Trends in commutative algebra

PREFACE :

In 2002, an introductory workshop was held at the Mathematical Sciences Research Institute in Berkeley to survey some of the many directions of the commutative algebra field. Six principal speakers each gave three lectures, accompanied by a help session, describing the interaction of commutative algebra with other areas of mathematics for a broad audience of graduate students and researchers. This book is based on those lectures, together with papers from contributing researchers. David Benson and Srikanth Iyengar present an introduction to the uses and concepts of commutative algebra in the cohomology of groups. Mark Haiman considers the commutative algebra of n points in the plane. Ezra Miller presents an introduction to the Hilbert scheme of points to complement Professor Haiman's paper. Further contributors include David Eisenbud and Jessica Sidman; Melvin Hochster; Graham Leuschke; Rob Lazarsfeld and Manuel Blickle; Bernard Teissier; and Ana Bravo.

 

 

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Title :Trends in commutative algebra   

author(s) : Luchezar L. Avramov, Mark Green, Craig Huneke, Karen E. Smith, Bernd Sturmfels

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Newtonian physics

PREFACE :

This book is for life-science majors who havent learned calculus or are learning it concurrently with physics.

 

 

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Title :    Newtonian physics

author(s) : Benjamin Crowell

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Convexity

PREFACE :

Convexity provides a wide-ranging introduction for final year undergraduates and graduate students. Convex sets and functions are studied in the Euclidean space IRn, thus allowing an exposition demanding only an elementary knowledge of analysis and linear algebra, and enabling concepts to bemotivated through simple geometric examples. The fundemental ideas of convexity are natural and appealing, and does not have to travel far along its path, before meeting significant, aesthetically pleasing results. It develops geometric intuition, and is a showcase for displaying interconnections amongst different parts of mathematics, inaddition to have ties with economics, science and engineering. Despite being an active research field, it abounds in unsolved problems having an instant intuitive appeal. One distinctive feature of the book is the diverse applications that it highlights: number theory, geometric extremum problems, combinatorial geometry, linear programming, game theory, polytopes, bodies of constant width, the gamma function, minimax approximation, and linear, classical and matrixinequalities. Several topics make their first appearance in a general introduction to convexity, while a few have not appeared outside research journals. The account has a self-contained treatment of volume, thus permitting a rigorous discussion of mixed volumes, is operimetry and Brunn-Minkowskitheory. Full solutions to most of the 241 exercises are provided and detailed suggestions for further reading are given.

 

 

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Title :   Convexity

author(s) : Roger Webster

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The Square Root of 2: A Dialogue Concerning a Number and a Sequence

PREFACE :

The square root of 2 is a fascinating number – if a little less famous than such mathematical stars as pi, the number e, the golden ratio, or the square root of –1. (Each of these has been honored by at least one recent book.) Here, in an imaginary dialogue between teacher and student, readers will learn why v2 is an important number in its own right, and how, in puzzling out its special qualities, mathematicians gained insights into the illusive nature of irrational numbers. Using no more than basic high school algebra and geometry, David Flannery manages to convey not just why v2 is fascinating and significant, but how the whole enterprise of mathematical thinking can be played out in a dialogue that is imaginative, intriguing, and engaging. Original and informative, The Square Root of 2 is a one-of-a-kind introduction to the pleasure and playful beauty of mathematical thinking.

 

 

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Title :   The Square Root of 2- A Dialogue Concerning a Number and a Sequence

author(s) : David Flannery

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Evolution algebras and their applications

PREFACE :

Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to  some further research topics.

 

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Title :   Evolution algebras and their applications

author(s) : Jianjun Paul Tian

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Matrix Analysis

PREFACE :

Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.

 

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Title :   Matrix Analysis

author(s) : Roger A. Horn, Charles R. Johnson

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Advanced Euclidean Geometry

PREFACE :

For many years, this elementary treatise on advanced Euclidean geometry has been the standard textbook in this area of classical mathematics; no other book has covered the subject quite as well. It explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. Several hundred theorems and corollaries are formulated and proved completely; numerous others remain unproved, to be used by students as exercises. The author makes liberal use of circular inversion, the theory of pole and polar, and many other modern and powerful geometrical tools throughout the book.

In particular, the method of "directed angles" offers not only a powerful method of proof but also furnishes the shortest and most elegant form of statement for several common theorems. This accessible text requires no more extensive preparation than high school geometry and trigonometry.

 

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Title :  Advanced Euclidean Geometry

author(s) : Roger A. Johnson

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Transform methods for solving partial differential equations

PREFACE :

Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations. While in some ways similar to separation of variables, transform methods can be effective for a wider class of problems. Even when the inverse of the transform cannot be found analytically, numeric and asymptotic techniques now exist for their inversion, and because the problem retains some of its analytic aspect, one can gain greater physical insight than typically obtained from a purely numerical approach.

