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Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
"Theory of Numbers: A Textbook" is aimed at students of Mathematics who are graduates or even undergraduates. Very little prerequisites are needed. The reader is expected to know the theory of functions of a real variable and in some chapters complex integration and some simple principles of complex function theory are assumed. The entire book is self contained except theorems 7 and 9 of chapter 11 which are assumed. The most ambitious chapter is chapter 11 where the most attractive result on difference between consecutive primes is proved.
Factor fearlessly, conquer the quadratic formula, and solve linear equationsThere’s no doubt that algebra can be easy to some while extremely challenging to others. If you’re vexed by variables, Algebra I For Dummies, 2nd Edition provides the plain-English, easy-to-follow guidance you need to get the right solution every time!Now with 25% new and revised content, this easy-to-understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems with confidence.
This broad introduction to vector and tensor analysis is designed for the advanced undergraduate or graduate student in mathematics, physics, and engineering as well as for the practicing engineer or physicist who needs a theoretical understanding of these essential mathematical tools. In recent years, the vector approach has found its way even into writings on aspects of biology, economics, and other sciences.The many and various topics covered include: the algebra of vectors — linear dependence and independence, transformation equations, the inner product, the cross product, and the algebra of matrixes; the differentiation of vectors — geometry of space curves, kinematics, moving frames of reference, Newtonian orbits and special relativity theory; partial differentiation of vectors — geometry of space curves, kinematics, moving frames of reference, Newtonian orbits and special relativity theory; partial differentiation and associated concepts — surface representations, bases in general coordinate systems, and maxima and minima of functions of two variables; the integration of vectors — line integrals, surface integrals, surface tensors and volume integrals; tensor algebra and analysis — fundamental notions of n-space, transformations and tensors, Riemannian geometry, tensor processes of differentiation, geodesics, the curvature tensor and its algebraic properties, and general relativity theory.T
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students’ understanding of these concepts is vital to their mastery of the subject.
David Poole’s innovative LINEAR ALGEBRA: A MODERN INTRODUCTION, 4e emphasizes a vectors approach and better prepares students to make the transition from computational to theoretical mathematics. Balancing theory and applications, the book is written in a conversational style and combines a traditional presentation with a focus on student-centered learning. Theoretical, computational, and applied topics are presented in a flexible yet integrated way. Stressing geometric understanding before computational techniques, vectors and vector geometry are introduced early to help students visualize concepts and develop mathematical maturity for abstract thinking.
Authors: Fomenko, Anatoly, Fuchs, DmitryUpdates a popular textbook from the golden era of the Moscow school of I. M. GelfandPresents material concisely but rigorouslyIlluminates the subject matter with a range of technical and artistic illustrations, along with a wealth of examples and computations meant to provide a treatment of the topic that is both deep and broadContains an entirely new chapter on K-theory and the Riemann-Roch theoremThis textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I.
For new algebra students or those seeking a refresher, this book offers a series of simple 20-step lesson plans that emphasize quick learning of practical, essential skills.
This book gives applications of the theory of process algebra, or Algebra of Communicating Processes (ACP), that is the study of concurrent or communicating processes studied using an algebraic framework. The approach is axiomatic; the authors consider structures that are some set of mostly equational axioms, which are equipped with several operators. Thus the term ‘algebra’ is used in the model-theoretic sense. The axiomatic approach enables one to organize the field of process theories. The theory is applied systematically to a number of situations, including systolic algorithms, semantics of an object-oriented language, and protocols.
Passage to Abstract Mathematics facilitates the transition from introductory mathematics courses to the more abstract work that occurs in advanced courses. This text covers logic, proofs, numbers, sets, induction, functions, and more–material which instructors of upper-level courses often presume their students have already mastered but are in fact missing from lower-level courses. Students will learn how to read and write mathematics–especially proofs–the way that mathematicians do. The text emphasizes the use of complete, correct definitions and mathematical syntax.
