 Welcome to choose this class!
 For any questions regarding enrollment, please contact Prof. Ettinger: bree.d.ettinger@emory.edu.
 There is no class meeting on Monday April 12th due the rest day of the week.
 Contacts
 Course description
 Textbook
 Coverage
 Prerequisite
 Learning outcomes
 Students obligations
 Homework
 Midterm tests
 Due dates for homework and tests
 Final exam
 Attendance
 Assessment
 Text and slides
 Tentative schedule
 Gradescope
 Feedback
 Netiquette
 Honor code
 Accessibility
 Harassment
 Some fun links
 Acknowledgement
Lecture Instructor  Dr. Le Chen 
Lab Instructor  Xingjian Li 
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 Math2211 and 11:20AM  12:10PM for Math2212 
Zoom link for class  https://emory.zoom.us/j/94863155226?pwd=NjducFE0b3hFQ2V0MVYxVXptS2Rxdz09 
 The password for both Zoom links are on Canvas page.
 The Zoom link for class is for all synchronous/lab sessions, office hours, and independent appointments.

When you send us emails, please do include the keyword
Math221
in the subject field of your email to ensure a timely response.
_{(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 GramSchmidt process are examined. At the end of the class, you will understand how google ranks web pages.
We will use the following online book which is free to download:
Original Textbook  Customized Textbook  

Bookcover  
For a hard copy  https://lyryx.com/linearalgebraapplications/  
Download  NicholsonOpenLAWA2019A.pdf  Adapted_Textbook_Math2211_2_EmorySpring2021.pdf 
Edition  2019 Revision A  Check the date on the front page in red 
 We will update the adapted textbook throughout the semester; please double check the date on the front page in the red color for versions.
The book consists of eleven chapters, we will cover most parts of the first eight chapters:
 Chapter 1. Systems of Linear Equations.
 Chapter 2. Matrix Algebra
 Chapter 3. Determinants and Diagonalization
 Chapter 4. Vector Geometry
 Chapter 5. Vector Space \(\mathbb{R}^n\)
 Chapter 6. Vector Spaces
 Chapter 7. Linear Transformations
 Chapter 8. Orthogonality

Chapter 9. Change of Basis 
Chapter 10. Inner Product Spaces 
Chapter 11. Canonical Forms
 Six hours of AP BC credit, or
 Math 12 or 112Z
By the end of this course, students will be able to
 Solve system of linear equations, perform matrix operations, find the inverse of a matrix, check vectors for linear independence.
 List the vector space properties for \(\mathbb{R}^n\), give examples of subspaces, find bases for subspaces, find its dimension, find orthogonal bases for subspaces, identify linear transformations.
 Find eigenvalues and eigenvectors, determinants, characteristic polynomial, perform diagonalization of a matrix.
 Give examples of vector spaces, check for linear independence, find bases, dimension, identify linear transformations and find matrix representation for linear transformations.
In order to successfully master the material and complete the course, you are expected to
 Read the textbook and watch video posted on Canvas.
 Take the advantage of the lab session and office hours, which give you additional chance to interact lively with the instructors.

Since problems solved or question/answers in the office hour will be beneficial to other students, be default the office hours will be recorded automatically.
In case you do not want put the office hours on Canvas, please let me know.  Attend weekly Zoom class meeting and weekly lab session, and watch video recordings for the asynchronous materials.
 Participate actively in group activities during Zoom meetings.
 Complete and submit weekly homework through Gradescope.
 Read solutions and any feedback you receive for each problem set.
 Complete three midterm tests and one final exam.
 Use appropriate etiquette and treat other students with respect in all discussions.
 Do not hesitate to ask for help whenever needed.
Note: The syllabus was created in Nov. 2020, and it is subject to changes during the semester.
 There will be roughly thirteen weekly homework assignments scheduled as follows:
Releasing  Due at 

Monday 6:00pm EST  Friday, 6pm EST 
 No late homework will be accepted.

The homework consists two phases:

In Phase I, you need to complete questions on canvas.
 You will have two attempts, and the best score will be recorded.
 There is no time limit on Phase I. But be mindful that by the deadline line, the unfinished quiz will be automatically submitted by the system.
 In Phase II, you need to write details of your solutions and upload them to gradescope.

In Phase I, you need to complete questions on canvas.

The lowest grade will be dropped, that is, the final score for the homework will be averaged over the rest HWs.

Note that the drop policy is not a bonus. It aims at accounting for all circumstances
such as sickness, injuries, family emergencies, religion holidays, etc.

