mathematical guide

http://ebooksclub.org/?module=showThread&id=20741

About This Guide

Why this Guide

This guide was created in an effort to classify the most important books in Mathematics here at ebooksclub.org. ebooksclub categories is so broad that it's almost inconvenient, but when you look for a certain topic in the many subtopics of mathematics, things gets little messy.


What is this Guide *NOT

This is not an exhaustive list of all Mathematics books at ebooksclub, it only highlights the famous, standard, helpful books around here. If you intend to search for a specific mathematics book, please refer to ebooksclub.org search facility.


Criticism
Please, your constructive criticism is all welcomed, but please this work is still requires much time and energy, for now I classify books for Top Level topics of MSC classification and it's of course still
Under Construction
You're welcome to suggest new books, correct classifications and all that.

About the classification
I use the AMS(Americal Mathematical Society)'s MSC 2000(Mathematical Subject Classification).
However I had to drift a little to include broad topics such as the so called College Algebra, College Geometry and all that.
The MSC classification is as the following



* 00: General material including elementary mathematics
* 01: History and biography
* 03: Mathematical logic and foundations
* 05: Combinatorics and graph theory
* 06: Order, lattices, ordered algebraic structures
* 08: General algebraic systems
* 11: Number theory
* 12: Field theory and polynomials
* 13: Commutative rings and algebras
* 14: Algebraic geometry
* 15: Linear and multilinear algebra; matrix theory
* 16: Associative rings and algebras
* 17: Nonassociative rings and algebras
* 18: Category theory, homological algebra
* 19: K-theory
* 20: Group theory and generalizations
* 22: Topological groups, Lie groups
* 26: Real functions and elementary calculus
* 28: Measure and integration
* 30: Functions of a complex variable
* 31: Potential theory
* 32: Several complex variables and analytic spaces
* 33: Special functions including trigonometric functions
* 34: Ordinary differential equations
* 35: Partial differential equations
* 37: Dynamical systems and ergodic theory
* 39: Difference and functional equations
* 40: Sequences, series, summability
* 41: Approximations and expansions
* 42: Fourier analysis
* 43: Abstract harmonic analysis
* 44: Integral transforms, operational calculus
* 45: Integral equations
* 46: Functional analysis
* 47: Operator theory
* 49: Calculus of variations and optimal control; optimization
* 51: Geometry, including classic Euclidean geometry
* 52: Convex and discrete geometry
* 53: Differential geometry
* 54: General topology
* 55: Algebraic topology
* 57: Manifolds and cell complexes
* 58: Global analysis, analysis on manifolds
* 60: Probability theory and stochastic processes
* 62: Statistics
* 65: Numerical analysis
* 68: Computer science
* 70: Mechanics of particles and systems
* 74: Mechanics of deformable solids
* 76: Fluid mechanics
* 78: Optics, electromagnetic theory
* 80: Classical thermodynamics, heat transfer
* 81: Quantum Theory
* 82: Statistical mechanics, structure of matter
* 83: Relativity and gravitational theory
* 85: Astronomy and astrophysics
* 86: Geophysics
* 90: Operations research, mathematical programming
* 91: Game theory, economics, social and behavioral sciences
* 92: Biology and other natural sciences
* 93: Systems theory; control
* 94: Information and communication, circuits
* 97: Mathematics education





* 00: General material including elementary mathematics
The Mathematics Subject Classification uses the classification 00 principally for non-subject-specific materials, such as conference proceedings, dictionaries, handbooks, and problem books. It also includes subject-specific items not typically noted in the Mathematical Reviews database by the AMS, such as elementary mathematics, recreational mathematics, and elementary applications of mathematics.
In general, such material is not included in this collection either. In many cases an occasion arises to treat an elementary question in a non-elementary way, and to so illustrate some branch of more advanced mathematics. When such an illustration is saved in this collection, it is classified according to the tool used (contrary to AMS guidelines for the use of the MSC!).

