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Enrichment • Series

AoPS: Counting and Probability Study Group

Tony T

Series Details

Sessions

Public Discussion

This series ended on September 4, 2022. All 1:1 and group chats related to this series are disabled 7 days after the last session.

Series Details

About

Hello everyone!
Counting and probability are essential components of mathematics -- it is pretty much guaranteed to comprise significant amounts of any math contest! However, in my experience, it is rare to see an advanced and in-depth study of counting in curriculums. Herein lies the goal of this study group: to introduce everyone to the strategies of solving problems of this sort, and to develop the skills to apply these strategies in the unfamiliar situations we are sure to run into in any math contest.
Learners in this series can expect:
a) regular sessions beginning with content from the AoPS book and later delving much deeper into the fascinating world of math
b) real math contest questions thoroughly explained, with a focus on developing our problem solving skills when faced with a new problem
c) plenty of fun and interactive group problem solving sessions
d) question and answer periods -- dedicated times or at the end of sessions -- for individualized support

Feel free to send me a message if there are any questions or requests for content to be covered.
Thanks everyone, and cheers!

Tutor Qualifications

- Several past AoPS series here on schoolhouse!

- 2x AIME invitee

- AMC Distinguished Honor Roll

- 8x Honor Roll in various Canadian math contests

- Check tutor profile for past learner feedback!

✋ ATTENDANCE POLICY

Attendance at every session is strongly recommended, but is not mandatory. The series is designed so newer sessions build off of content from previous sessions (earlier sessions you may find easy, but the difficulty ramps up very quickly), so you'll make the most out of our study group by attending all our meets!

Our schedule is not set in stone! Feel free to send me a message if certain times do not work for you.

Dates

August 2 - September 4

Learners

11 / 15

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

Aug

Session 1

AoPS Math

Tue Aug 2, 2022, 9:30 PM

Prologue: Introduction to Counting and Probability
Hi all! Today's learning objectives are:
> What is counting, and why is it so important?
> What is randomness, and what is probability?
> What does it really mean for something to be probable?

Aug

Session 2

AoPS Math

Thu Aug 4, 2022, 9:30 PM

1.1: The Selection Problem
Hey all! Today's learning objectives are:
> The factorial
> Choose notation
> Complementary counting
> How to use combinations to solve complex problems!

Aug

Session 3

AoPS Math

Sat Aug 6, 2022, 9:30 PM

1.2: The Ordering Problem
Hi everyone! Today's learning objectives are:
> Permutations
> When to P and when to C?
> Solving the (very common!) ordering problem
> How to use permutations to solve very challenging problems!

Aug

Session 4

AoPS Math

Tue Aug 9, 2022, 9:30 PM

1.3: Distinguishability
Hi all! Today's learning objectives are:
> Recognize distinguishability and understand why it is critical to any counting problem
> Lots of practice problems and problem solving strategies

Aug

Session 5

AoPS Math

Thu Aug 11, 2022, 9:30 PM

1.4: Counting Models
Hi everyone! Today's learning objectives are:
> The ball-and-urn model (and under which distinguishability configurations should it be used?)
> The insertion strategy (and under which distinguishability configurations should it be used?)
> Analysis of complex systems by division into subsystems

Aug

Session 6

AoPS Math

Sat Aug 13, 2022, 9:30 PM

1.5: Unit Wrap-Up
Hey everyone! Next week, we'll be moving into 2.1. This session is for all your questions to do with this unit, and will be filled with intriguing practice problems!

Aug

Session 7

AoPS Math

Wed Aug 17, 2022, 2:30 AM

2.1: The Essence of Probability
Hi all! Today's learning objectives are:
> What is probability (important definition!)
> The tree diagram, and when to use it
> Probability tables (a little bit of game theory involved!)

Aug

Session 8

AoPS Math

Fri Aug 19, 2022, 2:30 AM

1.6 Grid Counting
Learning Objectives:
> All sorts of miscellaneous and new counting problems to do with grids

Aug

Session 9

AoPS Math

Sun Aug 21, 2022, 2:30 AM

2.2 Pascal's Triangle and Proofs
Learning Objectives:
> What is the Pascal's triangle, and how do we use it?
> The many many ways why Pascal's Triangle is magical
> Miscellaneous counting proofs

Aug

Session 10

AoPS Math

Wed Aug 24, 2022, 2:30 AM

2.3 Extended Binomial Theorem
Learning Objectives:
> What is the extended binomial theorem, and in what way is it extended?
> How can we prove the extended binomial theorem given the existing binomial theorem?
> Surprise guest from Calculus: The Maclaurin series as an alternative to the extended binomial theorem? (don't worry, this is a completely miscellaneous topic and understanding of calc is not required moving forward)

Aug

Session 11

AoPS Math

Sun Aug 28, 2022, 2:30 AM

2.4 Geometric Probability
Learning Objectives:
> The concept of infinite possibilities
> How can we do counting problems that have infinite probabilities?
> Geometry as the essential tool of handling infinities

Aug

Session 12

Review

Wed Aug 31, 2022, 2:30 AM

Unit 2: Review Session 1
Hey all! This session is for any questions you may have regarding anything we have worked through in the series. We will also be going over Extension Problem Set 1: Grid Counting so give those questions a try prior to the session!

Sep

Session 13

Review

Fri Sep 2, 2022, 2:30 AM

Unit 2: Review Session 1
Hey all! This session is for any questions you may have regarding anything we have worked through in the series. We will also be going over the Parallelogram Counting questions in Extension Problem Set 1: Grid Counting.

Sep

Session 14

Review

Sun Sep 4, 2022, 2:30 AM

LAST SESSION: Unit 2: Review Session 2
Hey all! This session is for any questions you may have regarding anything we have worked through in the series. We will also be going over several extension problems!

Public Discussion

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