LinAlg-F21

Linear Algebra Fall 2021

An Asynchronous Online Course

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 Playlist of Four Videos

The textbook is free at this link: “A First Course in Linear Algebra" by Robert Beezer.

This course can be completed on a tablet with the youtube and googledocs apps. Lehman College has loaner tablets that can be used for this course if you need one. Please email the professor (sormanic@gmail.com) from a gmail address introducing yourself.

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 those playlists and the corresponding class notes will be found under each lesson in the schedule of lessons below. Students will watch all the videos, take notes on pencil and paper, and pause the videos to complete classwork assigned in the videos before watching the solutions. Everything should be written neatly and clearly including the assigned questions, the completed solutions to the classwork, and the corrections of the classwork. If there is a problem viewing or hearing any video, please email the professor (sormanic@gmail.com) with the subject header MAT313 Video Trouble.

Lehman College requires proof of attendance. To prove that each lesson is completed the student will 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. 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 should complete the homework for each lesson and submit it with that lesson's classwork before starting the next lesson. Two to three hours of homework is assigned in each lesson and will be checked by a grader. The grader may suggest that a student resubmit their work. 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.

Schedule: Students are allowed to complete each lesson at their own pace. To complete the course on time, students must complete two lessons per week. That is about four hours of classwork while watching videos and four-six hours of homework each week because this is a 4 credit course. Students who fall behind schedule may be allowed to request an incomplete in the course. Students may only request an incomplete if they have passed three exams by December 5. Students who fail one of these exams should withdraw from the course because an F would hurt their GPA.

Grading: There are four one hour Exams (each worth 15%) and a Final Exam (worth 40%). Homework and classwork is not part of the grade but must be completed before scheduling the exams. Every student will be given a unique exam similar to a sample exam. Students may consult notes and textbooks and online calculators during exams but may not seek help from people. There will have only 25 minutes to complete each parts of an exam so there will not be much time to consult notes or textbooks. It is best to create a page of notes to consult quickly during each exam.

Exam 1: Each student will schedule their personal 1 hour Exam I after they have completed Lessons 1-5. No students may take Exam I before submitting all their classwork and homework for these lessons. Students should complete two lessons per week and take Exam I in September.

Exam 2: Each student will schedule their personal 1 hour Exam II after they have completed Lessons 7-12. No students may take Exam II before submitting all their classwork and homework for these lessons. Students should complete two lessons per week and take Exam II in mid October.

Exam 3: Each student will schedule their personal 1 hour Exam III after they have completed Lessons 14-19. No students may take Exam III before submitting all their classwork and homework for these lessons. Students should complete two lessons per week and take Exam III in early November.

Exam 4: Each student will schedule their personal 1 hour Exam IV after they have completed Lessons 20-25. No students may take Exam IV before submitting all their classwork and homework for these lessons. Students should complete two lessons per week and take Exam IV in the first week of December. Students who have passed three exams by December 5 but need more time to complete Lessons 20-28 may request an Incomplete in the course and finish in January.

Final Exam: The Final Exam will be given during Finals Week. Students must complete Lessons 26-28 before taking the Final Exam. Students who have passed three exams by December 5 but need more time to complete Lessons 20-28 may request an Incomplete in the course. Students with incompletes must submit Lessons 27-28 before scheduling their personal Final Exam in January.

Materials, Resources and Accommodating Disabilities:

Textbook: The textbook is free at this link: “A First Course in Linear Algebra" by Robert Beezer

Resources: Each lecture will have a google doc and videos that can be viewed and reviewed as needed.

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

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:

**********

(click on the lesson for the link to the lesson videos and homework)

Lesson 1: Linear Equations, Vectors in Euclidean Space, and Complex Numbers (watch Aug 26- Aug 27, do HW before next lesson)

Lesson 2: Solving Linear Systems (watch on or before Aug 28 - Aug 29, do HW before next lesson)

Lesson 3: Solving Linear Systems with Matrices and Reduced Row Echelon Form (watch on or before Sept 1-2)

Lesson 4: Dot Products and Hyperplanes and Proofs (watch on or before Sept 3-Sept 4)

Due to the hurricane many students are behind schedule, so we postpone Exam 1.

Lesson 5: Homogeneous Linear Systems (watch on or before Sept 9-16)

Guest Lecture: Dr. Alexander Diaz Lopez on Popular Games (Sept 17-18)

Recommended Lecture: Dr. Wheaton Manhattan Norm on Financial Gains (Sept 17-18)

Lesson 6: Exam 1 (aim to take Sept 21-22)

on Lessons 1-5 may only be taken after completing HW from Lessons 1-5.

Lesson 7: A Matrix times a Vector and Null Spaces (watch on or before Sept 23-24)

Lesson 8: Identity Matrices, Permutation Matrices, Nonsingular Matrices (Sept 27-30)

Lesson 9: Proofs with Matrices and Vectors (Oct 4-5)

Lesson 10: Linear Combinations, Spans, Linear Independence, and Basis of a Subspace of Euclidean Space (Oct 7-8)

Lesson 11: Dimension, Finding a Basis (using Pivot columns or Gram-Schmidt) (Oct 11-12)

Lesson 12: Nullity, Range, and Rank of a Matrix (Oct 14-15)

Lesson 13: Exam 2 (aim to take on Oct 18-19) (or following week)

on Lessons 7-12 may only be taken after completing HW from Lessons 7-12.

Lesson 14: Multiplying Matrices (Oct 21-22)

Lesson 15: Proofs about Matrix Addition and Multiplication (Oct 25-26)

Lesson 16: Inverses of Matrices (Oct 28-29)

Lesson 17: Determinants (Nov 1-2)

Lesson 18: Properties of Determinants (Nov 4-5)

Lesson 19: Inverse, Determinant, Trace, and Transpose of a Matrix and Review (Nov 8-9)

Lesson 20: Exam 3 (aim to take on Nov 11-12)

on Lessons 14-19 may only be taken after completing HW from Lessons 14-19.

Lesson 21: Eigenvalues and the Characteristic Polynomial (Nov 15-16)

The final deadline for Lesson 21 for all students is Thursday Dec 9.

Lesson 22: Eigenvalues, Eigenvectors and Eigenspaces (Nov 18-19)

Lesson 23: Similar Matrices and Diagonalization (Nov 22-23)

Recommended Lecture: Dr. Urschel Jacobi's Eigenvalue Algorithm

Lesson 24: Vector Spaces (Nov 29-30)

The final deadline for Lesson 24 for all students is Saturday Dec 11.

Lesson 25: Linear Maps and Linear Transformations (Dec 2-3)

Lesson 26: Exam 4 (aim to take Dec 6-7) Alert

on Lessons 21-25 may be taken after completing HW from Lessons 21-24. Exam 4 will be given on Wed Dec 8 at 8pm or Tue Dec 14 at 8pm. Please complete Lessons 21-25 by the Sunday before the exam doing at most one lesson per day. Do not wait for my feedback.

Lesson 27: Basis and Dimension of a Vector Space, Infinite Dimensional Spaces (Dec 9-10) Note this is ordinarily two lessons but it is in one lesson so we can review for the final.

Lesson 28: Review for the Final (Dec 13-14)

The final will be given during finals week

on Tuesday December 21 at 8pm or

Wednesday December 22 at 3pm.

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 by 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

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

Department of Mathematics and Computer Science, Lehman College, City University of New York