Libros de Matemáticas, página 18 de 1069

Building on the authors previous edition on the subject (Introduction to Linear Algebra, Jones & Bartlett, 1996), this book offers a refreshingly concise text suitable for a standard course in linear algebra, presenting a carefully selected array of essential topics that can be thoroughly covered in a single semester. Although the exposition generally falls in line with the material recommended by the Linear Algebra Curriculum Study Group, it notably deviates in providing an early emphasis on the geometric foundations of linear algebra. This gives students a more intuitive understanding of the subject and enables an easier grasp of more abstract concepts covered later in the course. The focus throughout is rooted in the mathematical fundamentals, but the text also investigates a number of interesting applications, including a section on computer graphics, a chapter on numerical methods, and many exercises and examples using MATLAB. Meanwhile, many visuals and problems (a complete solutions manual is available to instructors) are included to enhance and reinforce understanding throughout the book. Brief yet precise and rigorous, this work is an ideal choice for a one-semester course in linear algebra targeted primarily at math or physics majors. It is a valuable tool for any professor who teaches the subject.

This textbook provides an accessible and concise introduction to numerical analysis for upper undergraduate and beginning graduate students from various backgrounds. It was developed from the lecture notes of four successful courses on numerical analysis taught within the MPhil of Scientific Computing at the University of Cambridge. The book is

This textbook provides an accessible and concise introduction to numerical analysis for upper undergraduate and beginning graduate students from various backgrounds. It was developed from the lecture notes of four successful courses on numerical analysis taught within the MPhil of Scientific Computing at the University of Cambridge. The book is easily accessible, even to those with limited knowledge of mathematics.

This text provides a hands-on introduction to writing software in Python, with no prior programming experience required. It offers sections designed for approximately one class period each, and proceeds gradually from procedural to object-oriented design. Examples, exercises, and projects are included from diverse application domains.

This text provides a hands-on introduction to writing software in Python, with no prior programming experience required. It offers sections designed for approximately one class period each, and proceeds gradually from procedural to object-oriented design. Examples, exercises, and projects are included from diverse application domains.

Accessible to all students with a sound background in high school mathematics, this popular text presents some of the most fundamental and beautiful ideas in pure mathematics. Along with numerous new exercises, this edition includes two new chapters that serve as an introduction to abstract algebra via the theory of groups, covering abstract reasoning as well as many examples and applications. It also contains new material on inequalities, counting methods, the inclusion-exclusion principle, and Eulers phi function.

This short book introduces the main ideas of statistical inference in a way that is both user friendly and mathematically sound. Particular emphasis is placed on the common foundation of many models used in practice. In addition, the book focuses on the formulation of appropriate statistical models to study problems in business, economics, and the social sciences, as well as on how to interpret the results from statistical analyses.The book will be useful to students who are interested in rigorous applications of statistics to problems in business, economics and the social sciences, as well as students who have studied statistics in the past, but need a more solid grounding in statistical techniques to further their careers.

Mathematical analysis offers a solid basis for many achievements in applied mathematics and discrete mathematics. This new textbook is focused on differential and integral calculus, and includes a wealth of useful and relevant examples, exercises, and results enlightening the reader to the power of mathematical tools. The intended audience consists of advanced undergraduates studying mathematics or computer science. The author provides excursions from the standard topics to modern and exciting topics, to illustrate the fact that even first or second year students can understand certain research problems. The text has been divided into ten chapters and covers topics on sets and numbers, linear spaces and metric spaces, sequences and series of numbers and of functions, limits and continuity, differential and integral calculus of functions of one or several variables, constants (mainly pi) and algorithms for finding them, the W - Z method of summation, estimates of algorithms and of certain combinatorial problems. Many challenging exercises accompany the text. Most of them have been used to prepare for different mathematical competitions during the past few years. In this respect, the author has maintained a healthy balance of theory and exercises.

Sets and Numbers.- Vector Spaces and Metric Spaces.- Sequences and Series.- Limits and Continuity.- Differential Calculus on R.- Integral Calculus on R.- Differential Calculus on R.- Double Integrals, Triple Integrals, and Line Integrals.- Constants.- Asymptotic and Combinatorial Estimates.

This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiins probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises are found throughout the book.

