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Approaches To Algebra
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Book Synopsis Approaches to Algebra by : N. Bednarz
Download or read book Approaches to Algebra written by N. Bednarz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.
Book Synopsis Educational Algebra by : Eugenio Filloy
Download or read book Educational Algebra written by Eugenio Filloy and published by Springer Science & Business Media. This book was released on 2007-10-12 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes a theoretical perspective on the study of school algebra, in which both semiotics and history occur. The Methodological design allows for the interpretation of specific phenomena and the inclusion of evidence not addressed in more general treatments. The book gives priority to "meaning in use" over "formal meaning". These approaches and others of similar nature lead to a focus on competence rather than a user’s activity with mathematical language.
Book Synopsis A Polynomial Approach to Linear Algebra by : Paul A. Fuhrmann
Download or read book A Polynomial Approach to Linear Algebra written by Paul A. Fuhrmann and published by Springer Science & Business Media. This book was released on 2012-10-01 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Polynomial Approach to Linear Algebra is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduction to other areas of mathematics, operator theory in particular. This technique is very powerful as becomes clear from the analysis of canonical forms (Frobenius, Jordan). It should be emphasized that these functional methods are not only of great theoretical interest, but lead to computational algorithms. Quadratic forms are treated from the same perspective, with emphasis on the important examples of Bezoutian and Hankel forms. These topics are of great importance in applied areas such as signal processing, numerical linear algebra, and control theory. Stability theory and system theoretic concepts, up to realization theory, are treated as an integral part of linear algebra. Finally there is a chapter on Hankel norm approximation for the case of scalar rational functions which allows the reader to access ideas and results on the frontier of current research.
Book Synopsis Concrete Approach to Abstract Algebra by : W. W. Sawyer
Download or read book Concrete Approach to Abstract Algebra written by W. W. Sawyer and published by Courier Dover Publications. This book was released on 2018-08-15 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brief, clear, and well written, this introductory treatment bridges the gap between traditional and modern algebra. Includes exercises with complete solutions. The only prerequisite is high school-level algebra. 1959 edition.
Download or read book Algebra 1 written by Sidney Lee Rachlin and published by . This book was released on 1992 with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebra written by William A. Adkins and published by Springer Science & Business Media. This book was released on 1992 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: First year graduate algebra text. The choice of topics is guided by the underlying theme of modules as a basic unifying concept in mathematics. Beginning with standard topics in group and ring theory, the authors then develop basic module theory and its use in investigating bilinear, sesquilinear, and quadratic forms. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis How to Solve Word Problems in Algebra, 2nd Edition by : Mildred Johnson
Download or read book How to Solve Word Problems in Algebra, 2nd Edition written by Mildred Johnson and published by McGraw Hill Professional. This book was released on 1993-01-21 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving word problems has never been easier than with Schaum's How to Solve Word Problems in Algebra! This popular study guide shows students easy ways to solve what they struggle with most in algebra: word problems. How to Solve Word Problems in Algebra, Second Edition, is ideal for anyone who wants to master these skills. Completely updated, with contemporary language and examples, features solution methods that are easy to learn and remember, plus a self-test.
Book Synopsis Abstract Algebra by : Charles C. Sims
Download or read book Abstract Algebra written by Charles C. Sims and published by John Wiley & Sons. This book was released on 1984 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebra written by and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebra and Number Theory by : Martyn R. Dixon
Download or read book Algebra and Number Theory written by Martyn R. Dixon and published by John Wiley & Sons. This book was released on 2011-07-15 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines—linear algebra, abstract algebra, and number theory—into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts. The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory. Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material. Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education.