Transform Methods for Solving Partial Differential Equations, Second Edition illustrates the use of Laplace, Fourier, and Hankel transforms to solve partial differential equations encountered in science and engineering. The author has expanded the second edition to provide a broader perspective on the applicability and use of transform methods and incorporated a number of significant refinements:

New in the Second Edition:
  Expanded scope that includes numerical methods and asymptotic techniques for inverting particularly complicated transforms

· Discussions throughout the book that compare and contrast transform methods with separation of variables, asymptotic methods, and numerical techniques

· Many added examples and exercises taken from a wide variety of scientific and engineering sources

· Nearly 300 illustrations--many added to the problem sections to help readers visualize the physical problems

  A revised format that makes the book easier to use as a reference: problems are classified according to type of region, type of coordinate system, and type of partial differential equation

·Updated references, now arranged by subject instead of listed all together

As reflected by the book's organization, content, and many examples, the author's focus remains firmly on applications. While the subject matter is classical, this book gives it a fresh, modern treatment that is exceptionally practical, eminently readable, and especially valuable to anyone solving problems in engineering and the applied sciences.

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Title : Transform methods for solving partial differential equations

author(s) :  Dean G. Duffy

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Digital signal and image processing using MATLAB

PREFACE :

This fully revised and updated second edition presents the most important theoretical aspects of Image and Signal Processing (ISP) for both deterministic and random signals. The theory is supported by exercises and computer simulations relating to real applications.

More than 200 programs and functions are provided in the MATLABÒ language, with useful comments and guidance, to enable numerical experiments to be carried out, thus allowing readers to develop a deeper understanding of both the theoretical and practical aspects of this subject.

This fully revised new edition updates :
- the introduction to MATLAB programs and functions as well as the Graphically displaying results for 2D displays
- Calibration fundamentals for Discrete Time Signals and Sampling in Deterministic signals
- image processing by modifying the contrast
- also added are examples and exercises.

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Title : Digital signal and image processing using MATLAB

author(s) :  Gérard Blanchet, Maurice Charbit

size : 5.6 Mb

file type : PDF

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Probability and Random Processes With Applications to Signal Processing and Communications

PREFACE :

Probability and Random Processes provides a clear presentation of foundational concepts with specific applications to signal processing and communications, clearly the two areas of most interest to students and instructors in this course.
It includes unique chapters on narrowband random processes and simulation techniques. It also includes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and other fields. The appendices provide a refresher in such areas as linear algebra, set theory, random variables, and more. Exceptional exposition and numerous worked out problems make the book extremely readable and accessible.
It is meant for practicing engineers as well as graduate students.
Exceptional exposition and numerous worked out problems make the book extremely readable and accessible The authors connect the applications discussed in class to the textbook The new edition contains more real world signal processing and communications applications Includes an entire chapter devoted to simulation techniques

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Title :  Probability and Random Processes With Applications to Signal Processing and Communications

author(s) :  Scott Miller, Donald Childers

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Solutions manual to Contemporary Abstract Algebra : 8th Edition

PREFACE :

Prepare for exams and succeed in your mathematics course with this comprehensive solutions manual! Featuring worked out-solutions to the problems in CONTEMPORARY ABSTRACT ALGEBRA, 8th Edition, this manual shows you how to approach and solve problems using the same step-by-step explanations found in your textbook examples.

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Title :  Solutions manual to Contemporary Abstract Algebra - 8th Edition

author(s) :  Joseph Gallian

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Contemporary Abstract Algebra : EIGHTH EDITION

PREFACE :

CONTEMPORARY ABSTRACT ALGEBRA, EIGHTH EDITION provides a solid introduction to the traditional topics in abstract algebra while conveying to students that it is a contemporary subject used daily by working mathematicians, computer scientists, physicists, and chemists. The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings giving the subject a current feel which makes the content interesting and relevant for students.

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Title : Contemporary Abstract Algebra - 8 th Edition

author(s) :  Joseph Gallian

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Problems in Real Analysis : Advanced Calculus on the Real Axis

PREFACE :

Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.

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Title : Problems in Real Analysis - Advanced Calculus on the Real Axis

author(s) :  Teodora-Liliana Radulescu, Vicentiu D. Radulescu, Titu Andreescu

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The book of numbers

PREFACE :

In THE BOOK OF NUMBERS, two famous mathematicians fascinated by beautiful and intriguing number patterns share their insights and discoveries with each other and with readers. John Conway is the showman, master of mathematical games and flamboyant presentations; Richard Guy is the encyclopedist, always on top of problems waiting to be solved. Together they show us why patterns and properties of numbers have captivated mathematicians and non-mathematicians alike for centuries. THE BOOK OF NUMBERS features Conway and Guy's favorite stories about all the kinds of numbers any of us is likely to encounter, and many others besides. "Our aim," the authors write, "is to bring to the inquisitive reader. . .an explanation of the many ways the word 'number' is used." They explore patterns that emerge in arithmetic, algebra, and geometry, describe these pattern' relevance both inside and outside mathematics, and introduce the strange worlds of complex, transcendental, and surreal numbers. This unique book brings together facts, pictures and stories about numbers in a way that no one but an extraordinarily talented pair of mathematician/writers could do.

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Title : The book of numbers

author(s) :  John H. Conway, Richard Guy

size : 2.5 Mb

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Mathematical Olympiads 1998-1999 : Problems and Solutions from Around the World

PREFACE :

This volume contains a large range of problems, with and without solutions, taken from 25 national and regional mathematics olympiads from around the world, and the problems are drawn from several years' contests. In many cases, more than one solution is given to a single problem in order to highlight different problem-solving strategies. The collection is intended as practice for students preparing for these competitions. Teachers and general readers looking for interesting problems will find also it very useful.

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Title : Mathematical Olympiads 1998-1999 - Problems and Solutions from Around the World

author(s) :  Titu Andreescu, Zuming Feng

size : 4 Mb

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