TAILIEUCHUNG - Linear Algebra Done Wrong

Such jobs would then be gone, to be replaced by jobs requiring much more sophisticated mathematical training. The mathematics needed for these machines, as was case with engines, has been the main impediment to actual wide-scale implementation of such robotic mechanisms. Recently, it has become clear that the key mathematics is available, (the mathematics of algebraic and geometric topology, developed over the last 80 - 90 years), and we have begun to make dramatic progress in creating the programs needed to make such machines work. Because of this, we have to anticipate that later generations of students will not have the options of such jobs, and we will have. | Linear Algebra Done Wrong Sergei Treil Department of Mathematics Brown UNivERSiTy Copyright Sergei Treil 2004 2009 Preface 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 audience 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 rigorous mathematics that 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 algebraist. 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 complex 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 disciplines. 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. .

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