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MATH 221: Linear Algebra

2021 Spring, Emory University


Contacts

Lecture Instructor Dr. Le Chen
Lab Instructor Xingjian Li
Email le.chen@emory.edu, xingjian.li@emory.edu (please include "Math 221" in the subject field of your email)
Synchronous Session Monday 11:20AM -- 12:35PM
Office hours Monday and Wednesday 1:00pm -- 2:00pm, or by appointments
Lab Sessions Friday, 9:40AM -- 10:30AM for Math221-1 and 11:20AM -- 12:10PM for Math221-2
Zoom link for class https://emory.zoom.us/j/94863155226?pwd=NjducFE0b3hFQ2V0MVYxVXptS2Rxdz09

Course description

(Image from Wikipedia)

Linear algebra is a branch of mathematics concerning linear equations such as \(a_1 x_1 + \cdots + a_n x_n = b\), linear maps such as \((x_1,\cdots,x_n) \mapsto a_1x_1 + \cdots + a_n x_n\), and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. It is also used in most sciences and engineering areas.

This course begins with the definition of a matrix and some fundamental operations that can be performed on matrices, such as adding or multiplying two matrices together. Vector spaces are also introduced. A connection is then formed by modeling vector spaces using matrices. Advanced topics involving matrices, such as diagonalization and quadratic forms, eigenvalues and eigenvectors, orthogonalization, and the Gram-Schmidt process are examined. At the end of the class, you will understand how google ranks web pages.

Textbook

We will use the following online book which is free to download:

  Original Textbook Customized Textbook
Bookcover
For a hard copy https://lyryx.com/linear-algebra-applications/  
Download Nicholson-OpenLAWA-2019A.pdf Adapted_Textbook_Math221-1_2_Emory-Spring2021.pdf
Edition 2019 Revision A Check the date on the front page in red

Coverage

The book consists of eleven chapters, we will cover most parts of the first eight chapters:

Prerequisite

Learning outcomes

By the end of this course, students will be able to

Students obligations

In order to successfully master the material and complete the course, you are expected to


Note: The syllabus was created in Nov. 2020, and it is subject to changes during the semester.


Homework

Releasing Due at
Monday 6:00pm EST Friday, 6pm EST

Midterm tests

  Releasing at Due at Coverage
Test I 02/12/2021, 6pm EST 02/13/2021, 6pm EST Chapters 1 & 2
Test II 03/05/2021, 6pm EST 03/06/2021, 6pm EST Chapters 3 & 4
Test III 04/02/2021, 6pm EST 04/03/2021, 6pm EST Chapters 5 & 6
Final Exam 05/06/2021, 8am EST 05/07/2021, 8am EST Chapters 1 -- 8, comprehensive
Details about Test I
  1. Test one covers Sections 1.1--1.3 and 2.1--2.7.
  2. Phase-I will consist of 5 choice-problems on Canvas Quiz: Two from Chapter 1 and three from Chapter 2. There are \(5\times 12=60\) points.
  3. Phase-II consists of three problems: all from Chapter 2. There are \(10+20+10=40\) points.

Due dates for homework and tests

  Monday Friday Saturday
Week 1 01/25 HW01 releases at 6pm EST 01/29 HW01 due at 6pm EST      
Week 2 02/01 HW02 releases at 6pm EST 02/05 HW02 due at 6pm EST      
Week 3 02/08 HW03 releases at 6pm EST 02/12 HW03 due at 6pm EST Test I releases at 6pm EST 02/13 Test I due at 6pm
Week 4 02/15 HW04 releases at 6pm EST 02/19 HW04 due at 6pm EST      
Week 5 02/22 HW05 releases at 6pm EST 02/26 HW05 due at 6pm EST      
Week 6 03/01 HW06 releases at 6pm EST 03/05 HW06 due at 6pm EST Test II releases at 6pm EST 03/06 Test II due at 6pm
Week 7 03/08 HW07 releases at 6pm EST 03/12 HW07 due at 6pm EST      
Week 8 03/15   03/19       (no assignment week)
Week 9 03/22 HW08 releases at 6pm EST 03/26 HW08 due at 6pm EST      
Week 10 03/29 HW09 releases at 6pm EST 04/02 HW09 due at 6pm EST Test III releases at 6pm EST 04/03 Test III due at 6pm
Week 11 04/05 HW10 releases at 6pm EST 04/09 HW10 due at 6pm EST      
Week 12 04/12 HW11 releases at 6pm EST 04/16 HW11 due at 6pm EST      
Week 13 04/19 HW12 releases at 6pm EST 04/23 HW12 due at 6pm EST      
Week 14 04/26 Review Session          

