Lecture is Tuesday 6-9 pm in SF1105. Student-Instructor hours are Tuesday 3-5 pm in HU 10th floor lounge.
The final two lectures will take place online due to COVID-19 precautions. Virtual student-instructor hours are here, and lectures are here.
This is a second course in linear algebra; we revisit introductory linear algebra but with definitions and proofs, emphasizing concepts as well as computation.
This lecture section is given as a blend of traditional lecture and active learning style:
Lecture: The definitions, statements of results, and outlines of examples are given in the slides (linked below), while the proofs of results, and details of examples are done at the chalk board.
Discussion: After each group of new concepts is introduced, a set of discussion questions are posted.
Students are given around 10 minutes to work on the problems and discuss with eachother, and then solutions are presented at the chalk board;
this portion of the class follows the usual 'think-pair-share' paradigm of active learning.
Warning: The slides below represent only a small subset of the information dispersed in class.
We recommend attending every lecture and actively engaging during the discussion periods to maximize learning.
Slides:
Lecture 1 - Introduction, vector spaces, and subspaces
Lecture 2 - Linear combinations, span, and independence
Lecture 3 - Basis and dimension addendum
Lecture 4 - Linear transformations and matrices, kernel and image
Lecture 5 - Conceptual overview and the dimension theorem (rank-nullity)
Lecture 6 - Problem solving tips and review
Lecture 7 - Composition of linear maps, isomorphisms, and change of basis
Lecture 8 - The Determinant
Lecture 9 - Eigenvalues, eigenvectors, and diagonalization
Lecture 10 - Vector spaces over fields and triangular form
Lecture 11 - Nilpotent and Jordan canonical forms
Lecture 12 - Overview and computation of nilpotent and Jordan forms