Florida Atlantic University • Spring 2022 • Markus Schmidmeier
Linear Algebra II
Welcome to Linear Algebra II !
You are registered for MAS 4107, 3 credits, CRN: 17212. We meet Monday, Wednesday and Friday, 9:00 - 9:50 a.m. in-person in Sanson Life Science 178.
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).
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 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)
- 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
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:
Homework: I will assign homework problems every week. The problems will not be graded, but some may show up on a quiz. Please bookmark the link:
Quizzes: We will have a quiz every Friday; the best eleven quizzes count for 50 % of the grade.
Presentation: One presentation during class will count for 10 % of the grade. 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).
Final Exam: The final exam is comprehensive and will count for 40 % of your grade. It is scheduled for Friday, April 29, 7:45 - 10:15 a.m. in our classroom. Please bring a picture id (Owl card or drivers licence)!
For 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.
Office hours: MW 10:00 - 11:30 a.m. in SE 272.
Web Site: math.fau.edu/markus
Last modified: by Markus Schmidmeier