C*-approximation theory has provided the foundation for many of the most important conceptual breakthroughs and applications of operator algebras. This book systematically studies (most of) the numerous types of approximation properties that have been important in recent years: nuclearity, exactness, quasidiagonality, local reflexivity, and others. Moreover, it contains user-friendly proofs, insofar as that is possible, of many fundamental results that were previously quite hard to extract from the literature.
A lighthearted, sometimes irreverent introduction to the concepts, vocabulary and strategies of first year algebra. Designed for people who learn best by reading, it includes no exercises. Beginning with some pre algebra concepts, like working with fractions, it explains linear equations, quadratic equations and graphing in easy to understand, non frightening language. Ideal for people who think they hate math to read before they take the class or as a supplement during it. It provides an additional explanation to the confused and comfort for the fearful.
Tough Test Questions? Missed Lectures? Not Enough Time?Fortunately, there’s Schaum’s. This all-in-one-package includes 612 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 25 detailed videos featuring Math instructors who explain how to solve the most commonly tested problems–it’s just like having your own virtual tutor! You’ll find everything you need to build confidence, skills, and knowledge for the highest score possible.M
"This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications." – "Electric Review"A comprehensive introduction, "Linear Algebra: Ideas and Applications, Fourth Edition "provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts.
Tough Test Questions? Missed Lectures? Not Enough Time?Fortunately, there’s Schaum’s. This all-in-one-package includes more than 1,900 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 30 detailed videos featuring Math instructors who explain how to solve the most commonly tested problems–it’s just like having your own virtual tutor! You’ll find everything you need to build confidence, skills, and knowledge for the highest score possible.M
Expert instruction and plenty of practice to reinforce advanced math skills Presents concepts with application to natural sciences, engineering, economics, computer science, and other branches of mathematics Complementary to most linear algebra courses or as a refresher text More than 500 exercises and answers Hundreds of solved problems The Practice Makes Perfect series has sold more than 1 million copies worldwide
The Blitzer Algebra Series combines mathematical accuracy with an engaging, friendly, and often fun presentation for maximum appeal. Blitzer’s personality shows in his writing, as he draws readers into the material through relevant and thought-provoking applications. Every Blitzer page is interesting and relevant, ensuring that students will actually use their textbook to achieve success!
Rongjin Huang examines teachers’ knowledge of algebra for teaching, with a particular focus on teaching the concept of function and quadratic relations in China and the United States.
David Poole’s innovative book prepares students to make the transition from the computational aspects of the course to the theoretical by emphasizing vectors and geometric intuition from the start. Designed for a one- or two-semester introductory course and written in simple, "mathematical English" the book presents interesting examples before abstraction. This immediately follows up theoretical discussion with further examples and a variety of applications drawn from a number of disciplines, which reinforces the practical utility of the math, and helps students from a variety of backgrounds and learning styles stay connected to the concepts they are learning.
The book consists of contributions related mostly to public-key cryptography, including the design of new cryptographic primitives as well as cryptanalysis of previously suggested schemes. Most papers are original research papers in the area that can be loosely defined as "non-commutative cryptography"; this means that groups (or other algebraic structures) which are used as platforms are non-commutative.
This proceedings volume is from the international conference on Banach algebras and their applications held at the University of Alberta (Edmonton). It contains a collection of refereed research papers and high-level expository articles that offer a panorama of Banach algebra theory and its manifold applications. Topics in the book range from $K$-theory to abstract harmonic analysis to operator theory. It is suitable for graduate students and researchers interested in Banach algebras.
Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra.The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible.
Exploring Linear Algebra: Labs and Projects with Mathematica® is a hands-on lab manual for daily use in the classroom. Each lab includes exercises, theorems, and problems that guide your students on an exploration of linear algebra.The exercises section integrates problems, technology, Mathematica® visualization, and Mathematica CDFs, enabling students to discover the theory and applications of linear algebra in a meaningful way. The theorems and problems section presents the theoretical aspects of linear algebra.
Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses. As such, they have become a vital part of any statistical education.
Showing 1–24 of 44 results