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AoPS: Counting and Probability Study Group

SAT Score Range

14 sessions

+8

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.

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!

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 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.

SESSION 1

2

Aug

SESSION 1

AoPS Math

AoPS Math

Tue 9:30 PM - 10:10 PM UTCAug 2, 9:30 PM - 10:10 PM UTC

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?
SESSION 2

4

Aug

SESSION 2

AoPS Math

AoPS Math

Thu 9:30 PM - 10:10 PM UTCAug 4, 9:30 PM - 10:10 PM UTC

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!
SESSION 3

6

Aug

SESSION 3

AoPS Math

AoPS Math

Sat 9:30 PM - 10:10 PM UTCAug 6, 9:30 PM - 10:10 PM UTC

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!
SESSION 4

9

Aug

SESSION 4

AoPS Math

AoPS Math

Tue 9:30 PM - 10:10 PM UTCAug 9, 9:30 PM - 10:10 PM UTC

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
SESSION 5

11

Aug

SESSION 5

AoPS Math

AoPS Math

Thu 9:30 PM - 10:10 PM UTCAug 11, 9:30 PM - 10:10 PM UTC

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
SESSION 6

13

Aug

SESSION 6

AoPS Math

AoPS Math

Sat 9:30 PM - 10:10 PM UTCAug 13, 9:30 PM - 10:10 PM UTC

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!
SESSION 7

17

Aug

SESSION 7

AoPS Math

AoPS Math

Wed 2:30 AM - 3:10 AM UTCAug 17, 2:30 AM - 3:10 AM UTC

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!)
SESSION 8

19

Aug

SESSION 8

AoPS Math

AoPS Math

Fri 2:30 AM - 3:10 AM UTCAug 19, 2:30 AM - 3:10 AM UTC

1.6 Grid Counting Learning Objectives: > All sorts of miscellaneous and new counting problems to do with grids
SESSION 9

21

Aug

SESSION 9

AoPS Math

AoPS Math

Sun 2:30 AM - 3:10 AM UTCAug 21, 2:30 AM - 3:10 AM UTC

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
SESSION 10

24

Aug

SESSION 10

AoPS Math

AoPS Math

Wed 2:30 AM - 3:10 AM UTCAug 24, 2:30 AM - 3:10 AM UTC

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)
SESSION 11

28

Aug

SESSION 11

AoPS Math

AoPS Math

Sun 2:30 AM - 3:10 AM UTCAug 28, 2:30 AM - 3:10 AM UTC

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
SESSION 12

31

Aug

SESSION 12

Review

Review

Wed 2:30 AM - 3:10 AM UTCAug 31, 2:30 AM - 3:10 AM UTC

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!
SESSION 13

2

Sep

SESSION 13

Review

Review

Fri 2:30 AM - 3:10 AM UTCSep 2, 2:30 AM - 3:10 AM UTC

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.
SESSION 14

4

Sep

SESSION 14

Review

Review

Sun 2:30 AM - 3:10 AM UTCSep 4, 2:30 AM - 3:10 AM UTC

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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Aug 2 - Sep 4

5 weeks

40 mins

/ session

SCHEDULE

Wednesdays

2:30AM

Sundays

2:30AM