00A05: General mathematics
What Is Mathematics?: An Elementary Approach to Ideas and Methods
The Mathematics of Infinity: A Guide to Great Ideas (Good as a supplement)


Abel's Theorem in Problems and Solutions

Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability



The Four-Color Theorem : History, Topological Foundations, and Idea of Proof

Kepler's Conjecture: How Some of the Greatest Minds in History Helped Solve One of the Oldest Math Problems in the World

College Algebra

Personally I don't consider this category as Algebra per se, it even discusses topics outside Algebra entirely as part of Algebra (such as Graphs, Sequences and so...)

College Algebra, Blitzer, Third Edition

College Algebra Demystified

Inner Algebra

Algebra Demystified

Schaum's Easy Outline Intermediate Algebra

501 Algebra Questions

Just in Time Algebra

Algebra Success In 20 Minutes A Day

Pre-Algebra Demystified

Schaum's Outline of College Mathematics


Problem Solving


Discusses techniques either explicitly or through problems, lots of categories overlap here, from Combinatorics and Algebra to Geometry and The Calculus, even Evolutionary Algorithms.

Problem-Solving Strategies *****

Problem Solving Through Problems *****

Mathematical Problems and Proofs : Combinatorics, Number Theory, and Geometry *****

Polynomials, Barbeau *****

Solving Equations With Physical Understanding

Engineering Problem Solving : A Classical Perspective

The IMO Compendium: A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2004 *****

How to Solve It: Modern Heuristics

103 Trigonometry Problems: From the Training of the USA IMO Team*****

How to Solve Word Problems in Calculus

Master Math : Solving Word Problems


* 01: History and biography

Unknown Quantity: A Real And Imaginary History of Algebra, Derbyshire

A Mathematician's Apology, Hardy


* 03: Mathematical logic and foundations

Set theory


Elements of Set theory, Enderton

Introduction to Set Theory, Hrbacek

Lectures in Logic and Set Theory, Tourlakis

Set Theory : Boolean-Valued Models and Independence Proofs, Bell


Mathematical Logic


Mathematical Logic, Ebbinghaus *****

A Mathematical Introduction to Logic, Enderton *****

Modal Logic, Chagrov

Language, Proof, and Logic

Incompleteness: The Proof and Paradox of Kurt Godel

Godel's Proof *****

Proof Writing

Usually discusses Set Theory, First order logic, and Number systems beside of course proof writing *techniques*.

Bridge to Abstract Mathematics

Math Proofs Demystified

Basic Concepts of Mathematics (No ISBN, Go to trillia.com)

Proofs from the Book
Note: This book isn't really about proof writing, but rather shows beautiful proofs in mathematics, should be used for inspiration.

* 05: Combinatorics and graph theory

TextBooks


Discrete Mathematics and its Applications, Rosen

Discrete and Combinatorial Mathematics: An Applied Introduction, Grimaldi

Discrete Mathematics, Lovasz

A First Course in Discrete Mathematics, Anderson

Discrete Mathematics for New Technology

Schaum's Outline of Discrete Mathematics

Handbook of Discrete and Combinatorial Mathematics

Concrete Mathematics, Knuth


Combinatorics


Combinatorics, Merris

Combinatorics : Topics, Techniques, Algorithms

Enumerative Combinatorics, Stanley

Handbook of Combinatorics, Graham

Combinatorial Species and Tree-like Structures


Graph theory


Fractional Graph Theory: A Rational Approach to the Theory of Graphs

Graph Theory With Applications

Algebraic Graph Theory

Graph Theory, Diestel

Eigenspaces of Graphs

Graph Algorithms and Applications

Modern Graph Theory, Bollobas


* 06: Order, lattices, ordered algebraic structures


* 08: General algebraic systems


* 11: Number theory



An Introduction to the Theory of Numbers, Hardy

Problems in Algebraic Number Theory

Analytic Number Theory, Newman

Transcendental Number Theory

Introduction to Analytic Number Theory, Apostol *****

Advanced Number Theory, Cohn

Elementary Methods in Number Theory, Nathanson

Analytic Number Theory: An Introductory Course

A Course in Number Theory and Cryptography

Number Theory, Shafarevich

The Book of Numbers, John Horton Conway *****

On Numbers and Games, John Horton Conway *****

Popular Level

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics *****



* 12: Field theory and polynomials

Abstract Algebra(Undergraduate level):


