|Mondays & Wednesdays 2:00-3:40 p.m. TH 404
|Calculus I (Math 226 or equivalent); Proof & Exploration (Math 301) recommended as a concurrent course
|Dr. Matthias Beck
|Thornton Hall 933
|Mondays 4-5, Wednesdays 11-12, Fridays 2-3 & by appointment
Course objectives. Linear algebra is motivated by solving system of linear equations. Despite this simple starting point, linear algebra plays deep and profound roles in both applied and "pure" mathematics, as well as many other fields such as computer science, data analysis, the natural sciences, economics, any many more. Our course will start with systems of linear equations and techniques of finding their solutions based on row operations and Gaussian elimination. This will naturally lead us to matrix algebra operation and abstract vector space notions. Representation of linear transformations by matrices and change of basis will be introduced with an eye towards diagonalization, and inner products will be used as a gateway to symmetric positive (semi-)definite matrices. Eigenvalues and eigenvectors will be introduced with applications of diagonalization in mind. We will conclude with spectral decomposition/factorization of symmetric matrices and singular value decomposition and its applications.
Syllabus. Topics in this course will include:
Participation. A nontrivial part of the material covered in this class will be worked out in small groups during class sessions. It will thus be essential that every student participates actively in every class. If you have to miss a class due to a medical or family emergency, please let me know before the class; otherwise, I expect you to be in class and actively engaged.
Homework. I will assign homework problems as we go through the material. You may (and should) work together with your class mates. We can discuss the homework problems at any time during class, and you can hand any of your solutions for feedback. We will have a homework quiz every Wednesday at the beginning of class, in which you will be asked one definition and one problem given in the previous week.
Grading system & exam dates.
|Midterm Exam (March 18, in class)
|Final Exam (May 20, 2:45-4:45 p.m.)
I want to ensure that each of you accomplishes the goals of this course as comfortably and successfully as possible. At any time you feel overwhelmed or lost, please come and talk with me.
The math. The way to learn math is through doing math. It is vital and expected that you attend every class meeting. You will get a good feel for the math from there, but it is even more crucial that you do the homework. Working in groups is not only allowed but strongly recommended. Our class is based on Federico Ardila's Axioms:
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This syllabus is subject to change. All assignments, as well as other announcements on tests, policies, etc., are given in class. If you miss a class, it is your responsibility to find out what's going on. I will try to keep this course web page as updated as possible, however, the most recent information will always be given in class. Always ask lots of questions in class; my courses are interactive. You are always encouraged to see me in my office.