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.
Info about this book :
Title :Trends in commutative algebra
author(s) : Luchezar L. Avramov, Mark Green, Craig Huneke, Karen E. Smith, Bernd Sturmfels
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.
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.
Info about this book :
Title : The Square Root of 2- A Dialogue Concerning a Number and a Sequence
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.
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.
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.
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.
Infos about the book
Title : Transform methods for solving partial differential equations
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.
Infos about the book
Title : Digital signal and image processing using MATLAB
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
Infos about the book :
Title : Probability and Random Processes With Applications to Signal Processing and Communications
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.
Infos about the book
Title : Solutions manual to Contemporary Abstract Algebra - 8th Edition
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.
Infos about the book :
Title : Contemporary Abstract Algebra - 8 th Edition
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.
Infos about the book
Title : Problems in Real Analysis - Advanced Calculus on the Real Axis
author(s) : Teodora-Liliana Radulescu, Vicentiu D. Radulescu, Titu Andreescu
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.
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.
Infos about the book
Title : Mathematical Olympiads 1998-1999 - Problems and Solutions from Around the World
Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics
courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof
techniques, analyzing proofs, and writing proofs of their own.
Written in a clear, conversational style, this book provides a
solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields
such as number theory, abstract algebra, and group theory.
It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses
Infos about the book
Title : Mathematical Proofs: A Transition to Advanced Mathematics
author(s) : Gary Chartrand, Albert D. Polimeni, Ping Zhang
The transition from school mathematics to university mathematics is seldom straightforward.
Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory.
The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas.
This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups.
While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward.
This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.
Contains the exercises and their solutions for Lang's second edition of "Undergraduate Analysis." The variety
of exercises, which range from computational to more conceptual and which are of varying difficulty, cover several subjects.
This volume also serves as an independent source for those interested in learning analysis or linear algebra.
Infos about the book :
Title : Problems and solutions for undergraduate analysis
The present English edition is not a mere translation of the German original. Many new problems have been
added and there are also other changes, mostly minor. Yet all the alterations amount to less than ten percent
of the text. We intended to keep intact the general plan and the original flavor of the work. Thus we have not
introduced any essentially new subject matter, although the mathematical fashion has greatly changed since 1924.
We have restricted ourselves to supplementing the topics originally chosen. Some of our problems first published
in this work have given rise to extensive research. To include all such developments would have changed the character
of the work, and even an incomplete account, which would be unsatisfactory in itself, would have cost too much labor
and taken up too much space. We have to thank many readers who, since the publication of this work almost fifty years
ago, communicated to us various remarks on it, some of which have been incorporated into this edition. We have not
listed their names; we have forgotten the origin of some contributions, and an incomplete list would have been even
less desirable than no list. The first volume has been translated by Mrs. Dorothee Aeppli, the second volume by
Professor Claude Billigheimer. We wish to express our warmest thanks to both for the unselfish devotion
and scrupulous conscientiousness with which they attacked their far from easy task.
Title : Problems and Theorems in Analysis - Series · Integral Calculus · Theory of Functions
author(s) : George Polya, Gabor Szegö, D. Aeppli, C.E. Billigheimer
Qu'est-ce que la statistique? La statistique est une science recouvrant plusieurs
dimensions. On emploie d'ailleurs très fréquemment le pluriel «statistiques» pour
désigner cette discipline et témoigner ainsi de sa diversité. La statistique englobe la
recherche et la collecte de données, leur traitement et leur analyse, leur interprétation,
leur présentation sous la forme de tableaux et graphiques, .le calcul d' indicateurs permettant
de les caractériser et synthétiser ... Ces différents éléments renvoient à ce que
l'on a coutume de nommer la statistique descriptive, fondée sur l'observation de données
relatives à toutes sortes de phénomènes (économiques, financiers, historiques,
géographiques, biologiques, etc.).
