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Linear Algebra

SAT Score Range

•

10 sessions

•

About

Hi everyone,
In this series we'll go over a full college-level linear algebra course covering matrix operations, linear independence, vector spaces, various decompositions (LU, CR, QR, diagonalization, SVD), determinants, eigenvalues and eigenvalues, as well as markov chains and systems of differential equations, among other topics.

We'll meet Mondays for about 90 minutes starting at 7:00 PM ET. Hopefully, I do not have to use the full time every session, but plan on utilizing the full time. Note that we will NOT meet on Monday, January 20 (MLK Day) nor Monday February 17th (Presidents Day), as well as for two weeks in March during my Spring Break. As much as I want to share Math, I also want to enjoy the end of my senior year in High School. I have all the sessions for the months of January and February loaded in right now, and I'll add more as needed.

This is NOT intended to replace an equivalent 200-level Applied Linear Algebra college course, but rather is intended either as a supplement or for any curious high-schoolers to learn some math for fun and get some exposure to Linear Algebra. I want to prioritize a broad overview of the topics rather than getting into the weeds of mathematical rigor (breadth over depth).

Completion of Calculus is not required but is strongly encouraged. Learners should be concurrently enrolled in some form of Calculus, however. Some basic familiarity with matrices, vectors, and matrix/vector multiplication is also preferred. Learners are expected to be proficient in Algebra 2 and Pre-Calculus.

Reference Text: https://docs.google.com/document/d/1HaTl5yhz2Hca89cfZB-Fk14rnt0nvlK5BwnvpDBTMnA/edit?usp=sharing


Lectures from the Spring 2024 Linear Algebra course which I took at a nearby four-year university.

Homework problems are included at the bottom of every section for extra practice, though they lean more on the theoretical side. Ignore all the MATLAB projects as we will not be doing them (I think Image Clipping is the first one). I may provide practice exams in case you guys wanted to see what a typical exam could look like for this class.

I want to offer take-home exams and quizzes. Because this does not count towards credit towards any institution, cheating on them would only be doing a disservice to yourself and I trust that everyone completes these honestly. We should have a quiz for most sections and have three practice exams. While I don't have many large blocks of time to host sessions, I'm more than open to take questions via DM throughout the day.

We will cover the following sections in this tentative order, assuming sufficient interest is sustained:
Unit 1: Introduction and the Fundamental Subspaces:
1.1 Introduction & Linear Combinations
1.2 Linear Systems
1.3 & 1.4 Gaussian Elimination
1.5 Parametric Vector Form
1.6 Matrix Multiplication
1.7 Matrix Inverse
2.5 Linear Independence
2.6 Four Fundamental Subspaces
1.8 LU & CR Factorization
Take-Home Test
-----
Unit 2: Determinants and Eigenvalues:
1.9 Linear Transformations
2.1 Families of Matrices
2.2 Determinants

2.4 Vector Spaces & Orthogonality
2.3 & 2.7 Eigenvalues and Eigenvectors
2.10 Diagonalization
2.8 Orthogonal Projection & Least Squares Solutions
2.9 QR Factorization & Orthonormalization
Take-Home Test
----
Unit 3: Applications of Linear Algebra:
3.3 Orthogonal Diagonalization
3.4 & 3.5 Singular Value Decomposition
3.1 Discrete Linear Dynamics (Markov Chains)
3.2 Continuous Linear Dynamics (Systems of 1st-order Differential Equations)
Take-Home Final Exam

Tutored by

Nathan J 🇺🇸

Certified in 5 topics

View Profile

Hi, I'm Nathan, a high school student from New Jersey. I'm currently taking Stochastic Processes for my Math class at a local university and have completed AP Calculus BC, AP Physics C, Calculus 3 in high school as well as Differential Equations, Linear Algebra, and Calculus-based Statistics at the university level so I can help with any high school or first or second-year university math class. In my free time, I like watching trains and operating my own model trains.

Schedule

✋ ATTENDANCE POLICY

You will be withdrawn from the series if you have more than 2 unexcused absences in a row. Please message the tutor in advance for any absences! I will do my best to post lesson summaries/recordings in the group chat.

SESSION 1

14

Jan

SESSION 1

Other Topics

Other Topics

Tue 12:00 AM - 1:30 AM UTCJan 14, 12:00 AM - 1:30 AM UTC

Introduction, Review Linear Systems and Linear Combinations, Gaussian Elimination, Parametric Vector Form.
SESSION 2

28

Jan

SESSION 2

Other Topics

Other Topics

Tue 12:00 AM - 1:30 AM UTCJan 28, 12:00 AM - 1:30 AM UTC

Matrix Multiplication, Matrix Inverse, Linear Independence
SESSION 3

4

Feb

SESSION 3

Other Topics

Other Topics

Tue 12:00 AM - 1:30 AM UTCFeb 4, 12:00 AM - 1:30 AM UTC

Four Fundamental Subspaces, Matrix Factorizations
SESSION 4

11

Feb

SESSION 4

Review

Review

Tue 12:00 AM - 1:30 AM UTCFeb 11, 12:00 AM - 1:30 AM UTC

Linear Transformations & Review. Take-home Exam 1 will be handed out following this class.
SESSION 5

25

Feb

SESSION 5

Other Topics

Other Topics

Tue 12:00 AM - 1:30 AM UTCFeb 25, 12:00 AM - 1:30 AM UTC

Families of Matrices, Determinants, Vector Spaces & Orthogonality
SESSION 6

4

Mar

SESSION 6

Other Topics

Other Topics

Tue 12:00 AM - 1:30 AM UTCMar 4, 12:00 AM - 1:30 AM UTC

Eigenvalues, Eigenvectors, Diagonalization
SESSION 7

10

Mar

SESSION 7

Other Topics

Other Topics

Mon 11:00 PM - Tue, 12:30 AM UTCMar 10, 11:00 PM - Mar 11, 12:30 AM UTC

Least Squares Solutions & QR Factorization. Take-home Exam 2 will be distributed following this class but I may hold a review session later in the week.
SESSION 8

31

Mar

SESSION 8

Other Topics

Other Topics

Mon 11:00 PM - Tue, 12:30 AM UTCMar 31, 11:00 PM - Apr 1, 12:30 AM UTC

Orthogonal Diagonalization & Singular Value Decomposition
SESSION 9

7

Apr

SESSION 9

Other Topics

Other Topics

Mon 11:00 PM - Tue, 12:30 AM UTCApr 7, 11:00 PM - Apr 8, 12:30 AM UTC

Discrete & Continuous-time Markov Chains
SESSION 10

14

Apr

SESSION 10

Review

Review

Mon 11:00 PM - Tue, 12:30 AM UTCApr 14, 11:00 PM - Apr 15, 12:30 AM UTC

Review for Take-home Final which will be distributed after class and is to be completed within a week for grading & feedback

Public Discussion

Please log in to see discussion on this series.

Jan 14 - Apr 15

14 weeks

90 mins

/ session

Next session on January 28, 2025

SCHEDULE

Tuesdays

12:00AM