We'll take a brief look at one of the first courses you will take in university if you would like to become a math major. We will begin with the fundamentals—learning some basic set theory, working with complex numbers, and setting the definitions of rings and fields. Then we'll prove some intuitive things that we know about number theory and modular arithmetic (i.e. working with remainders). From there we will generalize our methods to other areas, such as doing "number theory" and "modular arithmetic" with polynomials and much more! No calculus knowledge is necessary for this series; however, high-school Algebra 1 and Algebra 2 are necessary. BTW do you know that this series would be called "Algebra 1" in university?? 😂😜 (Note: This series has been recently restarted, so if you're looking to join us, you are still in a good position to do so!)

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. Prerequisites: -Algebra 2 with trig (with Calculus preferred but not required) 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 (UNIT II) Basic Vector Space Properties 2. Vector Spaces and Subspaces 3. Linear independence and Gram-Schmidt 4. Projections and Orthogonal Vector Decomposition (Unit III) Linear Transformations and Motivating Matrices 5. Linear Transformations, Properties, and Kernel 6. Matrix operations, special matrices, and matrix properties (Unit IV) Linear Systems 7. Determinants, Linear Systems, and Inverse Matrices 8. LU decomposition 9. Row, Column, and Null Space, Rank and Nullity (Unit V) Representing Linear Transformations as Matrices 10. Change of Basis and Matrix Multiplication 11. Eigenvectors and Diagonalizability (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 I will provide all reading and practice material. 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).

In this series we will cover the proofs behind well known theorems in Calculus. Learners will learn the techniques and strategies involved in proving and deriving mathematical theorems, as well as achieve a deeper understanding of each theorem they prove. Learners will engage by answering questions and doing exercises that will guide them to understand the proofs.

This is a series consisting of 8 back-to-back 3-hour sessions to make for a "mega-session" lasting for a total of 24 hours. 🎉 You are not required to join all eight sessions. Come and join us for the greatest, longest, most exciting study session EVER on Schoolhouse! We aim to shatter the record for the longest study session ever hosted by participating in this 24-hour mega study session. Come grind your summer plans, whether it be: - conducting research in the most esoteric depths of mathematical analysis, - cleaning out your bedroom which you have not been able to make yourself clean for the past year, - torturing your fingers to master La Campanella on the violin, - anything in between! You do not have to stay for the entire 24 hours, as long as you are able to come. We welcome as many tutors in as many different timezones as possible to cohost the session! This record-breaking event cannot happen without a joint effort of many, many tutors. In the spirit of most study space series on Schoolhouse, we will also use the well-celebrated Pomodoro technique of 25-minute study times and 5-minute breaks. We can do this! 💪

Welcome to this study space! Feel free to take a seat and make yourself comfortable. • I'll get some calm music going! Please feel free to suggest music that you like. • We'll use the Pomodoro technique: 25 min studying + 5 min break. • Cameras don't have to be on—you're welcome to do it either way! • Please keep your microphones muted for the 25 min studying periods. We can come off mute for the breaks! You're also welcome to use the chatbox at any time. • Due to my time zone, this series is particularly American (Eastern) time-zone friendly, but you are welcome to join whenever you have time. • I'll not schedule sessions too far ahead in the future to avoid unforseenable schedule conflicts.

We wish to help everyone on SHW. This series is created because we want to help as many students as we can. We enjoyed tutoring ourselves, and have experienced the hardships of focusing. Prior knowledge is not required for this session, but be sure to bring your homework, or tasks to let us help! This series is also based on the Flowtime Study Method, researched to be even effective than the Pomodoro Method, which allows your brain to have a longer rest than the Pomodoro method, storing more energy to focus and flow! Once one of our tutors have free time, we will create a study space to help others! Keep your eyes out for any study space available! ✨Recommended & Frequent tutors:✨ ✨Pranu: Major in AP Human Geography, AP Psychology, AP US Government and Politics, AP US History, AP Calculus AB, Python, Computer Science, Art, sculpturing, and has much experience in helping students. ✨Mengmeng: Tutors AP Statistics, Algebra 2, Precalculus, AP Calculus AB, Spanish up to AP level, Chemistry, Biology, Geoetry, Pre-algebra, Algebra 1, physics, some of ap physics 1 (unit 1), High school level physics, Chinese, SAT Math. ✨Jocelyn: Tutors Algebra 1, Geometry, Speech/Debate, Spanish 2, AP Language.

We'll cover the fundamental topics of linear algebra in this series. The link for our textbook is here (under a Creative Commons license): https://lyryx.com/linear-algebra-applications/. This supplementary text may also be useful (also available for free): https://textbooks.math.gatech.edu/ila/. Here's an overview of the content of the course (copied from the Table of Contents of our primary textbook). No previous calculus knowledge necessary. - Systems of linear equations - Matrix algebra - Determinants, eigenvalues, and diagonalization - Vector geometry - Vector spaces (both R^n and abstract vector spaces) - Linear transformations - Change of basis

Welcome! This is a study space series held through July and August (hopefully the series will continue indefinitely). • I'll get some calm music going! Most of the music will come from Pixabay. • We'll use the Pomodoro technique: 25 min studying + 5 min break. • Cameras don't have to be on—you're welcome to do it either way! • Please keep your microphones muted for the 25 min studying periods. We can come off mute for the breaks! You're also welcome to use the chatbox at any time. • Due to my time zone, this series is particularly Asian time-zone friendly, but you are welcome to join whenever you have time. • I'll not schedule sessions too far ahead in the future to avoid unforseenable schedule conflicts.

This is a Study Space series (revival of a former series that I used to do) • I'll get some calm music going! • We'll use the Pomodoro technique: 25 min studying + 5 min break. • Cameras don't have to be on—you're welcome to do it either way! • Please keep your microphones muted for the 25 min studying periods. We can come off mute for the breaks! You're also welcome to use the chatbox at any time. • Due to my time zone, this series is particularly Asian time-zone friendly, but you are welcome to join whenever you have time. • I'll not schedule sessions too far ahead in the future to avoid unforseenable schedule conflicts.