A Survey of Modern Algebra, MacLange

Algebra I, Basic Notions of Algebra, Shafarevich


Abstract Algebra (3rd Edition), Dummit and Foote

Applications of Abstract Algebra with MAPLE, Klima

Modern Algebra with Applications, Gilbert

Lectures in Abstract Algebra: Basic Concepts, Jacobson

Schaum's Outline of Abstract Algebra


Abstract Algebra Textbooks(Graduate level)


Algebra, Lang

Advanced Modern Algebra, Rotman

Algebra: A Graduate Course, Isaacs

* 13: Commutative rings and algebras

Introduction to Commutative Algebra, Atiyah

Undergraduate Commutative Algebra, Reid

Computational Commutative Algebra 1

Commutative Algebra : with a View Toward Algebraic Geometry

Computational Aspects of Commutative Algebra: From a Special Issue of the Journal of Symbolic Computation 1989

Grobner Bases: A Computational Approach to Commutative Algebra

Combinatorial Commutative Algebra

Matrices over Commutative Rings

Commutative Algebra, Matsumura

* 14: Algebraic geometry



Undergraduate Algebraic Geometry, Reid

Algebraic Geometry : A First Course, Harris

Sheaves in Geometry and Logic : A First Introduction to Topos Theory

The Geometry of Schemes, Harris

Commutative Algebra : with a View Toward Algebraic Geometry

Algebraic Geometry, Bump

Algebraic Geometry 1: From Algebraic Varieties to Schemes

Algebraic Geometry, Hartshorne

Principles of Algebraic Geometry, Griffiths and Harris

Basic Algebraic Geometry 1: Varieties in Projective Space, Shafarevich

Basic Algebraic Geometry 2: Schemes and Complex Manifolds, Shafarevich

* 15: Linear and multilinear algebra; matrix theory

Linear Algebra (Abstract)


Finite Dimensional Vector Spaces

Linear Algebra, Hoffman

Linear Algebra Done right, Axler

Lectures in Abstract Algebra Vol 2 Linear Algebra, Jacobson

Linear Algebra : Gateway to Mathematics, Messer



Linear Algebra (Less Abstract, More Applications)


