Pure Linear Algebra I

Jose Roberto Cossich G and Kindness C

Series Details

Sessions

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This series was cancelled by the tutor on September 10, 2024. We're very sorry–you can explore more Calculus series here. All 1:1 and group chats related to this series are disabled 7 days after the last session.

Series Details

About

This is a full first course on proof-based linear algebra.
Sessions are 1h30m daily except for Sunday, so the course is at an accelerated pace.
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Prerequisites:
-Algebra 2 with trig (with Calculus preferred but not required)
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Syllabus:
(UNIT I)  Basic Vector Operations
1. Vector geometry in R^n 
2. Planes in R^3
3. Span, subspaces, and dimension
4. Basis and orthogonality
5. Cross Products
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(UNIT II) Basic Vector Space Properties
2. Vector Spaces and Subspaces 
3. Linear independence and Gram-Schmidt
4. Projections and Orthogonal Vector Decomposition
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(Unit III) Linear Transformations and Motivating Matrices
5. Linear Transformations, Properties, and Kernel
6. Matrix operations, special matrices, and matrix properties 
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(Unit IV) Linear Systems
7. Determinants, Linear Systems, and Inverse Matrices 
8. LU decomposition
9. Row, Column, and Null Space, Rank and Nullity
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(Unit V) Representing Linear Transformations as Matrices
10. Change of Basis and Matrix Multiplication
11. Eigenvectors and Diagonalizability
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(Unit VI) Special Topics in Applied Linear Algebra:
-Euclidean Inner Spaces
-Least squares regression
-Markov chains
-Raising numbers to matrices
-Solving differential equations using matrices
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I will provide all reading and practice material.
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Note: Required reading of 25 pages a week + Weekly homework (with feedback) + 1 test per unit (with review in-class and the tests graded with feedback).
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✋ ATTENDANCE POLICY

I try to make the session times as accommodating as possible, however make-up sessions are always available. Please feel free to ask for one if needed!

Dates

August 10 - September 9

Learners

20 / 20

Total Sessions

About the Tutors

A little about me: I'm about the biggest Indie fan there is, I almost exclusively watch (John Hughes>>) 80s movies or the upcoming Star Wars series, and I read sci-fi in my spare time. I tutor for the sake of those aha moments, and have taken Multivariable Calc, Linear Algebra, Real Analysis, and Complex Analysis. Who knows what I'll tutor next, hope to see you soon.

View Jose Roberto Cossich G's Profile

Hi! I'm Kindness (aka Enci). As of 2024-25, I'm a junior year university student majoring in pure math! I graduated high school as part of the Class of 2023, and thanks to APs I skipped the freshman year of university. On Schoolhouse, I especially like to tutor in Enrichment as a study space host and advanced math tutor. I used to be quite active in tutoring the SAT, and I hope to return to doing that soon! In my free time (which I don't have much, lol), you can find me writing poems, playing the piano or violin, and scrapbooking.

View Kindness C's Profile

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