Book Review: Homology theory. An introduction to algebraic topology

Introduction to Applied Algebraic Topology

An Introduction to Rapid Review Articles

تاکنون در مجله دانشگاه، پیرامون انواع مطالعات مروری، مقالاتی را به رشته تحریر درآورده‌ایم [5-1]. در این سخن سردبیری، قصد داریم به یکی دیگر از مطالعات مروری با عنوان مرور سریع (Rapid Review)، بپردازیم. لازم به توضیح است که تاکنون تعریف جامع و یکسانی از مرور سریع به عمل نیامده است. این نکته به خاطر آن است که روش‌های متفاوتی برای انجام یک مرور سریع در نظر گرفته شده است. با این وجود، می‌توان بر روی...

Introduction to Algebraic Coding Theory

4 Ideals and cyclic codes 18 4.1 Ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 Cyclic codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Group of a code . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.4 Minimal polynomials . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.5 BCH and Reed-Solomon codes . . . . . . . . . . ....

Introduction to Algebraic Coding Theory

∗The first versions of this book were written in Fall 2001 and June 2002 at Cornell University, respectively supported by an NSF VIGRE Grant and a Department of Mathematics Grant. The current version was written in 2005 at Franklin W. Olin College of Engineering supported by NSF CCLI DUE-0410517 Grant. Edits were made in 2006 under the same grant. If you wish to use this book, please simply let...

Algebraic Topology: A brief introduction

The mechanisms by which these open sets may be assigned, is arbitrary as long they satisfy the above properties. In practice, the most common way to define open sets is by way of metrics. However, it is important to note that even in this case, the definitions of continuous maps can be much simplified using open sets especially for large dimensions. For example, the classical definition for con...