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Enrichment • Series

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

Tony T

Series Details

Sessions

Public Discussion

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.

Series Details

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!

Tutor Qualifications

- I have hosted numerous series on AoPS in the past, including Introduction to Geometry!

- I am an AMC honor roll recipient and 2x AIME qualificant

- I have lots of experience teaching math from the fundamentals to higher math

- I received a score of 5 on AP Physics (all 4)

- Tutor profile for student feedback

✋ 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!

Dates

February 1 - May 6

Learners

24 / 30

Total Sessions

About the Tutor

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!

View Tony T's Profile

Upcoming Sessions

Past Sessions

Feb

Session 1

AoPS Math

Tue Feb 1, 2022, 1:30 AM

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!

Feb

Session 2

AoPS Math

Tue Feb 8, 2022, 1:30 AM

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?

Feb

Session 3

Physics

Tue Feb 15, 2022, 1:30 AM

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

Feb

Session 4

Physics

Tue Feb 22, 2022, 1:30 AM

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

Feb

Session 5

Physics

Fri Feb 25, 2022, 2:15 AM

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

Mar

Session 6

Physics

Tue Mar 1, 2022, 12:30 AM

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

Mar

Session 7

Physics

Tue Mar 8, 2022, 1:30 AM

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?

Mar

Session 8

AoPS Math

Tue Mar 15, 2022, 12:30 AM

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

Mar

Session 9

Even More Math

Tue Mar 22, 2022, 12:30 AM

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

Mar

Session 10

Physics

Tue Mar 29, 2022, 12:30 AM

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

Apr

Session 11

AoPS Math

Fri Apr 15, 2022, 2:30 AM

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

Apr

Session 12

Even More Math

Fri Apr 22, 2022, 2:30 AM

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

Apr

Session 13

Even More Math

Fri Apr 29, 2022, 2:30 AM

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

May

Session 14

Physics

Fri May 6, 2022, 2:00 AM

[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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