Law of Cosines 2.3 The Law of Tangents 2.4 [...]
Vector Calculus TOC 1 Vectors in Euclidean Space 1.1 Introduction 1.2 Vector Algebra 1.3 Dot Product 1.4 Cross Product 1.5 Lines and Planes 1.6 Surfaces 1.7 Curvilinear Coordinates 1.8 Vector-Valued Functions 1.9 Arc Length 2 Functions of Several Variables 2.1 Functions of Two or Three Variables 2.2 Partial Derivatives 2.3 Tangent Plane to a Surface [...]
The Elements of Statistical Learning pdf, 763 pages, 12 MB TOC 1 Introduction 2 Overview of Supervised Learning 2.1 Introduction 2.2 Variable Types and Terminology 2.3 Two Simple Approaches to Prediction:Least Squares and Nearest Neighbors 2.3.1 Linear Models and Least Squares 2.3.2 Nearest-Neighbor Methods 2.3.3 From Least Squares to Nearest Neighbors 2.4 Statistical Decision Theory [...]
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 [...]
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