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مجموعة كتب روعة في الرياضيات

William E. Boyce, "Elementary Differential Equations and Boundary Value Problems, 9th Edition"
W,..ey | ISBN : 0470383348 | 2008 | 818 pages | PDF | 5,5 MB

Written from the perspective of the applied mathematician, the latest edition of this bestselling book focuses on the theory and practical applications of Differential Equations to engineering and the sciences. Emphasis is placed on the methods of solution, analysis, and approximation. Use of technology, illustrations, and problem sets help readers develop an intuitive understanding of the material. Historical footnotes trace the development of the discipline and identify outstanding individual contributions. This book builds the foundation for anyone who needs to learn differential equations and then progress to more advanced studies.

A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics) by A. Iserles
Publisher: Cambridge University Press (January 26, 1996) | ISBN: 0521553768 | Pages: 396 | DJVU | 3.83 MB

This book presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance among theoretical, algorithmic and applied aspects of the subject. In detail, topics covered include numerical solution of
ordinary differential equations by multistep and Runge-Kutta methods

Barbara D. MacCluer, "Elementary Functional Analysis"
Sp ger | 2009 | ISBN: 0387855289 | 208 pages | PDF | 5,6 MB

This nicely written manuscript takes a gentler approach than other functional analysis graduate texts, and includes an improved approach along with a better choice of topics. The concise treatment makes this ideal for a one-semester course. The exercises in this manuscript are numerous and of a very high quality. Interesting historical tidbits are scattered throughout the text, many of which will be new to most readers. The main prerequisites are

William Johnston, Alex McAllister, "A Transition to Advanced Mathematics: A Survey Course"
O..rd Un-ty Press | 2009 | ISBN: 0195310764 | 768 pages | PDF | 5,9 MB

A Transition to Advanced Mathematics: A Survey Course promotes the goals of a ``bridge'' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-level mathematics courses (where they will have to prove theorems and grapple with mathematical abstractions). The text simultaneously promotes the goals of a ``survey'' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics, including Logic, Abstract Algebra, Number Theory, Real Analysis, Statistics, Graph Theory, and Complex Analysis.
The main objective is "to bring about a deep change in the mathematical character of students -- how they think and their fundamental perspectives on the world of mathematics." This text promotes three major mathematical traits in a meaningful, transformative way: to develop an ability to communicate with precise language, to use mathematically sound reasoning, and to ask probing questions about mathematics. In short, we hope that working through A Transition to Advanced Mathematics encourages students to become mathematicians in the fullest sense of the word.
A Transition to Advanced Mathematics has a number of distinctive features that enable this transformational experience. Embedded Questions and Reading Questions illustrate and explain fundamental concepts, allowing students to test their understanding of ideas independent of the exercise sets. The text has extensive, diverse Exercises Sets; with an average of 70 exercises at the end of section, as well as almost 3,000 distinct exercises. In addition, every chapter includes a section that explores an application of the theoretical ideas being studied. We have also interwoven embedded

Michael D. Potter, "Sets: An Introduction"
Cla ndon | 1991 | ISBN: 0198533993, 0198533888 | 256 pages | Djvu | 5,9 MB

This book provides a first course in set theory suitable for final year undergraduates in mathematics. The book develops the subject from first principles and presupposes little more than an elementary grounding in logic. Throughout much attention is paid to the subject's historical and philosophical development. The book differs from most books on set theory in that it aims in its approach to introduce the axioms of set theory in a natural way and to show how they come to take the form they do. The text covers all the basic tools of set theory - the natural numbers, cardinals, ordinals, and the axiom of choice - in some detail. It also provides an account of the representation theory of lattices and how this is closely connected with various forms of the axiom of choice.

Probability and Statistics (4th Edition) by Morris H. DeGroot
Addison Wesley | ISBN : 0321500466 | 2011 | 911 pages | PDF | 6MB

The revision of this well-respected text presents a balanced approach of the classical and Bayesian methods and now includes a chapter on simulation (including Markov chain Monte Carlo and the Bootstrap), coverage of residual analysis in linear models, and many examples using real data. Calculus is assumed as a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus.

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Christopher Clapham, James Nicholson, "The Concise Oxford Dictionary of Mathematics"
Publisher: Oxford University Press | ISBN: 0199235945 | edition 2009 | PDF | 528 pages | 6.2 mb

Authoritative and reliable, this superb reference contains more than 3,000 alphabetically arranged entries, providing clear jargon-free definitions of even the most technical mathematical terms. Ranging widely from Achilles paradox to zero matrix, the dictionary uses graphs, diagrams, and charts to render definitions as comprehensible as possible, offering an ideal introduction to subjects such linear algebra, optimization, nonlinear equations, and differential equations. The Dictionary covers both pure and applied mathematics as well as statistics, and there are entries on major mathematicians and on mathematics of more general interest, such as fractals, game theory, and chaos. The volume also contains valuable appendices of useful and relevant extra information, including lists of Nobel Prize winners and Fields medalists and lists of formulae. Fully revised and updated, this edition features many entry-level web links, which are accessible and continually updated via the Dictionary of Mathematics companion website, making the book indispensable for students and teachers of mathematics and for anyone encountering mathematics in the workplace.

A. P. Kiselev "Kiselev's Geometry: Book II. Stereometry"
Sumizdat | English | 2008-09-01 | ISBN: 0977985210 | 180 pages | DJVU | 6,3 MB

The book is an English adaptation of a classical Russian grade school-level text in solid Euclidean geometry. It contains the chapters Lines and Planes, Polyhedra, Round Solids, which include the traditional material about dihedral and polyhedral angles, Platonic solids, symmetry and similarity of space figures, volumes and surface areas of prisms, pyramids, cylinders, cones and balls. The English edition also contains a new chapter Vectors and Foundations (written by A. Givental) about vectors, their applications, vector foundations of Euclidean geometry, and introduction to spherical and hyperbolic geometries. This volume completes the English adaptation of Kiselev's Geometry whose 1st part ( Book I. Planimetry ), dedicated to plane geometry, was published by Sumizdat in 2006 as ISBN 0977985202.

Both volumes of Kiselev's Geometry are praised for precision, simplicity and clarity of exposition, and excellent collection of exercises. They dominated Russian math education for several decades, were reprinted in dozens of millions of copies, influenced geometry education in Eastern Europe and China, and are still active as textbooks for 7-11 grades. The books are adapted to the modern US curricula by a professor of mathematics from UC Berkeley.



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