Linear Algebra (Spring 2020)

Math 4050/8056

Linear algebra is extensively utilized in the mathematical modeling of many natural phenomena. Many scientific and engineering disciplines, such as data science, chemical engineering and biology, make extensive use of the theory and techniques commonly present in basic to advanced linear algebra courses. This course will be focused on the theory of vector spaces, inner product spaces, linear transformations, eigenvalues, canonical forms, complex vectors, matrices and orthogonality.

Textbook: Sheldon Axler, Linear Algebra Done Right 3rd Edition, Springer 2015.

Instructor: Dr. Ying Hu
Email: yinghu@unomaha.edu
Office: DSC223
Office Hours: 3 - 4 pm on MTWR over Zoom (see Zoom information below).

Course syllabus.

book cover

Class schedule

*Homework problems in [ ] are optional.

Week Sections HW Comments
#1 01/14: 1A, 1B, 1C
01/16: 1C, 2A, 2B 		Chp1: 1B: 1, 2, 5; 1C: 1, 4, 10;
due on Jan 21.
#2 01/21: 2B, 2C
01/22: 2C 		Chp2: 2A: 5, [14], [16]; 2B: 4, 6; 2C: [5], 11, 12, 16;
due on Jan 30.
#3 01/28: 3A
01/30: 3B		 3A: 1, [3], 4, 7; 3B: [5], 9, 12, 13;
due on Feb 6.
#4 02/04: 3C
02/06: 3D		 3C: 3, 14, Prove statement (3.43); 3D: 7, 10;
due on Feb 13		 Hints:
3C #3, 3D # 7, 10.
#5 02/10: 3D 3E
02/12: 3E 		3E: [1], 4, 5, 12, 13;
due on Feb 20		 Hints:
3E #4, #5 without assuming
vector spaces are finite dim.
#6 02/18: 3F
02/20: 3F		 3F: Duality - definition: 1, 3, [8], 9, 13;
due on Feb 2		 Additional problems:
Duality - properties: 5, [12], [15], 16
Annihilator: 17, 20, 21, 22, 23
Dual basis: [31]
The dual space of the dual space: [34].
#7 02/24: 3F
02/27: Midterm.
Midterm exam covers chapters 1 - 3.
#8 03/03: 5A
03/05: 5B		 5A: [7], 8, 15, [16], [21]; due on March 05.
5B: 2, 4; due on March 10. 		Hints: 5A #15.
#9 03/10: 5C
03/12: 8A 		8A: 1, 2, 3;
due on March 30		 Final presentation topic March 15
Hints: 8A #3.
#10 No class Spring Break
#11 No class Spring Break
#12 03/31: 8B
04/02: 8B 		8B: 1, 2, 3
due on Tuesday April 7		 week12 class note
Hints: 8B #3
#13 04/07: 8D
04/09: 8C 		8C:3,4,5,6 (Examples should be in Jordan normal form.); 8D:1,2
due on Tuesday April 14 		week13 8D class note
week13 8C class note
#14 04/14: 10A
04/16: 10A10B 		10A: [9], 13; 10B: Prove statements (10.23) and (10.24)
due on Thursday April 23 		week14 9A 10A class note
week14-15 10A10B class note
Hints: 10B (10.24)
#15 04/21: 10B
04/23: 6A
6A: [13], [31] 		week14-15 10A10B class note
summary
week15 6A class note
#16 04/28: 6B;
04/30: Group presentations 		6B: [4,5]
week16 6B class note
#17 05/05: Final exam; 5:00 pm - 7:00 pm

Group Presentations: Applications of linear algebra

The group presentations are scheduded during the prep week of the semester over Zoom. We will have about 15 - 20mins for each group.

#1 David, Dongyue, Prakash Leontief input-output model
#2 Bibek, Jacob, Kamryn Neural networks
#3 Brian, Joel, Max Principal component analysis
#4 Alec, Matt, Nicolas Linear programming
#5 Conner, Liam Vibrational eigenmodes
#6 Bryan, Christopher, Trevor Boolean network, STP