Final exam

Attendance

Assessment

Grade (+) Grade Grade (-)
    A 92%-100% A- 90%-91.9%
B+ 87%-89.9% B 82%-86.9% B- 80%-81.9%
C+ 77%-87.9% C 72%-76.9% C- 70%-71.9%
D+ 67%-67.9% D 67%-67.9% D- 60%-61.9%
    F 0%-59.9%    

Text and slides

Chapter/Section Textbook Slides
Chapter 1. Systems of Linear Equations original text adapted text    
Section 1-1. Solutions and Elementary Operations original text adapted text presentation handout
Section 1-2. Gaussian Elimination original text adapted text presentation handout
Section 1-3. Homogeneous Equations original text adapted text presentation handout
Section 1-4. An Application to Network Flow original text      
Section 1-5. An Application to Electrical Network original text   presentation handout
Section 1-6. An Application to Chemical Reactions original text   presentation handout
Section 1-S. Supplementary Exercises for Chapter 1 original text adapted text    
Chapter 2. Matrix Algebra original text adapted text    
Section 2-1. Matrix Addition and Scalar Multiplication and Transportation original text adapted text presentation handout
Section 2-2. Matrix-Vector Multiplication original text adapted text presentation handout
Section 2-3. Matrix Multiplication original text adapted text presentation handout
Section 2-4. Matrix Inverses original text adapted text presentation handout
Section 2-5. Elementary Matrices original text adapted text presentation handout
Section 2-6. Linear Transformations original text adapted text presentation handout
Section 2-7. LU-Factorization original text adapted text presentation handout
Section 2-8. An Application to Input-Output Economic Model original text      
Section 2-9. An application to Markov Chains original text   presentation handout
Section 2-S. Supplementary Exercises for Chapter 2 original text adapted text    
Chapter 3. Determinants and Diagonalization original text adapted text    
Section 3-1. The Cofactor Expansion original text adapted text presentation handout
Section 3-2. Determinants and Matrix Inverses original text adapted text presentation handout
Section 3-3. Diagonalization and Eigenvalues original text adapted text presentation handout
Section 3-4. An Application to Linear Recurrences original text   presentation handout
Section 3-5. An Application to Systems of Differential Euqations original text      
Section 3-6. Proof of the Cofactor Expansion Theorem original text adapted text    
Section 3-S. Supplementary Exercises for Chapter 3 original text adapted text    
Chapter 4. Vector Geometry original text adapted text    
Section 4-1. Vectors and Lines original text adapted text presentation handout
Section 4-2. Projections and Planes original text adapted text presentation handout
Section 4-3. More on the Cross Product original text adapted text presentation handout
Section 4-4. Linear Operators on R3 original text adapted text presentation handout
Section 4-5. An Application to Computer Graphics original text      
Section 4-S. Supplementary Exercises for Chapter 4 original text adapted text    
Chapter 5. Vector Space Rn original text adapted text    
Section 5-1. Subspaces and Spanning original text adapted text presentation handout
Section 5-2. Independent and Dimension original text adapted text presentation handout
Section 5-3. Orthogonality original text adapted text presentation handout
Section 5-4. Rank of a Matrix original text adapted text presentation handout
Section 5-5. Similarity and Diagonalization original text adapted text presentation handout
Section 5-6. Best Approximation and Least Squares original text      
Section 5-7. An Application to Correlation and Variance original text adapted text    
Section 5-S. Supplementary Exercises for Chapter 5 original text adapted text    
Chapter 6. Vector Spaces original text adapted text    
Section 6-1. Examples and Basic Properties original text adapted text presentation handout
Section 6-2. Subspaces and Spanning Sets original text adapted text presentation handout
Section 6-3. Linear Independence and Dimensions original text adapted text presentation handout
Section 6-4. Finite Dimensional Spaces original text adapted text presentation handout
Section 6-5. An Application to Polynomials original text      
Section 6-6. An Application to Differential Equations original text      
Section 6-S. Supplementary Exercises for Chapter 6 original text adapted text    
Chapter 7. Linear Transformations original text adapted text    
Section 7-1. Examples and Elementary Properties original text adapted text presentation handout
Section 7-2. Kernel and Image of a Linear Transformation original text adapted text presentation handout
Section 7-3. Isomorphisms and Composition original text adapted text presentation handout
Section 7-4. A Theorem about Differential Equations original text      
Section 7-5. More on Linear Recurrences original text      
Chapter 8. Orthogonality original text adapted text    
Section 8-1. Orthogonal Complements and Projections original text adapted text presentation handout
Section 8-2. Orthogonal Diagonalization original text adapted text presentation handout
Section 8-3. Positive Definite Matrices original text adapted text presentation handout
Section 8-4. QR-Factorization original text adapted text presentation handout
Section 8-5. Computing Eigenvalues original text adapted text presentation handout
Section 8-6. The Singular Value Decomposition original text adapted text presentation handout
Section 8-7. Complex Matrices original text      
Section 8-8. An Application to Linear Codes over Finite Fields original text      
Section 8-9. An Application to Quadratic Forms original text      
Section 8-10. An Application to Constrained Optimization original text      
Section 8-11. An Application to Statistical Principal Component Analysis original text      

