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Bryan Flamig - Practical Algorithms in C++

danrop — Fri, 12 Sep 2008 04:26:00 GMT

Have you been looking for a C++ book that not only talks about some of the most popular algorithms of today, but also implements them? Then look no further. This book presents algorithms from a practical point of view, clearly explaining how the algorithms work, as well as fully implementing them in C++. Written to the intermediate C++ programmer, this book covers a wide range of subjects, from sorting and searching algorithms, to graph traversal algorithms, hashing algorithms, priority queues, finite state machines, and "algorithmic generators," a unique, object-oriented way of implementing algorithms.

Shapes and Geometries: Analysis, Differential Calculus, and Optimization

danrop — Fri, 12 Sep 2008 03:38:00 GMT

This book provides a self-contained presentation of the mathematical foundations, constructions, and tools necessary for studying problems where the modeling, optimization, or control variable is no longer a set of parameters or functions but the shape or the structure of a geometric object. Shapes and Geometries: Analysis, Differential Calculus, and Optimization presents the extensive, recently developed theoretical foundation to shape optimization in a form that can be used by the engineering community. It also clearly explains the state-of-the-art developments in a mathematical language that will attract mathematicians to open questions in this important field.

Bischof, Bücker, et al - Advances in Automatic Differentiation

danrop — Sat, 23 Aug 2008 19:59:00 GMT

This collection covers advances in automatic differentiation theory and practice. Computer scientists and mathematicians will learn about recent developments in automatic differentiation theory as well as mechanisms for the construction of robust and powerful automatic differentiation tools. Computational scientists and engineers will benefit from the discussion of various applications, which provide insight into effective strategies for using automatic differentiation for inverse problems and design optimization.

Jeff Edmonds - How To Think About Algorithms

danrop — Sat, 23 Aug 2008 19:42:00 GMT

There are many algorithm texts that provide lots of well-polished code and proofs of correctness. This book is not one of them. Instead, this book presents insights, notations, and analogies to help the novice describe and think about algorithms like an expert. By looking at both the big picture and easy step-by-step methods for developing algorithms, the author helps students avoid the common pitfalls. He stresses paradigms such as loop invariants and recursion to unify a huge range of algorithms into a few meta-algorithms. Part of the goal is to teach the students to think abstractly. Without getting bogged with formal proofs, the book fosters a deeper understanding of how and why each algorithm works. These insights are presented in a slow and clear manner accessible to second- or third-year students of computer science, preparing them to find their own innovative ways to solve problems.

D. Mumford, C. Series, D. Wright - Indra's Pearls: The Vision of Felix Klein

danrop — Wed, 04 Jun 2008 21:42:00 GMT

Felix Klein, a great geometer of the nineteenth century, rediscovered an idea from Hindu mythology in mathematics: the heaven of Indra in which the whole Universe was mirrored in each pearl in a net of pearls. Practically impossible to represent by hand, this idea barely existed outside the imagination, until the 1980s when the authors embarked on the first computer investigation of Klein's vision. In this extraordinary book they explore the path from some basic mathematical ideas to the simple algorithms that create delicate fractal filigrees, most appearing in print for the first time. Step-by-step instructions for writing computer programs allow beginners to generate the images.

Donal O' Shea - The Poincare Conjecture: In Search of the Shape of the Universe

danrop — Thu, 22 May 2008 02:51:00 GMT

Henri Poincaré was one of the greatest mathematicians of the late nineteenth and early twentieth century. He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincaré conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point.

Piergiorgio Odifreddi - The Mathematical Century: The 30 Greatest Problems of the Last 100 Year

danrop — Thu, 22 May 2008 02:35:00 GMT

Ben Longstaff, New Scientist
"The Mathematical Century gives us his selection of the subject's crowning achievements since 1900".

Alfred S. Posamentier - Math Charmers: Tantalizing Tidbits for the Mind

danrop — Thu, 22 May 2008 02:19:00 GMT

Choice, December 2003
"For a book that intends to convey the nature of pure mathematics, Posamentier's is far superior to many...highly recommended."

The Bookwatch, Midwest Book Review library newsletter, June 2004
"Designed as a combat to math phobias, this guide tells how to make math intriguing and fun."

