MATH 388: Honors Math III - Linear Algebra

Linear Algebra, 3rd Edition, by Larry Smith.

We will definitely cover the first fourteen chapters of the text but skip a few sections occasionally. We will also do our best to cover some of the later chapters (Ch. 15-18) as time permits.

Please note that we will work on developing your independent reading skills in Mathematics and your ability to learn and use definitions and theorems. I certainly won't be able to cover in class all the material you will be required to learn. As a result, you will be expected to do a lot of reading. The reading assignments will be on topics to be discussed in the following lecture to enable you to ask focused questions in the class and to better understand the material.

Topics covered: We will cover vector spaces, linear transformations, matrices, elementary matrix operations, systems of linear equations, determinants, diagonalization, eigenspaces, and inner product spaces. Topics are subject to change depending on the progress of the class, and various topics may be skipped due to time constraints.

For many of you, this will be the first mathematics course which uses a more mathematically sophisticated approach than that found in your standard calculus courses. Apart from being a course in linear algebra, this is one of the first courses where you will be asked to write an argument in order to solve a problem. That is, you will have to write "proofs". Most, if not all, of you should have experience with this through MATH 239 or Honors Math II, Introduction to Mathematical Proof. We will be doing a significant number of proofs, and everyone should be comfortable with the process by the end of this course.

The notions of linear algebra are fundamental in almost all higher mathematics. In calculus courses the concept of a function is what one arrives at after studying graphs and simple mechanical motion in physics and stripping away the information which is not essential to doing calculations. Similarly, the concepts of a vector space, linearity and other topics studied in linear algebra are what comes from stripping away the unnecessary information involved in solving simultaneous equations, studying systems of differential equations, higher order differential equations, multivariable calculus, as well as the physics of three (or four or higher) dimensional space and advanced econometrics models. Just as a function is a higher level of abstraction than the quantity the function represents, vector spaces are more abstract than the functions, equations, or physical or economic situations which they represent.

Your overall grade will be determined as follows:

• 25% - Homework and Class Participation
• 25% - Exam 1
• 25% - Exam 2
• 25% - Final Exam

Your overall grade for the course will reflect how well the class is doing, and will be high if everyone is working hard on the homework and doing well on the exams. Many of the questions on the exams will be in the same spirit as the homework questions. Therefore understanding how to do all the homework questions will enable you to do well on the exams.

Homework: There will be regular homework assignments which must be turned in by 8:00 pm on the due date. Follow this link for a Description of Homework requirements. Please note that you are STRONGLY ENCOURAGED to WORK IN GROUPS of 2 or 3 students. However, each student is responsible for writing up his or her own homework to be handed in. Moreover, each student must typeset their homework using LaTeX.

Exams: There will be two Midterm Exams and one Final Exam. Exams are closed book, closed notes, closed friends, and open brain. Calculators, cell phones, iPods, and other electronic devices will NOT be permitted in exams. The dates of the exams will be decided a week or two in advance.

Class Participation: Class participation will be based on your willingness to ASK and ANSWER questions in class. There will be active discussion at certain times, and you will also be required to present some proofs to the class. It is imperative that you keep up with the reading assignments. This will help you answer my questions and help you ask more essential, thought-provoking questions during the lectures.

It is essential not to fall behind because each lecture is based on previous work. If you have trouble with some material, SEEK HELP IMMEDIATELY in the following ways: