Linear Algebra Spring 2024
with Prof Sormani (Playlist about Myself)
MAT313 Elements of Linear Algebra: 4 hours, 4 credits. Vector spaces, systems of linear equations, determinants, linear transformations, and matrices. PREREQ: MAT 176. With Departmental permission, MAT 176 may be taken as a COREQ.
Course Website: with links to all lessons and videos:
https://sites.google.com/site/professorsormani/home/teaching/linalg-s24
Linear Algebra Welcome: Video Playlist
This is an Asychronous Course so students may watch the lessons and do homework at any time of day completing two lessons per week meeting the deadlines on the schedule below. This is a four credit course so each lesson has two hours of videos and up to four hours of homework. Students need a tablet, smart phone, or computer with a camera to photograph their classwork/homework and a google account to access googledocs and youtube. Lehman College can provide a loaner tablet. Graph paper and pens of various colors are needed. No textbook is required because every lesson has detailed notes.
Please email me at sormanic@gmail.com from your preferred email address and also from your gmail to introduce yourself to me if you have not already done so!
Course Syllabus and Schedule:
This is an asynchronous online course. Professor Sormani will create playlists of videos for each 2 hour lesson and post the videos to youtube. The links to these playlists and the corresponding class notes will be found under each lesson in the schedule of lessons below. If there is a problem viewing or hearing any video, please give the video a thumbs down and email the professor (sormanic@gmail.com) with the subject header MAT313 VIDEO TROUBLE. Students will watch all the videos, take notes with pen and paper, and pause the videos to complete classwork assigned in the videos before watching the solutions. Class notes are also provided so students can check their notes. Everything should be written neatly and clearly including the assigned questions, the completed solutions to the classwork, and the corrections of the classwork.
Lehman College requires proof of attendance. To prove that each lesson is complete, the student must submit their classwork and homework to the professor by sharing a googledoc full of photos of their work as explained at the top of each lesson and write down the time when they watched the videos. Students will include a photo of themselves holding up the first page of their classwork for each lesson or place their photo id next to the first page of their classwork. Students who do not complete at least the first lesson within 2 weeks will be removed from the course by Lehman College Policy. Students who suffer hardship may be granted to permission to submit some lessons late and take the corresponding quizzes late, but lessons must be completed in order unless
Homework: Students must complete the homework for each lesson and submit it with that lesson's classwork before starting the next lesson. Three to four hours of homework is assigned in each lesson and will be checked by the professor. Students may be required to resubmit their work to fix errors and complete missing problems. As in all math courses, write out the question and include any diagrams before solving the problem. Students may seek help and work together when doing homework. Always give credit for information learned online, with the help of a tutor, or a classmate by citing where the help came from (providing a link, or a textbook, or the full name of the assistant).
Office hours. Since this course meets asynchronously, there are no fixed office hours and no zoom meetings. Instead Professor Sormani will answer questions by email within 48 hours. Questions should be emailed to the professor (sormanic@gmail.com) with the subject MAT313 QUESTION with a link to the student's googledoc and a photo of the question in the googledoc next to the typed word QUESTION. Professor Sormani will then post a photo of the answer into the googledoc next to the question and email the student that the answer is ready. Sometimes Professor Sormani will make an extra video with the answer.
Grading:
There are eight 20-minute quizzes (each worth 10%), there is a group project (worth 10%) and a final project (worth 10%). Homework and classwork is not part of the grade but must be completed before taking the quizzes.
Quizzes (80%): There are eight 20-minute quizzes (each worth 10% of the course grade). A student may only take a quiz after completing the lessons leading to that quiz. Every student will be given a unique quiz similar to a sample quiz and must show all work as shown on the sample using the methods taught in this course. Work will be completed on paper and submitted by taking a photograph of that work and a selfie holding up the work. Students may consult notes and textbooks and online calculators during quizzes but may not seek help from people. Students who do not submit their quiz on time will earn a 0 on the quiz. Students are allowed to retake two quizzes per semester.