Book Synopsis Algebra in Context by : Amy Shell-Gellasch
Download or read book Algebra in Context written by Amy Shell-Gellasch and published by JHU Press. This book was released on 2015-10-15 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: An engaging new approach to teaching algebra that takes students on a historical journey from its roots to modern times. This book’s unique approach to the teaching of mathematics lies in its use of history to provide a framework for understanding algebra and related fields. With Algebra in Context, students will soon discover why mathematics is such a crucial part not only of civilization but also of everyday life. Even those who have avoided mathematics for years will find the historical stories both inviting and gripping. The book’s lessons begin with the creation and spread of number systems, from the mathematical development of early civilizations in Babylonia, Greece, China, Rome, Egypt, and Central America to the advancement of mathematics over time and the roles of famous figures such as Descartes and Leonardo of Pisa (Fibonacci). Before long, it becomes clear that the simple origins of algebra evolved into modern problem solving. Along the way, the language of mathematics becomes familiar, and students are gradually introduced to more challenging problems. Paced perfectly, Amy Shell-Gellasch and J. B. Thoo’s chapters ease students from topic to topic until they reach the twenty-first century. By the end of Algebra in Context, students using this textbook will be comfortable with most algebra concepts, including • Different number bases • Algebraic notation • Methods of arithmetic calculation • Real numbers • Complex numbers • Divisors • Prime factorization • Variation • Factoring • Solving linear equations • False position • Solving quadratic equations • Solving cubic equations • nth roots • Set theory • One-to-one correspondence • Infinite sets • Figurate numbers • Logarithms • Exponential growth • Interest calculations
Book Synopsis Geometric Methods in Algebra and Number Theory by : Fedor Bogomolov
Download or read book Geometric Methods in Algebra and Number Theory written by Fedor Bogomolov and published by Springer Science & Business Media. This book was released on 2006-06-22 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry
Download or read book Algebra 1 written by and published by . This book was released on 1991 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebra for Elementary and Middle School Teachers by : Sheryl Stump
Download or read book Algebra for Elementary and Middle School Teachers written by Sheryl Stump and published by . This book was released on 2012-06-28 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Abstract Algebra by : I. N. Herstein
Download or read book Abstract Algebra written by I. N. Herstein and published by Macmillan College. This book was released on 1990 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Undergraduate Algebra by : Matej Brešar
Download or read book Undergraduate Algebra written by Matej Brešar and published by Springer. This book was released on 2019-05-20 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers an innovative approach to abstract algebra, based on a unified treatment of similar concepts across different algebraic structures. This makes it possible to express the main ideas of algebra more clearly and to avoid unnecessary repetition. The book consists of two parts: The Language of Algebra and Algebra in Action. The unified approach to different algebraic structures is a primary feature of the first part, which discusses the basic notions of algebra at an elementary level. The second part is mathematically more complex, covering topics such as the Sylow theorems, modules over principal ideal domains, and Galois theory. Intended for an undergraduate course or for self-study, the book is written in a readable, conversational style, is rich in examples, and contains over 700 carefully selected exercises.
Book Synopsis Introductory Modern Algebra by : Saul Stahl
Download or read book Introductory Modern Algebra written by Saul Stahl and published by John Wiley & Sons. This book was released on 2013-09-30 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition "Stahl offers the solvability of equations from the historicalpoint of view...one of the best books available to support aone-semester introduction to abstract algebra." —CHOICE Introductory Modern Algebra: A Historical Approach, SecondEdition presents the evolution of algebra and provides readerswith the opportunity to view modern algebra as a consistentmovement from concrete problems to abstract principles. With a fewpertinent excerpts from the writings of some of the greatestmathematicians, the Second Edition uniquely facilitates theunderstanding of pivotal algebraic ideas. The author provides a clear, precise, and accessibleintroduction to modern algebra and also helps to develop a moreimmediate and well-grounded understanding of how equations lead topermutation groups and what those groups can inform us about suchdiverse items as multivariate functions and the 15-puzzle.Featuring new sections on topics such as group homomorphisms, theRSA algorithm, complex conjugation, the factorization of realpolynomials, and the fundamental theorem of algebra, the SecondEdition also includes: An in-depth explanation of the principles and practices ofmodern algebra in terms of the historical development from theRenaissance solution of the cubic equation to Dedekind'sideals Historical discussions integrated with the development ofmodern and abstract algebra in addition to many new explicitstatements of theorems, definitions, and terminology A new appendix on logic and proofs, sets, functions, andequivalence relations Over 1,000 new examples and multi-level exercises at the end ofeach section and chapter as well as updated chapter summaries Introductory Modern Algebra: A Historical Approach, SecondEdition is an excellent textbook for upper-undergraduatecourses in modern and abstract algebra.