Linear Algebra and It's Applications, Strang

Applied Linear Algebra and Matrix Analysis, Shores

Schaum's Outline of Theory and Problems of Linear Algebra, Lipschutz

Matrix Analysis and Applied Linear Algebra, Meyer

Applied Numerical Algebra, Demmel

Applied Linear Algebra, Usmani

* 16: Associative rings and algebras


* 17: Nonassociative rings and algebras


* 18: Category theory, homological algebra



Categories for the Working Mathematician, MacLane

Abelian Categories: An Introduction to the Theory of Functors

Categories and functors, Pareigis

Methods of Homological Algebra

A Course in Homological Algebra

An Elementary Approach to Homological Algebra

* 19: K-theory


* 20: Group theory and generalizations


Linear Groups with an Exposition of Galois Field Theory

Group Rings, Crossed Products, and Galois Theory

The Classification of the Finite Simple Groups

The theory of groups, Kurosh

Problems in Group Theory, Dixon

* 22: Topological groups, Lie groups



Lie Groups, Lie Algebras, and Representations, Hall

Matrix Groups, Baker

Lectures on Lie Groups, Hsiang

* 26: Real functions and elementary calculus

Elementary Calculus


Topics in Calculus include Continuity, Differentiation, Integration, Sequences, Series. The Calculus is developed using basic results of Geometry and Algebra without usage of point set topology. Limits will be studies/used extensively (Formal epsilon delta proofs not usually discussed in detail). Basic results of Calculus will be studies on Algebraic functions (Polynomials, Rational, Power) and Elementary transcendental functions (Logariths, Exponentials, Trigonometrics). Applications to the physical sciences to illustrate the power of the Calculus. Some courses will also Analytic Geometry along the way. Multi Variable Calculus will mostly use 3D Geometry to develop intuition, further generalization to higher dimensions most likely will be studied in a later course (usually Global Analysis). Some Elementary Numerical methods will be discussed without further study of error analysis.

Calculus, Vol. 1. Apostol *****

Calculus, Vol. 2. Apostol *****

Foundations of Differential Calculus, Euler

A Course of Pure Mathematics, Hardy *****

Foundations of Analysis, Landau ****

Inside Calculus ****

Calculus, Stewart

Calculus : Early Transcendentals, Stewart ***

Calculus, Gilbert Strang (MIT)

Schaum's Outline of Beginning Calculus

Calculus unlimited

Elementary Calculus: An Infinitesimal Approach

Advanced Calculus, Loomis

On the Shoulders of Giants: A Course in Single Variable Calculus

Calculus (Cliffs Quick Review)

Calculus for the Utterly Confused

Calculus: Single Variable, Smith and Minton

Schaum's Outline of Theory and Problems of Advanced Calculus

Advanced Calculus, Kaplan

Advanced Calculus with Applications in Statistics

Calculus of Vector Functions

Calculus Demystified

Schaum's Outline of Advanced Calculus



Introductory Mathematical Analysis:

Studies The Calculus in a rigorous, formal and generalized manner. (not too generalization however)

Basic Elements of Real Analysis, Protter ***

Real Mathematical Analysis, Pugh *****

Principles of Mathematical Analysis, Rudin *****

Mathematical Analysis, Apostol *****


* 28: Measure and integration


The Lebesgue-Stieltjes Integral : A Practical Introduction

The Elements of Integration and Lebesgue Measure *****

Real and Complex Analysis, Rudin *****

Real Analysis, Royden *****

Real Analysis, Lang ***

Measure theory and fine properties of functions, Evans *****

Measure, Integral and Probability, Capinski ****

Measure and Integral, Wheeden and Zygmund *****

Schaum's Outline of Theory and Problems of Real Variables; Lebesgue Measure and Integration With Applications to Fourier Series **


* 30: Functions of a complex variable

Elementary Textbooks:


Complex Analysis (Theory of analytic functions) at a level suitable for Undergraduate study where real analysis rerequisites.

A First Course in Complex Analysis with Applications, Zill

Calculus with Complex Numbers, Reade


Standard Textbooks:


Complex Analysis, Ahlfors *****

A Course of Modern Analysis, Whittaker and Watson ***** (A Classic for Transcendenting functions)

Complex Analysis through examplex and Exercises, Pap

Functions of One Complex Variable, Conway

Complex Variables and the Laplace Transform for Engineers, LePage

* 31: Potential theory


* 32: Several complex variables and analytic spaces

Several Complex Variables, Schneider

* 33: Special functions including trigonometric functions



Special Functions, Andrews

Orthogonal Polynomials and Special Functions, Askey

On a Class of Incomplete Gamma Functions with Applications

Chebyshev Polynomials, Mason


* 34: Ordinary differential equations

Introductory Differential Equations


Elementary Differential Equations and Boundary Value Problems, Boyce and DiPrima

Schaum's Easy Outline Differential Equations

Handbook of Differential Equations, Zwillinger

Schaum's Outline of Differential Equations

Differential Equations Demystified



Ordinary Differential Equations, Arnold

Differential Equations, Dynamical Systems, and Linear Algebra, Hirsch

Ordinary Differential Equations, Hartman




Numerical Solutions for Differential Equations


Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple, and MATLAB

Scientific Computing and Differential Equations : An Introduction to Numerical Methods

