Markus Schmidmeier
Mathematical Sciences
Florida Atlantic University

# Linear Algebra II

Fall 2017

Hi, here is some information about my course Linear Algebra II (CRN: 18033, MAS 4107, 3 credits). We meet Mondays and Wednesdays 4:00 - 5:20 p.m. 4:00 - 5:30 in PS 111. (To make up for class time missed due to Hurricane Irma, each class will be 10 minutes longer.)

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, third edition, Springer UTM, ISBN-10: 3319110799, ISBN-13: 978-3319110790

We are going to cover the following chapters:

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

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

Tutorials

The Math Learning Center provides free academic support.
• Hours of operation: M-R 9-6, F 9-4, U:1-5 in GS 211
• Appointments available at TutorTrac
• Remote online tutoring Schedule
• Contact: E-mail

Video Recordings by Textbook Author

Professor Axler has recorded a series of videos of his lectures. The videos are available on YouTube. Here is the link:
Video recordings

Credit

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

Quizzes:  We will have a quiz every Wednesday; the best twelve ten quizzes count for 60 % of the grade. Quiz 12 will take place on November 27. No calculators can be used during the quiz.

Final Exam: The final exam is comprehensive and will count for 40 % of your grade. It is scheduled for Monday, December 11, 4:00 - 6:30 p.m. in our classroom. 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, the FAU Attendance Policy Statement and Financial Assistance Opportunities please visit Infos for all my courses.

Contact Me

Office hours:  MW 9:30 - 11:30 a.m. and F 3:00 - 3:50 p.m. in SE 272.

Phone:  561-297-0275

E-mail:  markus@math.fau.edu.

Web Site:  math.fau.edu/markus