Florida Atlantic University • Fall 2023 • Markus Schmidmeier

## Linear Algebra II

Welcome to Linear Algebra II !

You are registered for MAS 4107, CRN: 10757, or MAS 5145, CRN: 16239 (3 credits). We meet Mondays and Wednesdays, 4:00 - 5:20 p.m. in Sanson Life Science 119.

Linear algebra is the branch of mathematics which has developed from a theoretical study of the problem of solving systems of linear equations. This problem is one of the oldest in mathematics and is still of fundamental importance in other areas in mathematics and for applications to science and engineering.

The abstract approach in linear algebra and the rich variety of concepts arising from vector spaces relate to --- and help understand --- topics and results in modern pure mathematics.

Of course, linear algebra is essential in applications as well; its methods apply to calculus, differential equations, coding and cryptography. Linear algebra techniques, in particular visualization, play an important role in modern physics, engineering, computer animation and the social sciences (particularly economics).

PrerequisiteNone in particular, but mathematical maturity (proof writing) is expected.

Textbook and TopicsWe will use the book by Sheldon Axler,

Linear Algebra Done Right,third edition, Springer Nature, ISBN 978-3-319-30765-7.We are going to cover the following chapters:

- Brief review of vector spaces and their basic properties (Chapter 1, 1 week)
- Linear independence, span, basis and dimension for finite-dimensional vector spaces (Chapter 2, 2 weeks)
- Linear maps, null space and range (Chapter 3, 3 weeks)
- Some background on polynomials (Chapter 4, 1 week)
- Eigenvectors and eigenvalues (Chapter 5, 3 weeks)
- A glimpse into applications like Coding Theory and Cryptography (1 week)
- 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, 2 weeks)

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 (MLC) provides free academic support.

- Link to online tutoring
- In person tutoring in GS211 M-R 10-5, F 10-4
- Appointments for small group tutoring
- 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

CreditI will assign homework problems every week. The problems will not be graded, but some may show up on a quiz. Please bookmark the link:Homework:Homework Problems.

We will have a quiz everyQuizzes:Wednesday; the best eleven quizzes count for50 %of the grade.

One presentation during class will count forPresentation:10 %of the grade. Graduate students need to givetwopresentations. The last day for the presentation is November 15. Unless there are volunteers, I will assign presentations for the next class meeting (at random among all registered students who have not given a talk yet).

The final exam is comprehensive and will count forFinal Exam:40 %of your grade. It is scheduled for Wednesday, December 13, 4:00pm - 6:30pm in our classroom. Please bring a picture id (Owl card or drivers licence)!

Further InformationFor the Disability Policy, the Make-Up Policy, the Code of Academic Integrity, Religious Accommodation, my Grading Scale, the FAU Attendance Policy Statement, Financial Assistance Opportunities and the FAU Covid Statement please visit Infos for all my courses.

Contact Me

MW 10:00 - 11:20 a.m. in SE 272.Office hours:

561-297-0275Phone:

E-mail:markus@math.fau.edu.

cescos.fau.edu/markusWeb Site:

Last modified:by Markus Schmidmeier