B Dacorogna - Weak Continuity and Weak Lower Semicontinuity of Non-Linear Functions

danrop — Wed, 14 May 2008 21:17:00 GMT

Dorin Bucur, Giuseppe Buttazzo - Variational Methods in Shape Optimization Problems

danrop — Sun, 11 May 2008 02:43:00 GMT

The study of shape optimization problems encompasses a wide spectrum of academic research with numerous applications to the real world. In this work these problems are treated from both the classical and modern perspectives and target a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems.

G. Giorgi, A. Guerraggio, J. Thierfelder - Mathematics of Optimization: Smooth and Non-smooth Case

danrop — Sun, 11 May 2008 00:51:00 GMT

The book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces). It contains a lot of material, from basic tools of convex analysis to optimality conditions for smooth optimization problems, for non smooth optimization problems and for vector optimization problems.

Terry S. Yoo - Insight Into Images

danrop — Wed, 05 Dec 2007 21:25:00 GMT

An introduction to the theory of modern medical image processing, including the analysis of data from - X-ray computer tomography, - magnetic resonance imaging, - nuclear medicine, - and ultrasound.
Using an algorithmic approach, and providing the mathematical, statistical, or signal processing as needed for background, the authors describe the principles of all methods implemented in the Insight Toolkit (ITK), a freely available, open- source, object-oriented library. The emphasis is on providing intuitive descriptions of the principles and illustrative examples of results from the leading filtering, segmentation, and registration methods.

J. R. Munkres - Analysis on Manifolds

danrop — Tue, 27 Nov 2007 21:51:00 GMT

V G Ivancevic, T T Ivancevic - Applied Differential Geometry: A Modern Introduction

danrop — Thu, 22 Nov 2007 21:32:00 GMT

This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator - "Human Biodynamics Engine", a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools - this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.

Stephen Abbott - Understanding Analysis

danrop — Fri, 16 Nov 2007 08:24:00 GMT

This book outlines an elementary, one-semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination.

Richard J. Bagby - Introductory Analysis: A Deeper View of Calculus

danrop — Sat, 13 Oct 2007 23:14:00 GMT

Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.

A. Wouk - A Course of Applied Functional Analysis

danrop — Thu, 04 Oct 2007 07:09:00 GMT

Professor Wouk has based his book on postgraduate lectures given to a mixed audience of applied mathematicians and engineers. He applies approximate and iterative methods of functional analysis to two main problems: the optimization of functionals and the solution of functional equations. Both linear and non-linear cases are considered.
This book arrives at a time when many syllabuses in mathematics are being rewritten to include new areas of applications, and Professor Wouk's choice of material is apposite. Although some mathematicians may regret the absence of the spectral theorem, the text lends solid support to a number of topical subjects such as approximation theory, numerical analysis, optimisation, and control theory ... a very useful addition to the literature on functional analysis--clear, well-written, and interesting to read.

Marek Capinski, Peter E. Kopp - Measure, Integral and Probability

danrop — Tue, 02 Oct 2007 00:34:00 GMT

Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student. The ideas are developed at an easy pace in a form that is suitable for self-study, with an emphasis on clear explanations and concrete examples rather than abstract theory. For this second edition, the text has been thoroughly revised and expanded. New features include: · a substantial new chapter, featuring a constructive proof of the Radon-Nikodym theorem, an analysis of the structure of Lebesgue-Stieltjes measures, the Hahn-Jordan decomposition, and a brief introduction to martingales · key aspects of financial modelling, including the Black-Scholes formula, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework. In addition, further exercises and examples are provided to encourage the reader to become directly involved with the material.

V. Feoktistov - Differential Evolution: In Search of Solutions

danrop — Sun, 30 Sep 2007 08:11:00 GMT

The human being aspires to the best possible performance. Both individuals and enterprises are looking for optimal - in other words, the best possible - solutions for situations or problems they face. Most of these problems can be expressed in mathematical terms, and so the methods of optimization undoubtedly render a significant aid.

Andrew Pressley - Elementary Differential Geometry

danrop — Sat, 29 Sep 2007 00:49:00 GMT

Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques. It is a subject that contains some of the most beautiful and profound results in mathematics, yet many of them are accessible to higher level undergraduates.