Numerical Methods for Ordinary Differential Equations

Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations

Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods

Numerical Methods for Elliptic and Parabolic Partial Differential Equations

Numerical Methods for Partial Differential Equations

Boundary and Finite Elements: Theory and Problems


* 35: Partial differential equations



An Introduction to Partial Differential Equations, Renardy

Introduction to Partial Differential Equations. : A Computational Approach

Lectures on Partial Differential Equations, V. I. Arnold

Partial Differential Equations, Evans

A First Course in Partial Differential Equations With Complex Variables and Transform Methods, Weinberger

Hilbert Space Methods for Partial Differential Equations

Nonlinear Partial Differential Equations for Scientists and Engineers

Partial Differential Equations and the Finite Element Method

Handbook of Linear Partial Differential Equations for Engineers and Scientists

Handbook of Nonlinear Partial Differential Equations

Partial Differential Equations, Volumes I, II, III by Taylor

Elementary Applied Partial Differential Equations: With Fourier Series and Boundary Value Problems

* 37: Dynamical systems and ergodic theory



Invitation to Dynamical Systems

Introduction to Dynamical Systems

Lectures on Chaotic Dynamical Systems

An Introduction to Chaotic Dynamical Systems *****

Dynamical Systems[img=http://www.ebooksclub.org/images/emoticons/icon_biggrin.gif a=biggrin][/img]ifferential Equations, Maps and Chaotic Behavior

Dynamical Systems, Birkhoff

Dynamical Systems and Ergodic Theory

Mathematics of dynamical systems

Chaos in Dynamical Systems

Introduction to Applied Nonlinear Dynamical Systems and Chaos

Fractals


Fractal Geometry : Mathematical Foundations and Applications, Falconer

Techniques in Fractal Geometry, Falconer

Fractal Geometry and Stochastics

* 39: Difference and functional equations


Difference Equations and Inequalities: Theory, Methods, and Applications

Lectures on Functional Equations and Their Applications

Difference Equations with Applications to Queues

Functional equations in a single variable, Kuczma

* 40: Sequences, series, summability


* 41: Approximations and expansions


Numerical Analysis 2000 : Approximation Theory

* 42: Fourier analysis



Fourier analysis studies approximations and decompositions of functions using trigonometric polynomials. Of incalculable value in many applications of analysis, this field has grown to include many specific and powerful results, including convergence criteria, estimates and inequalities, and existence and uniqueness results. Extensions include the theory of singular integrals, Fourier transforms, and the study of the appropriate function spaces. This heading also includes approximations by other orthogonal families of functions, including orthogonal polynomials and wavelets.

Fourier Analysis and Its Applications

Inside the FFT Black Box

Understanding the FFT

Understanding FFT Applications

Fourier Series, Transforms and Boundary Value Problems

Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness

Fourier Analysis of Time Series : An Introduction

A Student's Guide to Fourier Transforms

Wavelets


An Introduction to Wavelets Through Linear Algebra

First Course in Wavelets with Fourier Analysis

Wavelets, Approximation, and Statistical Applications

A First Course on Wavelets

Ten Lectures on Wavelets, Daubechies

Abstract Harmonic Analysis of Continuous Wavelet Transforms

* 43: Abstract harmonic analysis


Harmonic Function Theory, Axler

An Introduction to Harmonic Analysis, Katznelson

An Introduction to Harmonic Analysis on Semisimple Lie Groups

Harmonic Analysis, Stein

* 44: Integral transforms, operational calculus

Integral Methods in Science and Engineering

* 45: Integral equations



Handbook of Integral Equations

Integral Equations: A Practical Treatment, from Spectral Theory to Applications

Integral Equations, Hochstadt

Volterra and Integral Equations of Vector Functions

Numerical Analysis 2000 : Ordinary Differential Equations and Integral Equations

* 46: Functional analysis
Here we mean the study of vector spaces of functions. This can include the abstract study of topological vector spaces as well as the study of particular spaces of interest, including attention to their bases (e.g. Fourier Analysis), and linear maps on them (e.g. Integral Transforms).

