Linear Algebra Done Wrong by Sergei Treil

English | PDF | 2017 | 286 Pages | ISBN : N/A | 1.27 MB

The title of the book sounds a bit mysterious. Why should anyone read this book if it presents the subject in a wrong way? What is particularly done “wrong” in the book?

Before answering these questions, let me first describe the target au- dience of this text. This book appeared as lecture notes for the course “Honors Linear Algebra”. It supposed to be a first linear algebra course for mathematically advanced students. It is intended for a student who, while not yet very familiar with abstract reasoning, is willing to study more rigor- ous mathematics than what is presented in a “cookbook style” calculus type course. Besides being a first course in linear algebra it is also supposed to be a first course introducing a student to rigorous proof, formal definitions—in short, to the style of modern theoretical (abstract) mathematics. The target audience explains the very specific blend of elementary ideas and concrete examples, which are usually presented in introductory linear algebra texts with more abstract definitions and constructions typical for advanced books.

Another specific of the book is that it is not written by or for an alge- braist. So, I tried to emphasize the topics that are important for analysis, geometry, probability, etc., and did not include some traditional topics. For example, I am only considering vector spaces over the fields of real or com- plex numbers. Linear spaces over other fields are not considered at all, since I feel time required to introduce and explain abstract fields would be better spent on some more classical topics, which will be required in other dis- ciplines. And later, when the students study general fields in an abstract algebra course they will understand that many of the constructions studied in this book will also work for general fields.Visit My Blog For Daily Very Exclusive Content,We Are Here For You And Without You And Your Support We Can’t Continue

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