Markus Schmidmeier
Mathematical Sciences
Florida Atlantic University

# Linear Algebra II

Spring 2014

Hi, here is some information about my course Linear Algebra II (CRN: 26765, MAS 4107, 3 credits). We meet Mondays, Wednesdays and Fridays, 9:00 - 9:50 a.m. in PS 113.

Linear algebra is the branch of mathematics concerning vector spaces as well as linear mappings between such spaces. Such an investigation is initially motivated by finding all solutions to a system of linear equations containing several unknowns. Such equations are naturally represented using the formalism of matrices and vectors.
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 vector spaces of functions that you have seen in modern analysis. 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.

Prerequisite

None in particular, but mathematical maturity (proof writing) is expected.

Textbook and Topics

We will use the book by Sheldon Axler, Linear Algebra Done Right, second edition, Springer UTM, ISBN 0-387-98258-2

We are going to cover the following chapters:

• Vector spaces and their basic properties (Chapter 1)
• Linear independence, span, basis and dimension for finite-dimensional vector spaces (Chapter 2)
• Linear maps, null space and range (Chapter 3)
• Some background on polynomials (Chapter 4)
• Eigenvectors and eigenvalues (Chapter 5)
• Minimal polynomial, characteristic polynomial, and generalized eigenvectors. The Jordan Normal Form Theorem for linear operators on a finite dimensional complex vector space. (Chapter 8)
• As time permits, inner product spaces, orthonormal bases and the Gram-Schmidt algorithm (Chapter 6)

Objectives

• Work with abstract definitions and theorems in the familiar setup of vectors and matrices
• Revisit and understand algorithms to compute bases, eigenvalues, generalized eigenvectors etc.
• Pracise proof writing to ascertain basic results in linear algebra
• Seek examples to show that hypotheses in theorems are necessary

Tutoring
There is free math tutoring available in the Math Learning Center in GS 211. Open: Monday - Thursday, 9 a.m. - 6 p.m., Friday 9 a.m. - 4 p.m. For one-on-one tutoring e-mail mlc@sci.fau.edu or see the Assistant Director in GS 212E. For remote online tutoring go to http://www.math.fau.edu/MLC/remote/. Please let me know your experience with the Math Learning Center!

Credit

Homework:  I will assign homework problems every week. The problems will not be graded, but some may show up on a quiz:   Homework problems.

Quizzes:  We will have a quiz every Friday; the ten best quizzes count for 30 % of the grade. No calculators can be used during the quiz.

Presentation:  Modification: Presentations will be optional. Instead, two graded homework sets will count for 10% of the grade.

Midterm Exam:  The midterm exam on February 21 counts for 20 % of the grade.

Final Exam: The final exam on Friday, April 25, 7:45 a.m. - 10:15 a.m. in PS 113 is comprehensive and will count for 40 % of your grade. Please bring a picture id (Owl card or drivers licence)!

Further Information

For the Disability Policy, the Make-Up Policy, the Code of Academic Integrity, Religious Accommodation, my Grading Scale and Financial Assistance Opportunities please visit Infos for all my courses.

Contact Me

Office hours:  MWF 11 a.m. - noon in SE 230.