TAILIEUCHUNG - Elements of abstract and linear algebra

This book is a survey of abstract algebra with emphasis on algebra is online for students in mathematics, computer science, and physical sciences. The rst three or four chapters can stand alone as a one semester course in abstract algebra. However, they are structured to provide the foundation for the program linear algebra. Chapter 2 is the most di cult part of the book for group written in additive notation and multiplication, and the concept of coset is confusing at rst. Chapter 2 After the book was much easier as you go along | Elements of Abstract and Linear Algebra E. H. Connell ii . Connell Department of Mathematics University of Miami . Box 249085 Coral Gables Florida 33124 USA ec@ Mathematical Subject Classifications 1991 12-01 13-01 15-01 16-01 20-01 @1999 . Connell March 20 2004 iii Introduction In 1965 I first taught an undergraduate course in abstract algebra. It was fun to teach because the material was interesting and the class was outstanding. Five of those students later earned a . in mathematics. Since then I have taught the course about a dozen times from various texts. Over the years I developed a set of lecture notes and in 1985 I had them typed so they could be used as a text. They now appear in modified form as the first five chapters of this book. Here were some of my motives at the time. 1 To have something as short and inexpensive as possible. In my experience students like short books. 2 To avoid all innovation. To organize the material in the most simple-minded straightforward manner. 3 To order the material linearly. To the extent possible each section should use the previous sections and be used in the following sections. 4 To omit as many topics as possible. This is a foundational course not a topics course. If a topic is not used later it should not be included. There are three good reasons for this. First linear algebra has top priority. It is better to go forward and do more linear algebra than to stop and do more group and ring theory. Second it is more important that students learn to organize and write proofs themselves than to cover more subject matter. Algebra is a perfect place to get started because there are many easy theorems to prove. There are many routine theorems stated here without proofs and they may be considered as exercises for the students. Third the material should be so fundamental that it be appropriate for students in the physical sciences and in computer science. Zillions of students take calculus and .

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