1 Numbers 2 Induction 3 Euclids Algorithm 4 Unique Factorization 5 Congruences 6 Congruence Classes 7 Applications of Congruences 8 Rings and Fields 9 Fermats and Eulers Theorems 10 Applications of Fermats and Eulers Theorems 11 On Groups 12 The Chinese Remainder Theorem 13 Matrices and Codes 14 Polynomials 15 Unique Factorization 16 The Fundamental Theorem of Algebra 17 Derivatives 18 Factoring in Q[x],I 19 The Binomial Theorem in Characteristic p 20 Congruences and the Chinese Remainder Theorem 21 Applications of the Chinese Remainder Theorem 22 Factoring in Fp[x] and in Z[x] 23 Primitive Roots 24 Cyclic Groups and Primitive Roots 25 Pseudoprimes 26 Roots of Unity in Z/mZ 27 Quadratic Residues 28 Congruence Classes Mopdulo a Polynomial 29 Some Applications of Finite Fields 30 Classifying Finite Fields

Numbers.- Numbers.- Induction.- Euclids Algorithm.- Unique Factorization.- Congruence.- Congruence classes and rings.- Congruence Classes.- Rings and Fields.- Matrices and Codes.- Congruences and Groups.- Fermats and Eulers Theorems.- Applications of Eulers Theorem.- Groups.- The Chinese Remainder Theorem.- Polynomials.- Polynomials.- Unique Factorization.- The Fundamental Theorem of Algebra.- Polynomials in ?[x].- Congruences and the Chinese Remainder Theorem.- Fast Polynomial Multiplication.- Primitive Roots.- Cyclic Groups and Cryptography.- Carmichael Numbers.- Quadratic Reciprocity.- Quadratic Applications.- Finite Fields.- Congruence Classes Modulo a Polynomial.- Homomorphisms and Finite Fields.- BCH Codes.- Factoring Polynomials.- Factoring in ?[x].- Irreducible Polynomials.

The Second Edition offers a major re-organization of the book, with the goal of making it much more competitive as a text for students. The revised edition will be appropriate for a one- or two-semester introductory real analysis course. Like the first edition, the primary audience are students who will never take a graduate level analysis course.

Excerpt from A Correlational Analysis of Proficiency in Typing

Excerpt from A Correlational Analysis of Proficiency in Typing

A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant results and techniques that are of interest in their own right. This book develops the abstract theory along with a well-chosen selection of concrete examples that exemplify the results and show the breadth of their applicability. After a preliminary chapter containing the necessary background material on Banach algebras and spectral theory, the text sets out the general theory of locally compact groups and their unitary representations, followed by a development of the more specific theory of analysis on Abelian groups and compact groups. There is an extensive chapter on the theory of induced representations and its applications, and the book concludes with a more informal exposition on the theory of representations of non-Abelian, non-compact groups.Featuring extensive updates and new examples, the Second Edition:Adds a short section on von Neumann algebrasIncludes Mark Kacs simple proof of a restricted form of Wieners theoremExplains the relation between SU(2) and SO(3) in terms of quaternions, an elegant method that brings SO(4) into the picture with little effortDiscusses representations of the discrete Heisenberg group and its central quotients, illustrating the Mackey machine for regular semi-direct products and the pathological phenomena for nonregular onesA Course in Abstract Harmonic Analysis, Second Edition serves as an entree to advanced mathematics, presenting the essentials of harmonic analysis on locally compact groups in a concise and accessible form.

This is a comprehensive textbook on modern algebra written by an internationally renowned specialist. It covers material traditionally found in advanced undergraduate and basic graduate courses and presents it in a lucid style. The author includes almost no technically difficult proofs, and reflecting his point of view on mathematics, he tries wherever possible to replace calculations and difficult deductions with conceptual proofs and to associate geometric images to algebraic objects.The effort spent on the part of students in absorbing these ideas will pay off when they turn to solving problems outside of this textbook. Another important feature is the presentation of most topics on several levels, allowing students to move smoothly from initial acquaintance with the subject to thorough study and a deeper understanding. Basic topics are included, such as algebraic structures, linear algebra, polynomials, and groups, as well as more advanced topics, such as affine and projective spaces, tensor algebra, Galois theory, Lie groups, and associative algebras and their representations. Some applications of linear algebra and group theory to physics are discussed. The book is written with extreme care and contains over 200 exercises and 70 figures. It is ideal as a textbook and also suitable for independent study for advanced undergraduates and graduate students.

 ,Part 1 begins with an overview of properties of the real numbers and starts to introduce the notions of set theory. The absolute value and in particular inequalities are considered in great detail before functions and their basic properties are handled. From this the authors move to differential and integral calculus. Many examples are discussed. Proofs not depending on a deeper understanding of the completeness of the real numbers are provided. As a typical calculus module, this part is thought as an interface from school to university analysis.Part 2 returns to the structure of the real numbers, most of all to the problem of their completeness which is discussed in great depth. Once the completeness of the real line is settled the authors revisit the main results of Part 1 and provide complete proofs. Moreover they develop differential and integral calculus on a rigorous basis much further by discussing uniform convergence and the interchanging of limits, infinite series (including Taylor series) and infinite products, improper integrals and the gamma function. In addition they discussed in more detail as usual monotone and convex functions.Finally, the authors supply a number of Appendices, among them Appendices on basic mathematical logic, more on set theory, the Peano axioms and mathematical induction, and on further discussions of the completeness of the real numbers.Remarkably, Volume I contains ca. 360 problems with complete, detailed solutions._,