Linear Algebra 2021

Instructor: Carson Mosso

Time:           1 PM – 3 PM
Place:           Online via Zoom
Dates:          Weekdays 8/2 – 8/13 (except 8/12)

TA and office hours

TA: Ben Brown
Time:           3 PM – 4 PM
Place:          Online via Zoom
Dates:         Weekdays 8/2 – 8/13 (except 8/12)

 

The Sakai page will be used for lecture notes, assignments, solutions, and general announcements.

2020 List of Topics:

  1. Day 1: High Level Review of Vector Space and Linear Transformations
  2. Day 2: Matrices as Representations of Linear Transformations, Jacobians, and Taylor Series
  3. Days 3-4: Orthogonal and Projection Matrices, Eigenvectors
  4. Days 5-7: QR and SVD
  5. Day 8: Computation
  6. Day 9: Relation to Statistics and Optimization
  • The purpose of Day 1 is to establish basic definitions and concepts, but also for us to all get used to the new format. Day 2 is to help view matrices as functions. One thing we have noticed is that not all students are as comfortable with matrices as functions or Taylor series. So we will use this opportunity to go through this is a unified way. Days 3-4 will help relate the abstract notion of linear transformations to how useful linear approximations can be in practice.
  • Starting on Day 5 we will try to dig into the details of numerical linear algebra that will be most useful to students. This will be done with as little assumptions as possible, in case students have not seen this before. Ideally this will really help students be prepared for their first year courses. Day 8 finishes this line of thought by discussing more computational aspects than mathematical aspects. Finally on day 9 we will relate everything back to statistics and optimization.
  • There will be no textbook for this course, please refer to the lecture notesThe notes might be updated from day to day.

(Old) Homework Assignments:

One set of problems will be assigned each day. Exercise numbers refer to the lecture notes.

Day 1: 2.1, 2.2, 2.7, 2.8

Day 2: 2.11, 5.2

Day 3: 3.1, 3.2, 3.3, 3.4, 3.6, 3.8

Day 4: 4.1, 4.2, 5.1, 6.1

Day 5: 6.4, 6.5, 6.6