Linear Algebra Fall 2020
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.
Students will progress through the 28 lessons which will consist of videos posted on youtube and classwork posted in googledocs. Googledocs can be accessed from smart phones and tablets as well as laptops and computers.
The textbook is free at this link: “A First Course in Linear Algebra" by Robert Beezer
Expectations: Students are expected to learn both the mathematics covered in class and the mathematics in the textbook, as well as any other assigned reading. Completing homework is a significant part of the learning experience. Students should review topics from prior prerequisite courses as needed.
Online Asynchronous Lessons: Students should plan to complete two lessons per week which will appear linked below starting on August 26. For each lesson students will watch videos and do classwork between videos for 100 minutes. The solutions to the classwork will be included in the videos. Some students may choose to spend more time on the classwork before watching the solution. Some students may choose to complete a single lesson in two sittings.
Homework and Office Hours: Approximately three hours of homework will be assigned per lesson. It should be completed and submitted before starting the next lesson. All proofs should be written in numbered lines with statements and justifications in the style taught in class. All students will create a google doc following this template with their course number (MAT313) and their full name (for example MAT313-Sormani-Chris) and share it with the professor as an editor (sormanic@gmail.com). Photos of the homework and other questions will be uploaded into the document and the professor will answer your questions inside the document but you must email the professor telling them what to look at in your document. Office hours are asynchronous. Questions may be asked any time of day and will be answered within 24 hours after the professor receives the email. 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. Simply cite where the help came from by providing a link, or a textbook, or the full name of the assistant.
Examinations: There will be four 2-part 60-minute exams and an accumulative 4-part 120-minute final exam. Each part must be completed in 30 minutes and each student will have a slightly different exam. Students may consult books, notes, videos, and online resources, but students may not seek help from people or tutoring services during exams. Students must show all work and use the techniques taught in this course. Students will schedule the date and time of their exams with their professor when they are prepared for the exam sometime between Sunday 10pm and Monday 11pm. There will be no retakes of any exams.
Grading Policy: Each exam is worth 15%. The final is worth 30%. The homework is worth 10%.
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
Tentative Schedule: do two lessons per week to stay on 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 Planes and Proofs (watch on or before Sept 3-Sept 4)
Lesson 5: Homogeneous Linear Systems (watch on or before Sept 8-9)
Lesson 6: Exam 1 (aim to take Sept 13-14) (must take before Oct 6)
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 15-16) (must complete before Oct 12)
Lesson 8: Identity Matrices, Permutation Matrices, Nonsingular Matrices and a talk by Dr. Alexander Diaz Lopez (Sept 20-21) (must complete before Oct 14)
Lesson 9: Proofs with Matrices and Vectors (Oct 2-3) (must complete before Oct 18)
Lesson 10: Linear Combinations, Spans, Linear Independence, and Basis of a Subspace of Euclidean Space (Oct 5-6) (must complete before Oct 20)
Lesson 11: Dimension, Finding a Basis (using Pivot columns) and an Orthonormal Basis (using Gram-Schmidt) (Oct 10-11) (must complete before Oct 23)
Lesson 12: Nullity, Range, and Rank of a Matrix (Oct 12-13) (must complete before Oct 25)
Lesson 13: Exam 2 (aim to take on Oct 18-19)(must take before Nov 3 even if planning on an inc in the course)
on Lessons 7-12 may only be taken after completing HW from Lessons 7-12. (Sample Exams)
Lesson 14: Multiplying Matrices (Oct 20-21)
Lesson 15: Proofs about Matrix Addition and Multiplication (Oct 22-23)
Lesson 16: Inverses of Matrices (Oct 25-26)
Lesson 17: Determinants (Nov 1-2)
Lesson 18: Properties of Determinants (Nov 3-4)
Lesson 19: Inverse, Determinant, Trace, and Transpose of a Matrix (Nov 5-6)
Lesson 20: Exam 3 (aim to take on Nov 8-9)(must take before Dec 3 to get at least an inc in the class)
on Lessons 14-19 may only be taken after completing HW from Lessons 14-19.
Lesson 21: Eigenvalues and the Characteristic Polynomial (Nov 9-10)
Lesson 22: Eigenvalues, Eigenvectors and Eigenspaces (Nov 14-15)
Lesson 23: Similar Matrices and Diagonalization (Nov 16-17)
Lesson 24: Vector Spaces (Nov 23-24)
Lesson 25: Linear Maps and Linear Transformations (Dec 4-5)
Lesson 26: Exam 4 (aim to take Dec 6-7)
on Lessons 21-25 may be taken after completing HW from Lessons 21-24.
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 14-15)
A nice set of videos reviewing linear algebra
The final will be given during finals week.
Friday Dec 18 at 3pm or 10pm.
An emergency final will be held Sun Dec 20 at 10 pm
Only students with a C or up on Exams 1 to 3
may take an incomplete in this course.
These students will receive an INC, then
complete all lessons through Lesson 25 by Sun Jan 10,
take Exam 4 on Tuesday Jan 12 at 9pm,
complete lessons 27-28 by Sun Jan 17,
and take the Final on Tuesday Jan 19 at 9pm,
and I will change the INC to a grade,
before Spring semester.
Guest speakers give Inspiring Talks you are encouraged to watch and email the speakers.
An application of Linear Algebra to Markov Chains: https://youtu.be/Uz3JIp6EvIg
An application of Linear Algebra to Balancing Chemical Equations: https://youtu.be/t8-SGrSLUsY
An application of Linear Algebra to study data sats called Principal Component Analysis: https://youtu.be/jPmV3j1dAv4
Department of Mathematics and Computer Science, Lehman College, City University of New York