Functional Analysis Textbooks:


Functional analysis also called Modern Analysis is the study of infinite dimensional vector spaces (mainly Topological vector spaces), and mapping between these spaces (operators), transformations of these operators (e.g differential operators or self-adjoint operator), some approaches will associate algebraic structures (e.g ring structures such as Banach algebras and C-* algebras), an important application is Quantum mechanics.


Introductory Real Analysis, Kolmogorov ***

Functional analysis, Yoshida ***

Functional Analysis, Rudin *****

Functional Analysis in Modern Applied Mathematics, Curtain ***

Foundations of Modern Analysis, Friedman

Beginning Functional Analysis, Saxe *

Functional Analysis: An Introduction, Eidelman ****

Functional Analysis and Semigroups, Hille

A Course in Modern Analysis and its Applications, Cohen

Geometric Aspects of Functional Analysis, Milman



Applications

Physical questions (Especially quantum physics) helped in the development of Functional analysis, Modern Mathematical physics makes heavy use of functional analysis.

Methods of Modern Mathematical Physics, Functional Analysis, Reed *****

Functional Analysis in Mechanics, Lebedev

Operator Methods in Quantum Mechanics

Operator Algebras and Quantum Statistical Mechanics

Infinite Dimensional Groups and Algebras in Quantum Physics

Foundations of Quantum Mechanics *****


Infinite dimensional vector spaces

Topological vector spaces in general, Hilbert and Banach Spaces.

Topological Vector Spaces I, Koethe *****

Introduction to Hilbert Spaces with Applications *****


* 47: Operator theory

Theory of Operator Algebras, Takesaki

Theory of Linear Operators in Hilbert Space *****

Spectral Theory of Self-Adjoint Operators in Hilbert Space *****

Fundamentals of the Theory of Operator Algebras

Spectral Theory and Differential Operators

Lectures on Entire Operators, M.G. Kreins

An Invitation to C*-Algebras, Arveson

Hilbert C*-Modules : A Toolkit for Operator Algebraists

A Short Course on Spectral Theory *****

Spectral Theory and Nonlinear Functional Analysis

* 49: Calculus of variations and optimal control; optimization



Introduction To The Calculus Of Variations, Dacorogna

Calculus of Variations, Weinstock



Introduction to Optimization, Pedregal

Optimization, Lange

An Introduction to Optimization, Chong

Introduction to Linear Optimization

Convexity and Optimization in Rn
* 51: Geometry, including classic Euclidean geometry

51M: Real and complex geometry (also College Geometry)


Geometry Demystified

Fundamentals of College Geometry, Hemmerling

51N: Analytic and descriptive geometry


Exploring Analytical Geometry with Mathematica

Geometry Surveys


Introduction to Geometry, Coxeter *****

Geometry Revisited, Coxeter

Glimpses of Algebra and Geometry

Flavors of Geometry

Non-Euclidean Geometry, Coxeter

Geometry, Audin


* 52: Convex and discrete geometry


Handbook of Discrete and Computational Geometry


* 53: Differential geometry
Classical Differential Geometry:


Differential Geometry and Its Applications

Elements of Differential Geometry, Millman

Classical Differential Geometry of Curves and Surfaces


Modern Differential Geometry:


