Algebra From A To Z Volume 5

This book presents a thorough explanation of the notation of summation, some unusual material on inequalities, an extended treatment of mathematical induction, and basic probability theory (including the explanation that all gambling systems must fail). It also contains a complete treatment of vector algebra (including the dot and cross product). This is usually reserved for a calculus course, but is properly algebra, and so belongs in any algebra book.Since this book deals with algebra from A to Z, it starts at the beginning with the arithmetic of the counting numbers and their extensions, i.e. the negative numbers and the rational numbers. However, these very elementary items are treated from an advanced point of view. The teacher should assign the first three chapters as outside reading, using only one day per chapter for classroom discussion.The remaining chapters cover all of the usual topics in college algebra, but they contain many unusual items not found in the standard college algebra course. As an example, the circle notation for a composite function is now standard material, but this book explains just why that notation is needed.The book concludes with a presentation of the Peano Axioms. This advanced topic should be available to all mathematics students, whether they are first year algebra students or are working for a PhD degree.

Problem-solving is an art central to understanding and ability in mathematics. With this series of books, the authors have provided a selection of worked examples, problems with complete solutions and test papers designed to be used with or instead of standard textbooks on algebra. For the convenience of the reader, a key explaining how the present books may be used in conjunction with some of the major textbooks is included. Each volume is divided into sections that begin with some notes on notation and prerequisites. The majority of the material is aimed at the students of average ability but some sections contain more challenging problems. By working through the books, the student will gain a deeper understanding of the fundamental concepts involved, and practice in the formulation, and so solution, of other problems. Books later in the series cover material at a more advanced level than the earlier titles, although each is, within its own limits, self-contained.

International Journal of Neutrosophic Science (IJNS) is a peer-review journal publishing high quality experimental and theoretical research in all areas of Neutrosophic and its Applications. IJNS is published quarterly. IJNS is devoted to the publication of peer-reviewed original research papers lying in the domain of neutrosophic sets and systems. Papers submitted for possible publication may concern with foundations, neutrosophic logic and mathematical structures in the neutrosophic setting. Besides providing emphasis on topics like artificial intelligence, pattern recognition, image processing, robotics, decision making, data analysis, data mining, applications of neutrosophic mathematical theories contributing to economics, finance, management, industries, electronics, and communications are promoted.

This is the fifth volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume include theory of linear algebras and Lie algebras. The book contains many dozens of original exercises (with difficult exercises being solved) and a list of about 900 research problems and themes.

Explains algebra from basic concepts to college-level skills.