Tentative schedule

  Monday -- Friday Coverage
Week 1 01/25 -- 01/29 1.1 -- 1.3
Week 2 02/01 -- 02/05 2.1 -- 2.4
Week 3 02/08 -- 02/12 2.5 -- 2.7 (Test I)
Week 4 02/15 -- 02/20 3.1 -- 3.2
Week 5 02/22 -- 02/27 3.3
Week 6 03/01 -- 03/05 4.1 -- 4.3 (Test II)
Week 7 03/08 -- 03/12 5.1 -- 5.2, 5.4
Week 8 03/15 -- 03/19 5.3 and 5.5 (no assignment week)
Week 9 03/22 -- 03/26 6.1 -- 6.2
Week 10 03/29 -- 04/02 6.3 -- 6.4 (Test III)
Week 11 04/05 -- 04/09 7.1, 8.1 -- 8.2
Week 12 04/12 -- 04/16 8.3 -- 8.4 (Rest day on Monday)
Week 13 04/19 -- 04/23 7.2 -- 7.3, 8.6
Week 14 04/26 Reviewing week

Gradescope


Feedback


Netiquette

Not all forms of communication found online are appropriate for an academic community or respectful of others. In this course (and in your professional life that follows), you should practice appropriate etiquette online (``netiquette''). Here are some guidelines:

Honor code

Accessibility

Your success in this class is important to me. We will all need accommodations because we all learn differently. If there are aspects of this course that prevent you from learning or exclude you, please let me know as soon as possible. Together we’ll develop strategies to meet both your needs and the requirements of the course.

I encourage you to visit the Office of Accessibility Services (OAS) to determine how you could improve your learning as well. You can register and make a request for services from OAS. In this case, please do inform me of such requests. See the following link for more information:

Harassment

Discriminatory harassment of any kind, whether it is sexual harassment or harassment on
the basis of race, color, religion, ethnic or national origin, gender, genetic
information, age, disability, sexual orientation, gender identity, gender expression,
veteran’s status, or any factor that is a prohibited consideration under applicable law,
by any member of the faculty, staff, administration, student body, a vendor, a contractor,
guest or patron on campus, is prohibited at Emory.
  1. Why study linear algebra?
  2. Fun Linear Algebra Problems
  3. An Intuitive Guide to Linear Algebra
  4. The $25,000,000,000 eigenvectorthe linear algebra behind Google

Acknowledgement


© Le Chen, Emory, 2021.