An Introduction to Differentiable Manifolds and Riemannian Geometry, Boothby

Natural Operations in Differential Geometry

Notes on differential geometry

A Panoramic View of Riemannian Geometry

The Geometry of Four-Manifolds

Gauge Theory and the Topology of Four-Manifolds

Index Theory, Coarse Geometry and Topology of Manifolds

Geometry, Topology and Physics

Curvature and Homology, Goldberg

Riemannian Geometry, do Carmo

Geometry and Billiards

Modern Differential Geometry for Physicists, Isham

Riemannian Geometry: A Beginner's Guide



* 54: General topology



Topology, Munkres *****

Elementary Concepts of Topology

Counterexamples in Topology *****

Lecture Notes on Elementary Topology and Geometry

Schaum's Outline of General Topology

* 55: Algebraic topology



A Concise Course in Algebraic Topology, May

Lectures on Algebraic Topology

Algebraic Topology: An Intuitive Approach, Sato

Algebraic Topology, Hatcher

Algebraic Topology from a Homotopical Viewpoint

Homotopical Algebra, Quillen

Algebraic Topology, Lefschetz

Simplicial Homotopy Theory


* 57: Manifolds and cell complexes

57M: Low-dimensional topology, including Knot theory


The Geometry and Physics of Knots

Knots and Surfaces, Gilbert

57N: Topological manifolds
Introduction to Topological Manifolds *****

57R: Differential topology
Differential Topology, Guillemin

Differential Topology, Hirsch

* 58: Global analysis, analysis on manifolds



Calculus on Manifolds, Spivak

Analysis on Manifolds, Munkres

Manifolds, Tensor Analysis, and Applications, Abraham

An Introduction to Differentiable Manifolds and Riemannian Geometry, Boothby

Introduction to Differentiable Manifolds, Lang

Foundations of differentiable Manifolds and Lie Groups, Warner

Differential Forms

Differential Forms : A Complement to Vector Calculus, Weintraub

Advanced Calculus : A Differential Forms Approach, Edwards

Differential Forms with Applications to the Physical Sciences


* 60: Probability theory and stochastic processes

60A: Foundations of probability theory


An Introduction to Probability Theory and Its Applications, Volume 1, Feller

Probability, Random Variables and Stochastic Processes, Papoulis

Schaum's Outline of Probability, Random Variables, and Random Processes

Introduction to Probability, Grinstead

Foundations of Modern Probability, Kallenberg

Probability Theory I and II, Loeve

Schaum's Outline of Theory and Problems of Probability and Statistics

Counterexamples in Probability

Probability : Theory and Examples

Probability and Statistical Inference

A Course in Probability Theory, Kai Lai Chung

Probability Theory : The Logic of Science

Probability: A Graduate Course

Basic Principles and Applications of Probability Theory, Skorokhod

Applied Probability, Lange

60Hxx Stochastic analysis


Stochastic Differential Equations, Oksendal

Stochastic Differential Equations and Applications

Introduction to Stochastic Integration

Stochastic Integration and Differential Equations, Protter

* 62: Statistics

* 65: Numerical analysis



Theoretical Numerical Analysis, A Functional Analysis Framework, Atkinson

Introduction to Numerical Analysis, Stoer

Numerical Analysis: The Mathematics of Scientific Computing

Elementary Numerical Analysis: An Algorithmic Approach

Numerical Analysis Using MATLAB and Spreadsheets

Applied Numerical Methods Using MATLAB

Numerical Methods Using MATLAB, Mathews

* 68: Computer science

* 70: Mechanics of particles and systems

* 74: Mechanics of deformable solids

* 76: Fluid mechanics

* 78: Optics, electromagnetic theory

* 80: Classical thermodynamics, heat transfer

* 81: Quantum Theory

* 82: Statistical mechanics, structure of matter

* 83: Relativity and gravitational theory

* 85: Astronomy and astrophysics

* 86: Geophysics

* 90: Operations research, mathematical programming

* 91: Game theory, economics, social and behavioral sciences

* 92: Biology and other natural sciences

* 93: Systems theory; control

* 94: Information and communication, circuits

* 97: Mathematics education