Advanced Linear Algebra

In Spring 2015 I taught the Advanced Linear Algebra, MATH 3170. I used the following course design, and I used the book: Linear Algebra Done Right by Axler.

What is it good for?

• • The following is a quote from the Wikipedia website, and you may further read about it here.

    • • Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations. Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, computer animation, and the social sciences (particularly in economics). Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear ones.

  • The following is from the Purdue University for prospective graduate students:

    • • Question: You mentioned that I should take the `right' classes. What are the `right' classes?

      • Answer: For grad school in math, linear algebra, real analysis and abstract algebra are absolutely essential. Taking the honors versions (where available) is almost essential. You should also squeeze in as many other math classes as you can. Other valuable classes would include a second course in linear algebra, complex analysis, advanced calculus and topology.

Requirements

• Prerequisite: Linear Algebra (MATH 2160) AND Introduction to Mathematical Proof (MATH 3000).

  • 50% of the course grade is homework, and 50% is Quiz.

  • Good work ethic and study habit are required throughout the semester.

  • There will NOT be 50-minute tests, but the final exam will be given.

Homework

• • Homework will be assigned after each class meeting, and they are collected and graded.

  • Homework provides students with opportunities to review concepts, practice standard problems, and challenge themselves with advanced problems which require independent and critical thinking.

Quizzes

• • At the beginning of each class, a 15-min quiz is given.

  • The purpose of quizzes in my courses is

  • (1) To examine whether students worked on good performance skill.

  • (2) To examine whether students properly studied the materials.