Note that the drop policy is not a bonus. It aims at accounting for all circumstances
 There will be three midterm tests starting from the following three Fridays.
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 

Please note down the above three dates. The setup has taken into account of different time zones.
Hence, no late exam and further extension will be given. 
The test consists two phases:
 In Phase I, you need to complete questions on canvas.
 In Phase II, you will have 24 hours to complete takehome problems and upload your solutions to Gradescope.

Unlike the homework, the phase I of tests will have a time limit of 60 minutes:
 Once it is started, please do complete it in 60 minutes.
 Make sure your start before 5pm of the second day.
 At 6pm your ongoing quiz will be automatically submitted by the system.
 You will have two attempts and the best score will be counted as your test score.
 Test one covers Sections 1.11.3 and 2.12.7.
 PhaseI will consist of 5 choiceproblems on Canvas Quiz: Two from Chapter 1 and three from Chapter 2. There are \(5\times 12=60\) points.
 PhaseII consists of three problems: all from Chapter 2. There are \(10+20+10=40\) points.
 Here are a list of due dates for 12 homeworks and three tests (the Phase II part).
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 will be cumulative, which covers Chapters 18.
 It will be in a similar form as the midterm tests, namely, you will have two phases.

Exam will be released on May 6th Thursday at 8am EST and be due on May 7th Friday at 8am EST.
You need to complete both Phases in 24 hours. 
For Phase I, once you start, you will have only 150 minutes to complete.
There will be two attempts and the best one will be recorded.
There will be 15 problems and 5 points for each problem: \(5\times 15=75\) points.
There will be one bonus problem in Phase I. So do not be surprised to see 16 problems.
If you score 80 in Phase I, it will be counted as 75.
You will have two attempts and the highest attempt will be recorded. 
Phase II consists of two randomized problems, 25 points in total.
At around 7:50am on May 6th EST, the phase II part will be sent out by email.
You need to upload your solutions to Gradescope by May 7th 8am EST.
 The attendance will be collected during Zoom automatically.
 Attendance will not directly counted into your final score.
 But sufficient attendance will make your eligible for grade curving at the end of semester.
 The final score will be determined as follows:
 Based on the final score (plus potential bonus points), the final letter grade will be determined as follows:
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% 
 Since we will have scores in both Canvas and Gradescope, you are encouraged to can download this spread sheet to keep track of your progress.
 You can download text for each chapter or section below.
 Slides will be updated constantly throughout the semester and please check the time stamp on the front page.
 The application parts of each chapter will be skipped due to lack of time. However, the materials are given for motivated students to study.
Chapter/Section  Textbook  Slides  

Chapter 1. Systems of Linear Equations  original text  adapted text  
Section 11. Solutions and Elementary Operations  original text  adapted text  presentation  handout 
Section 12. Gaussian Elimination  original text  adapted text  presentation  handout 
Section 13. Homogeneous Equations  original text  adapted text  presentation  handout 

original text  

original text  presentation  handout  

original text  presentation  handout  
Section 1S. Supplementary Exercises for Chapter 1  original text  adapted text  
Chapter 2. Matrix Algebra  original text  adapted text  
Section 21. Matrix Addition and Scalar Multiplication and Transportation  original text  adapted text  presentation  handout 
Section 22. MatrixVector Multiplication  original text  adapted text  presentation  handout 
Section 23. Matrix Multiplication  original text  adapted text  presentation  handout 
Section 24. Matrix Inverses  original text  adapted text  presentation  handout 
Section 25. Elementary Matrices  original text  adapted text  presentation  handout 
Section 26. Linear Transformations  original text  adapted text  presentation  handout 
Section 27. LUFactorization  original text  adapted text  presentation  handout 

original text  

original text  presentation  handout  
Section 2S. Supplementary Exercises for Chapter 2  original text  adapted text  
Chapter 3. Determinants and Diagonalization  original text  adapted text  
Section 31. The Cofactor Expansion  original text  adapted text  presentation  handout 
Section 32. Determinants and Matrix Inverses  original text  adapted text  presentation  handout 
Section 33. Diagonalization and Eigenvalues  original text  adapted text  presentation  handout 

original text  presentation  handout  

original text  
Section 36. Proof of the Cofactor Expansion Theorem  original text  adapted text  
Section 3S. Supplementary Exercises for Chapter 3  original text  adapted text  
Chapter 4. Vector Geometry  original text  adapted text  
Section 41. Vectors and Lines  original text  adapted text  presentation  handout 
Section 42. Projections and Planes  original text  adapted text  presentation  handout 
Section 43. More on the Cross Product  original text  adapted text  presentation  handout 
Section 44. Linear Operators on R3  original text  adapted text  presentation  handout 