Il arrive cependant fréquemment que les données représentatives du phénomène que
l'on souhaite étudier ne so ient pas parfaitement connues, c'est-à-dire pas toutes parfaitement
observables, au sens où elles ne fournissent qu' une information partielle
sur !'ensemble du phénomène que l'on analyse. Afin de pouvoir en réaliser une étude
statistique, il est alors nécessaire d' inférer des informations à partir des quelques éléments
dont on dispose. En d' autres termes, le statisticien devra effectuer des hypothèses
concernant les lois de probabilité auxquelles obéit le phénomène à analyser. La
statistique fait alors appel à la théorie des probabi lités et est qualifiée de stati stique
mathématique ou encore de statistique inférentielle.
Un bref retour sur l'histoire. Même si le terme de «stati stique» est généralement
considéré comme datant du xvme siècle1
, le recours à cette discipline remonte à un
passé bien plus éloigné. On fait en effet souvent référence à la collecte de données en
Chine en 2238 av. J. -C. concernant les productions agricoles, ou encore en Égypte en
1700 av. J.-C. en référence au cadastre et au cens. La collecte de données à des fins
descriptives est ainsi bien ancienne, mais ce n'est qu'au xvme siècle qu'est apparue
l'idée d' utiliser les statistiques à des fins prévisionnelles. Ce fut le cas en démographie
où les statistiques collectées lors des recensements de la population ont permis
l'élaboration de tables de mortalité en Suède et en France.
Du côté des mathématiciens, les recherches sur le calcul des probabilités se sont développées
dès le XVIIe siècle, au travers notamment des travaux de Fermat et Pascal.
Même si Condorcet et Laplace ont proposé quelques exemples d'application de la
théorie des probabilités, ce n'est qu ' au cours de la deuxième moitié du XIXe siècle,
grâce aux travaux de Quételet, que l' apport du calcul des probabilités à la statistique
fut réellement mis en évidence, conduisant ainsi aux prémisses de la statistique mathématique.
Cette dernière s' est ensuite largement développée à la fin du XIXe siècle
et dans la première moitié du XXe siècle.
Par la suite, grâce notamment aux progrès de l' informatique peu avant la deuxième
moitié du XXe siècle, de nouvelles méthodes d'analyse ont vu le jour, comme l'analyse
multidimensionnelle permettant d'étudier de façon simultanée plusieurs types de
données. La deuxième moitié du xxe siècle est aussi la période durant laquelle plusieurs
courants de pensée en statistiques' affrontent, notamment autour de la notion de
probabilité .
Les domaines d' application de la statistique sont multjples. Initialement employée en
démographie, elle est en effet utilisée dans toutes les sciences humaines et sociales
comme l'économje, la finance, la gestion, le marketing, l'assurance, l'histoire, la sociologie,
la psychologie, etc., mais aussi en médecine, en sciences de la terre et du vivant
(biologie, géologie ... ), météorologie, etc. Cet éventail des domaines illustre ainsi
toute la richesse de la statistique dont cet ouvrage vise à rendre compte.
Comment synthétiser et interpréter l’information contenue dans des
données économiques et financières ? Comment analyser et quantifier la
relation entre plusieurs séries ? Qu’est-ce qu’une loi de probabilité ?
Comment estimer un modèle et mettre en oeuvre des tests statistiques ?
Alliant
théorie et pratique, ce manuel met l’accent sur l’acquisition des
méthodes et des compétences indispensables à tout étudiant pour réussir
sa licence ou
son bachelor. Il propose :
des situations concrètes pour introduire les concepts ;
un
cours visuel et illustré par de nombreux exemples pour acquérir les
connaissances fondamentales en statistique et probabilités ;
des
conseils méthodologiques et des interviews pour traduire la théorie en
pratique et montrer comment la statistique est utilisée par les
professionnels ;
des éclairages sur les grands auteurs de la discipline ;
des exercices progressifs et variés (QCM, problèmes, sujets d’examen) pour s’évaluer et s’entraîner.
Title : Statistique et probabilités en économie-gestion
