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Exploring Monte Carlo Methods
Exploring Monte Carlo Methods

Exploring Monte Carlo Methods is a basic text that describes the numerical methods that have come to be known as "Monte Carlo." The book treats the subject generically through the first eight chapters and, thus, should be of use to anyone who wants to learn to use Monte Carlo. The next two chapters focus on applications in nuclear...

Linear Algebra and Geometry
Linear Algebra and Geometry

This book is the result of a series of lectures on linear algebra and the geometry of multidimensional spaces given in the 1950s through 1970s by Igor R. Shafarevich at the Faculty of Mechanics and Mathematics of Moscow State University.

Notes for some of these lectures were preserved in the faculty library, and these were used...
Differential Geometry: Bundles, Connections, Metrics and Curvature (Oxford Graduate Texts in Mathematics, Vol. 23)
Differential Geometry: Bundles, Connections, Metrics and Curvature (Oxford Graduate Texts in Mathematics, Vol. 23)

Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects.

Many of the tools used in differential topology are introduced and the
...

The Theory of Differential Equations: Classical & Qualitative
The Theory of Differential Equations: Classical & Qualitative

Differential equations first appeared in the late seventeenth century in the work of Isaac Newton, Gottfried Wilhelm Leibniz, and the Bernoulli brothers, Jakob and Johann. They occurred as a natural consequence of the efforts of these great scientists to apply the new ideas of the calculus to certain problems in mechanics, such as the paths of...

Algebraic Models in Geometry (Oxford Graduate Texts in Mathematics)
Algebraic Models in Geometry (Oxford Graduate Texts in Mathematics)
Rational homotopy is a very powerful tool for differential topology and geometry. This text aims to provide graduates and researchers with the tools necessary for the use of rational homotopy in geometry. Algebraic Models in Geometry has been written for topologists who are drawn to geometrical problems amenable to topological methods and also...
Handbook of Numerical Analysis : Special Volume: Foundations of Computational Mathematics
Handbook of Numerical Analysis : Special Volume: Foundations of Computational Mathematics
A long time ago, when younger and rasher mathematicians, we both momentarily harboured the ambition that one day, older and wiser, we might write a multivolume treatise titled “On the Mathematical Foundations of Numerical Analysis”. And then it dawned that such a creation already exists: it is called ‘a mathematics library’....
MATLAB Differential and Integral Calculus
MATLAB Differential and Integral Calculus

MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or...

Calculus Know-It-ALL: Beginner to Advanced, and Everything in Between
Calculus Know-It-ALL: Beginner to Advanced, and Everything in Between

If you want to improve your understanding of calculus, then this book is for you. It can supplement standard texts at the high-school senior, trade-school, and college undergraduate levels. It can also serve as a self-teaching or home-schooling supplement. Prerequisites include intermediate algebra, geometry, and trigonometry. It will help if...

Linear Algebra: A Geometric Approach
Linear Algebra: A Geometric Approach
One of the most enticing aspects of mathematics, we have found, is the interplay of ideas from seemingly disparate disciplines of the subject. Linear algebra provides a beautiful illustration of this, in that it is by nature both algebraic and geometric. ...
Probability Theory: A Comprehensive Course (Universitext)
Probability Theory: A Comprehensive Course (Universitext)

This second edition of the popular textbook contains a comprehensive course in modern probability theory. Overall, probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us in understanding magnetism, amorphous media, genetic diversity and the perils...

Calculus: A Complete Course
Calculus: A Complete Course

Adams Calculus is intended for the three semester calculus course. Classroom proven in North America and abroad, this classic text has been praised for its high level of mathematical integrity including complete and precise statements of theorems, use of geometric reasoning in applied problems, and the diverse range of applications across the...

Theory of Sobolev Multipliers: With Applications to Differential and Integral Operators (Grundlehren der mathematischen Wissenschaften)
Theory of Sobolev Multipliers: With Applications to Differential and Integral Operators (Grundlehren der mathematischen Wissenschaften)
The purpose of this book is to give a comprehensive exposition of the theory of pointwise multipliers acting in pairs of spaces of differentiable functions. The theory was essentially developed by the authors during the last thirty years and the present volume is mainly based on their results.

Part I is devoted to the theory of multipliers and...

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