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(AoPS + Physics) Vectors and Coordinate Geometry Study Group!

SAT Score Range

14 sessions

+21

This series ended on May 6, 2022. All 1:1 and group chats related to this series are disabled 7 days after the last session.

About

Hello all! Geometry is a huge part of problem solving: not only serving as a staple in math contests but also very applicable in areas such as physics or engineering. The purpose of this series is to explore how the mathematics of vector and coordinate geometry are hugely important instruments in math and physics problems. Those who are interested can expect fun and challenging problem-based sessions on vectors and coordinate geometry in 2D and 3D. Come prepared to dive deep into interesting (and sometimes rather challenging) questions and real-world applications! This series would be a perfect fit for learners interested in math and how it serves as the essential tool belt of other fields of study. Overview: (each section will be comprised of multiple sessions, and are subject to change based on learner feedback) Section 1: [AoPS] Euclidean Geometry and the Cartesian Plane Section 2: [Pre-Calc] Introductions to Vectors and Vector Operations Section 3: [Physics] 2D Vector Interactions Section 4: [AoPS] How to Deal With the Third Dimension Cheers all and hope to see you in one of the sessions below!

Tutored by

Tony T 🇨🇦

Certified in 8 topics

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Hello! I'm Tony, a Grade 12 student in Canada. I love creatively solving problems, whether they may be theoretical or applicable to the real world. I have a strong background in math up to multivariable differential calculus, all four AP Physics exams, and AoPS books. Furthermore, I am also fascinated by real world or competition math / physics, Python programming, and discrete maths such as topology or set theory. Feel free to start a chat with me if you have questions regarding any of the above! My sessions are typically chill and fun, and I hope to provide a space for both collaborative learning / problem solving and individualized support. My goal here at schoolhouse is to share a passion and fascination of math + science, and become a better communicator and leader. Cheers, nice to meet you, and hope you'll find my stuff interesting and helpful!

Schedule

✋ ATTENDANCE POLICY

Attendance is not mandatory, but it is highly recommended that learners attend each session as they are ordered very deliberately to enforce understanding. The more you engage with this series, the more you will get out of it!

SESSION 1

1

Feb

SESSION 1

AoPS Math

AoPS Math

Tue 1:30 AM - 2:10 AM UTCFeb 1, 1:30 AM - 2:10 AM UTC

Welcome all to the first session! Learning outcomes (session 1.1): - Getting to know everyone! - What is geometry? - The Cartesian Plane - Axioms of Euclidean Geometry - Q&A for the series!
SESSION 2

8

Feb

SESSION 2

AoPS Math

AoPS Math

Tue 1:30 AM - 2:10 AM UTCFeb 8, 1:30 AM - 2:10 AM UTC

Hello all! This session is when the plane we were introduced to last week gets really exciting. Stay tuned! Learning outcomes (session 1.2): - Lines and their Properties - Shapes - Circles and Ellipses - The Shoelace Theorem - Modelling: Is a point inside a shape?
SESSION 3

15

Feb

SESSION 3

Physics

Physics

Tue 1:30 AM - 2:10 AM UTCFeb 15, 1:30 AM - 2:10 AM UTC

Hello all! Today, we will make the math of previous chapters much more powerful using vectors. Learning outcomes (session 2.1): - Norm of a Vector - Unit Vector - Components - Vector Addition
SESSION 4

22

Feb

SESSION 4

Physics

Physics

Tue 1:30 AM - 2:10 AM UTCFeb 22, 1:30 AM - 2:10 AM UTC

Hello all! This session will demonstrate why vectors are essential in mathematics and beyond. Learning outcomes (session 2.2): - Introduction to physics (d,v,a, and force) - Orthogonal Projections - Modelling: Collisions
SESSION 5

25

Feb

SESSION 5

Physics

Physics

Fri 2:15 AM - 2:45 AM UTCFeb 25, 2:15 AM - 2:45 AM UTC

Hello all! This session will demonstrate why vectors are essential in mathematics and beyond. Learning outcomes (session 2.2): - Displacement, velocity, and force vectors in complex situations - F = ma!!!! - Modelling: Trajectories
SESSION 6

1

Mar

SESSION 6

Physics

Physics

Tue 12:30 AM - 1:10 AM UTCMar 1, 12:30 AM - 1:10 AM UTC

Back to vectors after a short detour in the wonders of physics! Learning outcomes (session 2.3): - Orthogonal projection - Applications of projection in physics - Modelling: Collisions
SESSION 7

8

Mar

SESSION 7

Physics

Physics

Tue 1:30 AM - 2:10 AM UTCMar 8, 1:30 AM - 2:10 AM UTC

This session, we will cover the dot product and all the ways in which it is useful in mathematics and beyond. Learning outcomes (session 2.4): - The dot product - Scalar/Vector properties - What does the dot product tell us about motion?
SESSION 8

15

Mar

SESSION 8

AoPS Math

AoPS Math

Tue 12:30 AM - 1:10 AM UTCMar 15, 12:30 AM - 1:10 AM UTC

This session is very focused on the application of the vectors we have learnt so far. Modelling, modelling, and more modelling! Learning Outcomes (session 2.5): - Modelling ball bouncing on ramp - Modelling ball colliding with ball
SESSION 9

22

Mar

SESSION 9

Even More Math

Even More Math

Tue 12:30 AM - 1:10 AM UTCMar 22, 12:30 AM - 1:10 AM UTC

Hello All! In this session, we will use vectors to prove some very important AoPS theorems! Learning outcomes (session 2.6): - How do we write a geometric proof? - Proofs, proofs, and more proofs
SESSION 10

29

Mar

SESSION 10

Physics

Physics

Tue 12:30 AM - 1:10 AM UTCMar 29, 12:30 AM - 1:10 AM UTC

Up until now everything we have been doing is in two dimensions, yet the world is in 3 dimensions. How can we adapt out models? Learning Outcomes (session 3.1): - Vector addition, products, and projections in 3 dimensions - Cartesian plane equation and the normal vector
SESSION 11

15

Apr

SESSION 11

AoPS Math

AoPS Math

Fri 2:30 AM - 3:10 AM UTCApr 15, 2:30 AM - 3:10 AM UTC

Hello all! This session, we will cover important geometrical ideas in 3 dimensions. This session will be a bit less practical, and a bit more theoretical, but will lay important groundwork for our work in the future. Learning Outcomes (session 3.2): - Visualization in the 3rd dimension - Visualization practice - Spherical and Cylindrical coordinates
SESSION 12

22

Apr

SESSION 12

Even More Math

Even More Math

Fri 2:30 AM - 3:10 AM UTCApr 22, 2:30 AM - 3:10 AM UTC

Continued work in the 3rd dimension! Learning Outcomes (session 3.3): - Equations of geometry in 3 dimensions
SESSION 13

29

Apr

SESSION 13

Even More Math

Even More Math

Fri 2:30 AM - 3:10 AM UTCApr 29, 2:30 AM - 3:10 AM UTC

Important 3 dimensional tools for your ever expanding toolbelt. Learning Outcomes (session 3.4): - Cross product - Norm Vector to a plane
SESSION 14

6

May

SESSION 14

Physics

Physics

Fri 2:00 AM - 2:40 AM UTCMay 6, 2:00 AM - 2:40 AM UTC

[MAYBE?] The Final Session of the Series! It's been a great 3 months everyone! - Requests for more sessions are still open - Bring any questions about anything we've covered - Review and Fun Physics + Vectors Questions!

Public Discussion

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Feb 1 - May 6

14 weeks

30 - 40 mins

/ session