MATH 333: Linear Algebra

Linear Algebra, 4th edition, by Stephen Friedberg, Arnold Insel, and Lawrence Spence.

We will cover roughly chapters 1-6. Topics are subject to change depending on the progress of the class, and various topics may be skipped due to time constraints.

Please note that we will work on developing your independent reading skills in Mathematics. 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 week's lectures to enable you to ask focused questions in the class and to better understand the material.

We will probably make use of the TI-89 calculators. Therefore, it is probably in your best interest to have one (or something equivalent that can calculate integrals.)

It may be helpful to make use of mathematical programs such as MATLAB, Maple, or Mathematica periodically. These are available in most student computer labs throughout campus.

Topics covered: We will cover vector spaces, linear transformations, matrices, elementary matrix operations, systems of linear equations, determinants, diagonalization, eigenspaces, and inner product spaces.

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, 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.

MATH 233 is a prerequisite for this course. That course was mostly computational, and you learned many of the basic concepts and calculations of linear algebra. MATH 333 covers most of the same topics and computations; however, it is a proof-based course and will thus be much more theoretical.

Your overall grade will be determined as follows, with your lowest 25% being dropped.

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

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. Almost all the questions on the exams will be in the same spirit with 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 weekly homework assignments which are due each Wednesday by 4:00 pm. Follow this link for a Description of Homework requirements.

Exams: There will be two Midterm Exams and one Final Exam. The Final Exam will have two parts. The first part is cumulative, covering material from the first two exams. The second part will cover material learned after the second midterm exam. Exams are closed book, closed notes, closed friends, and open brain. Cell phones, iPods, and other electronic devices will NOT be permitted in exams. Whether or not calculators are allowed on an exam will be determined at a later time.

Quizzes and Class Participation: There will be occasional, unannounced quizzes in class to make sure students are understanding and keeping up with the course material. Quizzes may be based on material from the reading assignment which we have not yet covered during lectures. Therefore, it is imperative that you keep up with the reading assignments. Any given quiz may cover topics from a previous lecture, from the reading assignment, or both. NO MAKE-UP QUIZZES WILL BE GIVEN. Class participation will be based on your willingness to ASK and ANSWER questions in class.

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: