Math 423, Spring 2023: Linear Algebra II

Meeting: T-Th 2:20-3:35 BLOC  160  

Office hours: Mon. 1-2pm, Wed. 1-2pm or by appointment


 
Instructor: Joseph (JM) Landsberg
office 601H.

  E-mail: jml@math.tamu.edu please include "423" in the subject line when emailing me
 

my cv


Textbook:

  1. Linear Algebra Done Right, Axler, third edition, Springer

Videos made by Axler of the content of the book


Course Description

This is a continuation of Math 323 (Linear Algebra).


Course Prerequisites


MATH 300 or CSCE 222/ECEN 222; MATH 304 or MATH 323, or approval of instructor.




Course Learning Outcomes

You will learn both the practical and theoretical aspects of linear algebra. Linear algebra is vital for nearly all scientific computation and you will learn techniques for such computations. The course has a central theoretical component which develop your skills in rigorous mathematical reasoning.


Grading Policy


  • In class exams

  • 15% each for a total of 45%

  • tentative exam dates: 2/9, 3/9, 4/20

  • Final Exam

  • 20%

  • May 9, 1-3pm

  • Weekly Homework Assignments

  • 35%: Generally due in class on Tuesday each week

  • Total:

  • 100%
  
Honors project: 
Homework will be assigned each week. Tests

Additional resource from the author, slides and videos: https://linear.axler.net/LADRvideos.html

 

Homework

Due Tues. 1/24: 1A: 1, 1B: 3,5, 1C: 1a,1b,3,4,10,19,20,24. Honors problem: show that our three descriptions of the complex numbers in class agree in the sense that there are bijective set maps between them that preserve addition and multiplication.


Due Tues. 1/31: 2A: 3,9,16,17, 2B: 3,5,6,8. Honors problem, click here.


Due Tues. 2/7: 2C: 4,8,9,12,14, 3A: 1,2,4,7,10. Honors problems: 1. Find a basis of L(F^n,F^m), the space of linear maps from F^n to F^m. In particular, determine its dimension. 2. Let L(U,V:W) denote the set of bilinear maps from UxV to W, that is, if f is in L(U,V:W), then for all u in U, f(u, -) is a linear map from V to W and for all v in V, f(-,v) is a linear map from U to W. Show L(U,V:W) is a vector space and compute its dimension in terms of dim(U),dim(V),dim(W).

Due Tues. 2/14: 3B 4,11,19,20,29. Honors problem: Show that there is a natural (i.e., independent of choices) injective linear map from the vector space V into the vector space L(L(V,F),F), the space of linear maps from {linear maps V-> F)} to F.

Due Tues. 2/21: 3C 2,4,5,11 plus these problems

Due Tues. 2/28 3D: 2,7,16, 3E: 8,9,11,15,16, honors question

Due Tues. 3/7: 3E: 20, 3F: 4,6,8,11,16,21,28,32, honors question

Due THURSDAY 3/30 5A: 7,12,15,20,21,26,29,35. Honors students: hand in a summary of your progress so far on your project (hand in separately from regular homework).

Due Tues. 4/11: 5B:1a,2,4,5,11, 5C: 1,6,7,16

Due Tues. 4/25: 8A: 4,5,10,16,20, 8B: 1,8,10,11

TAMU policy statements
Academic integrity
The Aggie Honor Code states: “An Aggie does not lie, cheat or steal, or tolerate those who do.” Information about the Honor Council Rules and Procedures can be found at the website of the Aggie Honor System Office.
Americans with Disabilities Act (ADA) 
This federal antidiscrimination statute provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services in Room B118 of Cain Hall, or call 979-845-1637. For additional information visit the website of Disability Services.
Attendance
See Student Rule 7.

 


Grade complaints: If you think a homework  was graded incorrectly you
have one week from the time the graded assignment was returned to you to bring the
issue to the instructor's attention. No complaints after that time will be considered.
  
 
 
Policy regarding absences related to injury or illness: All such absences will be excused
if sufficient documentation is provided as per University policy and
the instructor will help the student make up any missed material.
 

Americans with Disabilities Act (ADA) Policy Statement

The following ADA Policy Statement (part of the Policy on Individual Disabling Conditions) was submitted to the University Curriculum Committee by the Department of Student Life. The policy statement was forwarded to the Faculty Senate for information.

The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services, currently located in the Disability Services building at the Student Services at White Creek complex on west campus or call 979-845-1637. For additional information, visit http://disability.tamu.edu.

Academic Integrity Statement

“An Aggie does not lie, cheat, or steal or tolerate those who do.” All syllabi shall contain a section that states the Aggie Honor Code and refers the student to the Honor Council Rules and Procedures on the web http://www.tamu.edu/aggiehonor