original text  
Section 4S. Supplementary Exercises for Chapter 4  original text  adapted text  
Chapter 5. Vector Space Rn  original text  adapted text  
Section 51. Subspaces and Spanning  original text  adapted text  presentation  handout 
Section 52. Independent and Dimension  original text  adapted text  presentation  handout 
Section 53. Orthogonality  original text  adapted text  presentation  handout 
Section 54. Rank of a Matrix  original text  adapted text  presentation  handout 
Section 55. Similarity and Diagonalization  original text  adapted text  presentation  handout 

original text  

original text  adapted text  
Section 5S. Supplementary Exercises for Chapter 5  original text  adapted text  
Chapter 6. Vector Spaces  original text  adapted text  
Section 61. Examples and Basic Properties  original text  adapted text  presentation  handout 
Section 62. Subspaces and Spanning Sets  original text  adapted text  presentation  handout 
Section 63. Linear Independence and Dimensions  original text  adapted text  presentation  handout 
Section 64. Finite Dimensional Spaces  original text  adapted text  presentation  handout 

original text  

original text  
Section 6S. Supplementary Exercises for Chapter 6  original text  adapted text  
Chapter 7. Linear Transformations  original text  adapted text  
Section 71. Examples and Elementary Properties  original text  adapted text  presentation  handout 
Section 72. Kernel and Image of a Linear Transformation  original text  adapted text  presentation  handout 
Section 73. Isomorphisms and Composition  original text  adapted text  presentation  handout 

original text  

original text  
Chapter 8. Orthogonality  original text  adapted text  
Section 81. Orthogonal Complements and Projections  original text  adapted text  presentation  handout 
Section 82. Orthogonal Diagonalization  original text  adapted text  presentation  handout 
Section 83. Positive Definite Matrices  original text  adapted text  presentation  handout 
Section 84. QRFactorization  original text  adapted text  presentation  handout 
Section 85. Computing Eigenvalues  original text  adapted text  presentation  handout 
Section 86. The Singular Value Decomposition  original text  adapted text  presentation  handout 

original text  

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 Below is the tentative schedule that may change during the semester:
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 

We will use Gradescope to handle submissions of homework, takehome tests and exams,
which allows us to provide fast and accurate feedback on your work. 
As soon as grades are posted, you will be notified immediately so that you can log in and see your
grades and feedback. 
Your Gradescope login is your university email, and your password can be changed there. The same
link can be used if you need to set your password for the first time. You should have received an email from Gradescope for the registration by 20210123.

If you do not receive this email, please use the Entry Code to register yourself:
BPPGR4
.
 If you have any questions regarding Gradescope, please send your message to

Printer+scanner or tablet

The easiest way to submit the homework/tests/exams is the following steps:
 print the given template;
 complete the problem sets;
 scan the resulting paper (make sure it is legible);
 upload the scanned file to gradescope.

Alternatively, if you have a tablet that you can write on it, you may simply write on the
template pdf file and upload the resulting file.  Make sure that you make the correct association of your solutions to the problems.
 Double check your scan quality and make sure your solutions are legible.

The easiest way to submit the homework/tests/exams is the following steps:

The following short video (1 minutes 40 seconds) shows the basic usage of gradescope, which should
explain everything you need to be able to do.
 More instruction will be available towards the fall 2020.
 Your feedbacks are important for us to improve the teaching and make the learning process more effective and enjoyable.

Here are two ways that you could let me know what your think:
 You may send me an email.
 If you want to send me some feedback in an anonymous way, you may fill in the following form:
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:
 You should read and follow Rasmussen College's 10 Netiquette guidelines every online students needs to know.
 If you need extra accommodations, please contact the instructor as soon as possible.
 You are encouraged to login Zoom in time (preferably one or two minutes early) and stay until the end.

During the zoom class session,
 please silence all cell phones and other electronic devices;
 Please do not read email or look at websites, social media, etc;

please actively participate in the zoom class meeting:
 You are highly encouraged to ask and answer questions.

You should also expect that I randomly pick students to help me solve exercises
and/or answer specific questions. 
There will be Zoom Poll from time to time:
You need to response the questions during Zoom Sessions to justify your active attendance.
 Students should familiarize themselves with the Emory College honor code here

Students are encouraged to share ideas and solutions on problem sets and labs, but must
express those ideas in their own words in their submitted work.  Students are not authorized to view or use the work of another student during exams.
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:
 According to the Emory University policies: http://policies.emory.edu/1.3
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.
 Why study linear algebra?
 Fun Linear Algebra Problems
 An Intuitive Guide to Linear Algebra
 The $25,000,000,000 eigenvectorthe linear algebra behind Google
 The page is powered by VimWiki.
 Both textbook and slides are shared under Creative Common licences (CC BYNCSA).