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• Series

Introductory Linear Algebra

Next session on Jul 1, 2022

Hosted by Iqra A


Enrollment for this series has closed.

This series is part of Schoolhouse Summer Camp. Explore Summer Camp

Series Details

About

Linear algebra began as the study of linear systems of equations. Currently, linear systems remain of great importance, in part due to their relative simplicity. For true mastery in any field, from physics to computer science, an understanding of linear algebra is fundamental. One might even argue that linear algebra and its applications are even more important than those of calculus in today's world.
This course provides an introduction to linear algebra from a concrete point of view. We emphasize understanding through intuitive exposition and plenty of examples and applications. Whilst we will need to understand theory, we will focus on the concrete setting of Euclidean space and relegate more abstract ideas such as general vector spaces to a second course.
Co-taught with SHW tutor @Yu Heng L, who also developed the series idea, overview, and outline!
PREREQUISITES
High school Algebra I and II are required. Pre-calculus, trigonometry, and calculus are not necessary.
SYLLABUS
1. Linear Systems (~5 sessions)
2. Matrices (~4 sessions)
3. Determinants (~2 sessions)
4. Eigenvalues and Eigenvectors (~4 sessions)

✋ ATTENDANCE POLICY

Please do your best to show up to all sessions, as all covered concepts build on each other. If possible, let the instructor(s) know ahead of time if you must miss a day so they can help you catch up in a timely manner.

Dates

June 21 - August 5

Learners

34 / 40

Total Sessions

15

About the Tutor

I'm a graduating high school senior with academic interests in biology, chemistry, and the humanities. In my free time, I enjoy reading, writing, drawing, and ranting about the French Revolution!

View Iqra's Profile

Upcoming Sessions

11
1
Jul

Session 5

Meetup

DAY 5
We'll introduce homogeneous equations and their trivial and non-trivial solutions, writing solutions in parametric form, and linearly independent and dependent vectors.
5
Jul

Session 6

Meetup

DAY 6
We'll finish up Unit 1 (Linear Systems) by exploring common real-world applications of linear systems and matrices, such as in balancing chemical equations, analyzing traffic flow, and observing population change over time.
8
Jul

Session 7

Meetup

DAY 7
We'll delve into newer matrix operations and their practical applications.
12
Jul

Session 8

Meetup

DAY 8
We're halfway through! We'll introduce methods of calculating the inverse of a matrix. We'll also go over the Inverse Matrix Theorem (IVT), which will be crucial to the remainder of the course.
15
Jul

Session 9

Meetup

DAY 9
We'll go over partitioning larger matrices to more efficiently conduct large operations and then walk through factorizing a matrix by its upper and lower triangular forms and how this can help us with more advanced matrix operations in the future.
19
Jul

Session 10

Meetup

DAY 10
We'll look at real-world applications of matrix operations, inverses, and factorizations: the Leontief input-output model and computer graphics.
22
Jul

Session 11

Meetup

DAY 11
We'll begin unit three by introducing the concept of a matrix determinant, its importance, and different methods of calculating it. We'll also go over some fundamental properties of a determinant.
26
Jul

Session 12

Meetup

DAY 12
We'll go over different methods of using determinants to solve a system, including Cramer's Rule and the adjoint/adjugate. We'll also use matrices and determinants to calculate the area of a two-dimensional parallelogram and the volume of a three-dimensional parallelepiped.
29
Jul

Session 14

Meetup

DAY 13
We'll spend this session perusing a more abstract field of linear algebra to understand basic novel concepts and the important roles they will play in the following sessions. We'll go over bases and different types of matrix spaces, and what they can reveal about a matrix.
2
Aug

Session 15

Meetup

DAY 14
We'll begin our fourth and final unit on eigenvectors and eigenvalues by introducing their concepts and importance, as well as using the Characteristic Equation to relate the two.
5
Aug

Session 16

Meetup

DAY 15
We'll go over diagonalizing matrices to be able to easily compute high powers of matrices. We'll also introduce Markov chains and stochastic modeling, and then wind down the session with group discussion and series feedback.

Public Discussion

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