Linear Algebra Spring 2023
An Asynchronous Online Course
with Professor Sormani
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.
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 work 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 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.
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. 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. 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.
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:
Lesson 1: Linear Equations and Vectors in Euclidean Space (due Sun Jan 29)
Lesson 2: Solving Linear Systems with Row Reduction
to Echelon Form (due Th Feb 2)
Lesson 3: Solving Linear Systems with Augmented Matrices and
Echelon Form using our Algorithm (due Sun Feb 5)
Quiz 1 on Lessons 1-3 (sample quiz) (schedule when done with Lessons 1-3, Tu, Wed, or Th at 8pm)
Lesson 4: Dot Products and Hyperplanes and Proofs (due Sun Feb 12)
Group Project Part 1 on Lesson 4 begins here
Lesson 5: Reduced Echelon Form and Homogeneous Linear Systems (due Th Feb 16) must be fixed by Sunday to take Quiz 2.
Quiz 2 on Lessons 4-5 (sample quiz) (Must take on Tu Feb 21 4pm, Tu Feb 21 8pm or Wed Feb 22 8pm)
Lesson 6: A Matrix times a Vector (due Sun Feb 19)
Lesson 7: Null Spaces (due Th Feb 23) must be fixed by Sunday to take Quiz 3.
Quiz 3 on Lessons 6-7 (sample quiz) (Must take on Tu Feb 28 4pm, Tu Feb 28 8pm or Wed Mar 1 8pm or Wed Mar 1 11pm)
Lesson 8: Identity, Permutation, and Nonsingular Matrices (due Sun Feb 26)
Lesson 9: Proofs with Matrices and Vectors (due Th Mar 2)
Group Project Part 2 on Lesson 9 begins here on Friday Mar 3.
Lesson 10: Linear Transformations (due Sun Mar 5)
Lesson 11: Eigenvectors and Eigenvalues (due Th Mar 9)
Lesson 12: Extra Time for the Group Project (due Sun Mar 12)
Lesson 13: Guest Lecture: Dr. Alexander Diaz Lopez on Popular Games
Quiz 4 on Lessons 8, 10, and 11 (sample quiz) (Must take on Tu Mar14 4pm, Tu Mar 14 8pm or Wed Mar 15 8pm or Wed Mar 15 11pm)
Lesson 14: Multiplying Matrices (due Th Mar 16)
Lesson 15: Proofs about Matrix Addition and Multiplication (due Sun Mar 19)
Quiz 5 on Lessons 8 and 14 (sample quiz) (Must take Tu Mar21 4pm, Tu Mar21 8pm, Wed Mar22 8pm, Wed Mar22 11pm or 11:30pm)
Group Project Part 3 on Lesson 15 begins here on Monday Mar 20.
Lesson 16: Inverses of Matrices (due Th Mar 23 or Spring Break)
Lesson 17: Determinants found by Row Reduction (due Sun Mar 26)
Quiz6 is only HW on Lesson 16 (sample quiz) (due Th Mar 30 at 10pm)
Lesson 18: Properties of Determinants (2x2 and 3x3) (due Sun Apr 2)(access to Lesson 18 will be given only to students after they complete and correct Lesson 17)
Spring Break catch up: Lesson 7 due April 6 and Lesson 16 due April 10. Quiz3HW and Quiz6HW will be shared with you after the lessons are fixed.
Lesson 19: Trace and Transpose and Proofs (due Sun Apr 16)
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 20)
Lesson 21: Dimension, Finding a Basis using Pivot columns and the Method of Gram-Schmidt (due Sun Apr 23)
Group Project Deadline: Sunday April 23
Quiz 7 on Lessons 17-18 (sample quiz) (Must take on Tu Apr 25 4pm, Tu Apr 25 8pm, Wed Apr 26 8pm, Wed Apr 26 11pm)
Lesson 22: Null Space, Nullity, Range, and Rank of a Matrix (due Th Apr 27)
Lesson 23: Eigenspaces and the Characteristic Polynomial (due Sun Apr 30)
Lesson 24: Similar Matrices and Diagonalization (due Th May 4)
Quiz 8 on Lessons 20-22 (sample quiz) (Must take on Tu May 9 4pm, Tu May 9 8pm, Wed May 10 8pm or Wed May 10 at 11pm)
Final Project Part 1 on Lessons 19, 23, and 24
Lesson 25: Vector Spaces (due Sun May 7)
Extra Credit Lecture: Theorems about Eigenspaces
Lesson 26: Linear Maps (due Th May 11)
Lesson 27: Basis and Dimension of a Vector Space, Infinite Dimensional Spaces (due Sun May 14)
Final Project Part 2 on Lessons 25-27
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 16 4pm and 8pm Wed May 17 8pm and 11pm
(you must complete lessons by Sunday at 10pm to take a quiz)
Final Project Deadlines:
Part I 10pm Sat May 20 (best to submit right after Lesson 24)
Part II 10pm Tu May 23 (best to submit right after 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