Group Project (10%): There will be an asynchronous group project that students contribute to all semester long. Students do not have to meet with one another for the group project. This project involves many problems with many steps. Students will log into the project doc and read the work other students have done, add politely suggested corrections, and add more steps of their own. The professor will regularly visit the project, awarding students points for their personal contributions to the project. Students must submit Lesson 4 to join Part I of the Group Project, they must submit Lesson 9 to join Part II of the Group Project, and they submit Lesson 14 before joining Part III of this project. For full credit students must contribute to all three parts. It is recommended to log in to the group project 2-3 times a week.
Extra Credit (up to 5%): There are extra credit assignments in many lessons as part of the homework. Exceptional work on a project may also earn extra credit.
Final Project (10%): This is in place of a final exam. The final project (which must be completed alone) covers all the material in the course. Students must submit Lessons 23-24 before working on Part I and must submit Lessons 25-27 before working on Part II of this project. Students must complete the final project on paper and submit the work with selfies during the last month of the semester and can seek feedback and assistance from the professor. The final project is due at the end of finals week but may be completed earlier.
Materials, Resources and Accommodating Disabilities:
Internet Access: Students are required to have internet access to complete two 2-hour lectures per week and to upload homework and to take quizzes and work on projects.
Paper and Pens: Students should use graph paper and pens of multiple colors in this course. This work will be photographed and submitted in a googledoc, which can be done easily if you use the same devise to take the photo that has the googledocs app.
Resources: Below inside the schedule you will find a link to each lesson's googledoc which has detailed notes and links to videos posted on youtube. The course can easily be completed on a tablet or smartphone which has these apps or on a computer with a browser and internet access.
Textbook: There is no required textbook because we will be following the class notes. If you would like a textbook: A textbook is free at this link: “A First Course in Linear Algebra" by Robert Beezer.
MATLAB: Students are encouraged to use MATLAB to check their work. CUNY has MATLAB available here and MATLAB has a 2 hour MATLAB onramp course,
Accommodating Disabilities: Lehman College is committed to providing access to all programs and curricula to all students. Students with disabilities who may need accommodations are encouraged to register with the Office of Student Disability Services. For more information, please contact the Office of Student Disability Services, Shuster Hall, Room SH-238, telephone number, 718-960-8441. E-mail: disability.services@lehman.cuny.edu Some standard accomodations are extra time on quizzes.
Handling Stress: Many students encounter stress of some sort during the semester. Lehman Student Services can help students manage many kinds of hardship that may arise. Email: help.coach@lehman.cuny.edu to contact them. Students who are afraid of failing or earning a low grade may withdraw from the course but should consult with the professor first. The professor can work with the student to arrange a more manageable schedule that can still lead to a passing grade. Sometimes, if a student has been working hard and is progressing with passing grades but encouters hardship, the student can request an incomplete to finish work in June.
Course Outcomes
1. Learn to prove theorems. Students should be able to observe connections between different topics in the course description above, especially systems of equations, matrices and vector spaces.
2. Learn to perform calculations. Students must learn how to perform calculations in different settings. They should be comfortable doing algebra on matrices, solving systems of linear equations and working with vectors.
Math Major Outcomes incorporated into MAT313
A. Perform numeric and symbolic computations
B. Construct and apply symbolic and graphical representations of functions
C. Model real-life problems mathematically
E. State and apply mathematical definitions and theorems
F. Prove fundamental theorems
Schedule:
(links to lessons will be activated as the course progresses)
Lesson 1: Linear Equations and Vectors in Euclidean Space (Sept 1-4)
Lesson 2: Solving Linear Systems with Row Reduction
to Echelon Form (Sept 5-7)
Lesson 3: Solving Linear Systems with Augmented Matrices and
Echelon Form using our Algorithm (Sept 8-11) This is the algorithm we will use to do all problems thoughout the course.
