Spring 2018: Linear Algebra

Organization

Prerequisite: Calculus III or equivalent (vectors and coordinates in 2 and 3 dimensions, equations of lines and planes).

Textbook: Linear Algebra with Applications, 5th Edition, Otto Bretscher, ISBN-13: 9780321796974. You may work with the 4th edition but the references of HW exercises would not be correct, so you would have to check the exercises numbers on the fifth edition at the library.

Lectures:
Section 2: Monday-Wednesday 10:10am -- 11:25am, Room 203 Math building.
Section 3: Monday-Wednesday 1:10pm -- 2:25pm, Room 207 Math building.

Office hours: Monday-Wednesday 3:00 -- 4:00 Math 625


Homework: Due each Monday at 1:10pm. Late homework will not be accepted, but the two lowest homework scores will be dropped. Written homework need to be turned in the Math building 4th floor (in the appropriate box outside room 410 according to your section). Graded works will be left in a basket in front of office 625. Collaboration and discussion with your classmates is encouraged, but you must write up your final answers by yourself.

Grading: Homework: 15%, Midterm 1: 20%, Midterm 2: 20%, Final Exam:45%.

Exams: The use of course material, notes or calculators is not allowed during exams. In case of a scheduling conflict, please contact me at least one week ahead. If you are unable to take the exam because of a medical problem, please contact me as soon as you can-- you will need a medical note, as well as a note from your dean.

Course assistants

Section 2 Section 3 Each TA will hold office hours according to the math help room schedule. You may ask your questions to a TA of Section 2 or 3, the homeworks are the same in both sections.

Syllabus/Homework

Date Topic Chapters Homework Due Date
Jan. 17 Introduction, matrices, vectors, linear systems 1.1--1.2 Read 1.1, 1.2 Jan. 22
Jan. 22 Number of solutions of a linear system 1.3 HW 1 Jan. 29
Jan. 24 Introduction to linear transformations 2.1
Jan. 29 Linear transformations: geometric aspects 2.2--2.3 HW 2 Feb. 5
Jan. 31 Matrices: elementary properties 2.3--2.4
Feb. 5 Image and kernel 3.1 HW 3 Feb.12
Feb. 7 Subspaces, bases and linear independence 3.1--3.2
Feb. 12 Review Practice midterm 1 Read 3.3 Feb. 19
Feb. 14 Midterm 1
Feb. 19 Dimension of a vector space 3.3 HW 4 Feb. 26
Feb. 21 Coordinates 3.4
Feb. 26 Linear Spaces 4.1 HW 5 Mar. 5
Feb. 28 Linear transformations between spaces, isomorphisms 4.2--4.3
Mar. 5 Orthogonal projections and bases, Gram-Schmidt process 5.1 HW 6 Mar. 19
Mar. 7 Orthogonal transformations and matrices 5.2.--5.3
Mar. 12
Spring Break
Mar. 14
Spring Break
Mar. 19 Least squares 5.3--5.4 HW 7 Mar. 26
Mar. 21 Inner product spaces 5.5
Mar. 26 Review Practice midterm 2 Read 6.1 Apr. 2
Mar. 28 Midterm 2
Apr. 2 Determinants 6.1 HW 8 Apr. 9
Apr. 4 More about determinants 6.2 -- 6.3
Apr. 9 Diagonalization 6.3--7.1 HW 9 Apr. 16
Apr. 11 Finding eigenvalues 7.2
Apr. 16 Finding eigenvectors 7.3--7.4 HW 10 Apr. 23
Apr. 18 Complex eigenvalues 7.5
Apr. 23 Symmetric matrices 8.1 HW 11 Apr. 30
Apr. 25 More examples
Apr. 30 Review Practice final exam (exam of last year), Other practice final exam
May Final Exam (Section 2: May 9 09:00am -- 12:00pm, Math 203. Section 3: May 7 01:10pm -- 4:00pm, Math 207. )