I am back to host another wonderful series: VECTOR CALCULUS! I hope you all can join! This series will cover the content of a semester of college Vector Calculus PREREQ: Calculus 1 and Calculus 2 OR Successful Completion of AP® Calculus BC why Prereq? It is expected that you know how to take derivatives and integrals of single variable functions! STRUCTURE: 1. Lecture (45-60 min) 2. Homework *repeat above until unit is complete* 3. Problem Set for the Unit 4. Unit TEST Here is the syllabus for the series: Main Topics: 1. Vectors and the Geometry of Space 2. Partial Derivatives 3. Multiple Integrals 4. Subtopics in Vector Calculus

Dive into the world of higher dimensions with our comprehensive Multi-Variable Calculus Series. This course is auxiliary in nature where, unlike any standardized models like AP or IB, no "standardized" course framework exists; however, specific topics (linked below) generally associated with Multi-Variable Calculus will be covered. Nonetheless, this course is designed to broaden your mathematical horizon and provide a solid foundation for handling more problems with... well... multiple variables. Whether you're preparing for advanced studies in college or exploring mathematical concepts out of sheer curiosity, we highly recommend you join our series and learn with us. Note that we recommend that you have taken or currently are taking AP Calculus AB/BC or an equivalent course and are comfortable with general knowledge of Calculus I/II. This includes, but of course not limited to, general integration/differentiation proficiency. - - - - - - - - - - - Regarding sessions, this series plans to host around two sessions per week. Each session will be hosted on Friday and Sunday at 5:00 p.m. PST. Each session will be hosted for an hour, depending strictly; however, extra time past may be permitted, not obligated, and dependent on learners' and hosts' preferences. On Sunday, there will be a 'learning' session where the hosts will teach learners topics relevant to our week's points (such points are again listed in the doc linked below). We highly recommend you take notes (handwritten ones), as they will help you immensely with practice problems hosted on Friday. On Friday, there will be a 'practice' session where we will focus on practice problems concerning topics covered on Sunday. This will serve as an opportunity to clarify and sink in topics, aided by your own notes and collaborative guidance with other learners and hosts. We will discuss how these will look in our first introductory session on Friday. I wanted to write down a rough idea of our series format in case any learners join the series late. - - - - - - - - - - - Through a mix of engaging lectures, collaborative problem-solving, and independent exploration, you’ll build the skills to master Multi-variable Calculus at your own pace. While we may not cover all topics within the time limit, our focus remains on delivering a thorough and enjoyable learning experience. - - - - - - - - - - - - This course plans to cover the topics listed in the doc linked: [https://docs.google.com/document/d/1FIrmlTk6XKyfHpTJPYpS2BbkvaCQNLbex6Xo68QfMt0/edit?usp=sharing](https://docs.google.com/document/d/1FIrmlTk6XKyfHpTJPYpS2BbkvaCQNLbex6Xo68QfMt0/edit?usp=sharing) [](https://docs.google.com/document/d/1FIrmlTk6XKyfHpTJPYpS2BbkvaCQNLbex6Xo68QfMt0/edit?usp=sharing) Our reference material (tests, assignments, etc.) can be found [or later implemented] in: [https://drive.google.com/drive/folders/1znGWqvzN8-cZ275cc2SwqANAGNRj1IXz?usp=sharing](https://drive.google.com/drive/folders/1znGWqvzN8-cZ275cc2SwqANAGNRj1IXz?usp=sharing)[](https://drive.google.com/drive/folders/1znGWqvzN8-cZ275cc2SwqANAGNRj1IXz?usp=sharing)[](https://drive.google.com/drive/folders/1znGWqvzN8-cZ275cc2SwqANAGNRj1IXz?usp=sharing)

This series will cover everything you will learn in a traditional calc 3 course. I'm planning on doing 1 two hour session every Sunday or something like that but I'm open to any other suggestions as well. Ill add sessions as our series progresses

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](https://docs.google.com/document/d/1HaTl5yhz2Hca89cfZB-Fk14rnt0nvlK5BwnvpDBTMnA/edit?usp=sharing)[](https://shorturl.at/WA5bU)[](https://shorturl.at/WA5bU) 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 [](https://gillstbernardsschool-my.sharepoint.com/:w:/g/personal/nathanjiang25_gsbschool_org/EUEGWLX1hp9Kot-Z6cSsUEkBYgCd7doIls3vkv9hnu8JhQ?e=UzOjV7)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

Introduction to Linear Algebra and some matrix concepts that are taught in the course that usually taken after Calc 2 I will be going over: 1. Matrices and Systems of Equations 2. Matrix Operations 3. Determinants Requires basic knowledge on vector operations and matrices

I am back to host another wonderful series: LINEAR ALGEBRA! I hope you all can join! This series will cover the content of a semester of college Linear Algebra and is traditionally taken after Calculus PREREQ: Pre-Calculus (Surprising, right?) . . . but I STRONGLY recommend a successful completion of AP® Calculus BC why the Prereq? You don't use Calculus in this course, but understanding vectors and matrices well will get you ahead. The only part in AP® Calculus BC useful for this is the vectors unit, so please review that on your own because we will do a quick recap of the basics of vectors and matrices when this series begins! STRUCTURE: 1. Lecture (60-90 min) 2. Optional Homework *repeat above until unit is complete* 3. Problem Set for the Unit 4. Unit TEST Here is the syllabus for the series: 1. Matrices and Systems of Equations 2. Matrix Operations and Matrix Inverses 3. Determinants 4. Norm, Inner Product, and Vector Spaces 5. Basis, Dimension, and Subspaces 6. Linear Transformations 7. Eigenvalues and Eigenvectors