Quiz 1 on Lessons 1-3 (Sample Quiz 1) () Students who did not complete Lessons 1-3 correctly on time may take this quiz one week late.
Lesson 4: Dot Products and Hyperplanes and Proofs (due Sun Feb 11)
Group Project Part 1 on Lesson 4 begins Wed Feb 14 (students may only contribute one step per day to this project)
Lesson 5: Reduced Echelon Form and Homogeneous Linear Systems (due Th Feb 15) Lessons 1-5 must be fixed by 10pm Sunday Feb 18 to take Quiz 2 on time.
The Final deadline for Lessons 1-5 for late students is Sunday Feb 25. Students who cannot complete Lessons 1-5 correctly by Feb 25 are not able to complete the course because they are doing less than one lesson per week and cannot possibly pass a course with two lessons per week.
Practice row actions here.
Quiz 2 on Lessons 4-5 (Sample Quiz 2) (Tu Feb 20 8pm, Wed Feb 21 8pm, or Wed Feb 21 10pm) Students who did not complete Lessons 1-5 correctly on time, but have them all done well by Sun Feb 25, may take this quiz two weeks late at the same time as Quiz 3.
Lesson 6: A Matrix times a Vector (due Th Feb 22)
(late students do this shorter Lesson 6 before Th Feb 29)
Lesson 7: Null Spaces (due Sun Feb 25) (if late: skip and do later)
Lesson 8: Identity, Permutation, and Nonsingular Matrices (due Th Feb 29) (late students do this Lesson 8 by Th Feb 29)
Group Project Part 1 is done and graded (see the projects)
Quiz 3 on Lessons 6-8 (Sample Quiz 3) (Tu Mar 5 4pm, Tu Mar 5 8pm or Wed Mar 6 8pm or Wed Mar 6 10pm) Students who did not take Quiz 2 will take Quiz 2&3 together (Sample Quiz 2&3)
Lesson 9: Proofs with Matrices and Vectors (due Sun Mar 3)
Group Project Part 2 on Lesson 9 begins on Wed Mar 6 for students who corrected Lesson 9.
Lesson 10: Linear Transformations (due Th Mar 7)
Lesson 11: Eigenvectors and Eigenvalues (due Sun Mar 10)
Quiz 4 on Lessons 8, 10 and 11 (Sample Quiz 4) (Tu Mar 12 8pm, Wed Mar 13 8pm or Wed Mar 13 10pm) (All students will take this quiz this week and will have a deduction for not completing the lessons on time)
Lesson 12: Eigenspaces (due Th Mar 14) or catch up Lesson 7.
Lesson 13: Guest Lecture: Dr. Alexander Diaz Lopez on Popular Games (Mar 17) no HW, skip if behind schedule.
Lesson 14: Multiplying Matrices (due Th Mar 21)
Group Project Part 2 ends on Saturday Mar 23.
Lesson 15: Proofs about Matrix Addition and Multiplication (due Sun Mar 24)(students who cannot submit on time may skip this lesson)
Quiz 5 on Lessons 8 and 14 (Sample Quiz 5) (Tu Mar 26 4pm or Tu Mar 26 8pm or Wed Mar 27 8pm or Wed Mar 27 10pm) (Lessons 8 and 14 must be fixed by 10pm on Sunday to take this quiz)
Group Project Part 3 on Lesson 15 begins on Wed Mar 20 for students who fixed Lesson 15.
