Mathematics : Algebra

Given its abstract nature and the highly syntactical competence required by the use of symbolic algebra, research on its teaching and learning must rely on approaches that include semiotic concepts and analyses that recall the history of algebraic ideas, among others. Educational Algebra: A Theoretical and Empirical Approach deals with a theoretical perspective on the study of school algebra, in which both components (semiotics and history) occur. This perspective runs opposite to general theoretical models, since it submits components for the design of local frameworks for theoretical analysis. The Methodological design allows for the interpretation of specific phenomena and the inclusion, within such interpretative frameworks, of evidence not included in more general treatments. Such is the case of phenomena observed in subjects who are initiating the study of symbolic algebra, involving the production of personal sign systems at the intermediate level or the level previous to the mathematical sign system which is to be learned. Disciplines such as Linguistics, Logic, Psycholinguistics, Semiotics, general Cognitive Psychology, Mathematics Psychology, Mathematics Epistemology, History of Mathematics, and others have carried out research on the same topics approached by Mathematics Education and have redefined their results within the framework of their respective fields. Specifically, theorists in Linguistics, Information Processing and Didactics of Mathematics have done important work on the notion of code. Today, this notion is a key element to interpreting the idea of representation in the new explanatory models of cognitive problems placed by alternative teaching approaches, including those involving a technological environment. Additionally, Psycholinguistics and Artificial Intelligence in procedural models of human abilities have intended to explain how and why users of mathematical language naturally and commonly make mistakes in syntactical procedures. Educ more...

Price: $139.00

Volume two of this modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field more...

Price: $44.00

This work is an introduction to the theory of elliptic curves, ranging from its most elementary aspects to current research. This manuscript grew out of Tate's Haverford Lectures. For the second edition, the author has written three new chapters and there are also two new appendices which were written by S. Theisen and O. Forster. more...

Price: $79.95

This book provides a unified and innovative approach to much of the theories of equivalence and duality between categories of modules that has transpired over the last 45 years. The authors discuss the relationships between categories of modules over a pair of rings that are induced by both covariant and contravariant representable functors, in particular by tilting and cotilting theories. more...

Price: $52.00

All students need to master a variety of mathematical tools and concepts at the start of their university career. This distinctive book helps students learn these by doing. The approach is interactive, using experiments, performed in the symbolic algebra package Mathematica, to impart the fundamentals of many of the topics students encounter. A clear exposition of the topic accompanies every experiment. The modular style of the book allows students to study each topic independently. The sheer power of computer algebra software lets students develop and test their own conjectures, obtaining quick and instructive results. The software modules accompanying this course includes many custom functions designed to facilitate learning and testing process. more...

Price: $62.40