Lesson 16: Inverses of Matrices (due Th Mar 28)
Quiz 6 on Lesson 16 (Sample Quiz 6) (Will be distributed Tu Apr 2 at 8pm and due on Th Apr 4 at 10pm) (Lesson 16 must be completed by 10 pm Mon Apr 1 to take this quiz)
Lesson 17: Determinants found by Row Reduction (due Th Apr 4)(students who are late may submit by Tu Apr 9 at 10pm)
Lesson 18: Properties of Determinants (2x2 and 3x3) (due Sun Apr 7)(students who are late may submit the Short Lesson 18 by Th Apr 10 at 10pm)
Lesson 19: Trace and Transpose and Proofs (extra credit due finals week)
Last Week to Contribute to the Group Project
Lesson 20: Linear Combinations, Spans, Linear Independence, and the Basis of a Subspace of Euclidean Space (due Th Apr 11)(Students who are late may submit on Th Apr 18)
Lesson 21: Dimension, Finding a Basis using Pivot columns and the Method of Gram-Schmidt (due Sun Apr 14)(Students who are late may submit on Sun Apr 21)
Quiz 7 on Lessons 17-18 (Sample Quiz 7) (Wed Apr 17 8pm or Wed Apr 17 10pm or Th Apr 18 at 8pm) (Lessons 17-18 must be fixed by 10pm on Sunday to take this quiz)
Group Project Deadline: Tu April 16
Lesson 22: Null Space, Nullity, Range, and Rank of a Matrix (due Th Apr 18)(Students who cannot submit on time may submit during Spring Break on Th April 25)
Lesson 23: Eigenspaces and the Characteristic Polynomial (due Sun Apr 21)(Students who cannot submit on time may submit during Spring Break on Sunday April 28)(Students may submit later but no personalized feedback)(The final deadline is Sun May 12 but if submitted that late there is no time to complete the course)
April 22-30 Spring Break catch up!
Lesson 24: Similar Matrices and Diagonalization (due Th May 2)(Students may submit later but no personalized feedback)(The final deadline is Th May 16 but if submitted that late there is no time to complete the course)
Quiz 8 on Lessons 20-22 (Sample Quiz 8) ( Wed May 8 8pm, or Wed May 8 at 10pm or Th May 9 at 8pm)
Final Project Part 1 on Lessons 23 and 24 (must do this project before continuing with Lessons 25-28) (The final deadline is Sun May 19 but if submitted that late there is no time to complete the course)
Lesson 25: Vector Spaces (due Sun May 5)(Students may submit later after completing the Final Project Part I but no personalized feedback)
Lesson 26: Linear Maps (due Th May 9)(Students may submit later but no personalized feedback)
Lesson 27: Basis and Dimension of a Vector Space, Infinite Dimensional Spaces (due Sun May 12)(Students may submit later but no personalized feedback)
Final Project Part 2 on Lessons 25-27 (final deadline Sun May 26)
Lesson 28: Choose a guest lecture:
Guest Lecture: Dr. Urschel Jacobi's Eigenvalue Algorithm
Guest Lecture: Siraj Ravel Principal Component Analysis
Retake Quizzes: Finals Week (Tu May 21 4pm, Tu May 21 8pm, Wed May 22 4pm, Wed May 22 at 8pm, or Wed May 22 10pm)
(you must complete lessons by Sunday May 19 at 10pm to take a quiz)
Final Project Deadlines:
Part I 10pm Sun May 19 (best to submit right after fixing Lesson 24)
Part II 10pm Sun May 26 (best to submit right after fixing Lesson 27)
Students who are behind schedule but have a passing average based on their quizzes before the end of the semester, may request an incomplete so that they have time to complete Lessons 23-28 and the Final Project. All quizzes must be done before the end of the semester.
Applications of Linear Algebra for interested students:
Finding Eigenvectors and Eigenvalues using the Jacobi Algorithm by Dr. Urschel
An application of Linear Algebra to Markov Chains Michel van Biezen
An application of Linear Algebra to Balancing Chemical Equations by Rajendra Dahal
Principal Component Analysis of Data Sets using Linear Algebra by Siraj Raval
Dr. Wheaton Manhattan Norm on Financial Gains
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Additional Lessons for students who like proofs and might be interested in taking MAT314:
MAT314 Lesson 1: Direct Proofs and Indirect Proofs about Sets
MAT314 Lesson 2: Proof by Induction and the Well-Ordering Principle
MAT314 Lesson 3: Binary Operations and Sets
MAT314 Lesson 4: Groups and Matrices