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Enrichment • Series

Counting and Probability Study Group!

Tony T

Series Details

Sessions

Public Discussion

This series ended on August 12, 2021. All 1:1 and group chats related to this series are disabled 7 days after the last session.

Series Details

About

Hello Everyone! This will be a series which focuses on the AoPS book "Introduction to Counting and Probability". Sessions will be organized by topic, with each session starting with a simpler opening problem, then going over the tools to tackle more advanced problems. This means that different sessions should not range too much in difficulty -- rather each session with start off simple, then quickly become more and more challenging.

We will decide on a schedule as a group, and then sessions will be added.

Tutor Qualifications

I was introduced counting and probability using this book, and have gone on to learn more about it, using AoPS and other sources. I am also a past AMC distinguished honor roll recipient, and have held numerous AoPS sessions here on schoolhouse.world.

✋ ATTENDANCE POLICY

Feel free to hop in on sessions you would like to join, and skip ones regarding topics you feel comfortable with. Cheers!

Dates

July 22 - August 12

Learners

20 / 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

Jul

Session 1

Orientation

Thu Jul 22, 2021, 6:00 PM

Overview of the entire series! Here I will introduce the content and structure of each session, and we will decide on a schedule for future sessions. For this session in particular, please message me if you are unable to make it.
Current Plans: Sessions twice a week, time to be determined.
1.1 Counting Choices, 1.2 Ordering, 1.3 Grids and Pathways, 1.4 Expected Values, 1.5 Pascal's Triangle, 1.6 Geometric Probability
Feel free to mention other topics you would like covered!

Session 2

AoPS Math

Thu Jul 22, 2021, 6:30 PM

Session 1.0: Introduction. This session will cover exponents, factorials, combinations, permutations, and the technical details that will allow us to explore various interesting and useful topics in our future sessions. Optional, but recommended.

Jul

Session 3

AoPS Math

Mon Jul 26, 2021, 6:30 PM

Session 1.1: Ordering and Choices
Opening questions:
  - How many different strings of letters can be created by scrambling the word TOMATO?
  - How many ways are there to give 11 of the same candy to 3 different students?
  - How many ways are there to put 11 different books into 3 identical boxes?
  - How many ways are there to put 11 of the same candy into 3 identical boxes?

Jul

Session 4

Catchup

Wed Jul 28, 2021, 6:30 PM

For anyone who missed our two previous sessions. No one is obliged to come, however it is recommended for anyone who still is somewhat uncomfortable or would like review on factorials, the multiplicative principle, ordering, or choices.

Jul

Session 5

AoPS Math

Thu Jul 29, 2021, 6:30 PM

Will include catchup from previous sessions.
Session 2.1: Grids and Pathways
Opening questions:
There is a square grid of 64 1x1 squares.
  - Starting from the bottom-left corner and only moving up and right along grid lines, how many different paths can be taken to reach the top-right corner?
  - What if one line on the grid is removed? Does where it is removed matter?

Aug

Session 6

AoPS Math

Mon Aug 2, 2021, 6:30 PM

Session 2.2: Grids and Pathways
Opening questions:
There is a square grid of 64 1x1 squares.
  - How many squares are there of any size that is made up of only lines on the grid?
  - How many rectangles are there, following the same limitations as above?
  - What if it was a triangular grid, and we counted triangles? Trapezoids?
Will include catchup from previous sessions.

Aug

Session 7

Catchup

Wed Aug 4, 2021, 6:30 PM

This time will be used for catchup for 2: Grids and Pathways or a general probability Q&A if requested by students.

Aug

Session 8

AoPS Math

Thu Aug 5, 2021, 6:30 PM

Session 3.1: Expected Value
  - Opening Questions to be added.

Aug

Session 9

Catchup

Sun Aug 8, 2021, 8:30 PM

Catchup for everyone who would like review or missed the Ordering lessons, will include ordering strings, stars and bars, and the pathway problems.
Also a general counting and probability Q&A -- Feel free to bring your own questions.
Graphing linear inequalities will be required for the next session and will be briefly covered here if needed -- Please pop if you are not already comfortable with it.

Aug

Session 10

AoPS Math

Mon Aug 9, 2021, 6:30 PM

Session 4.1: Geometric Probability
Two numbers are randomly uniformly selected on the open interval ]0, 10[. What is the probability that they add up to less than 8?
This lesson WILL require understanding of graphing linear inequalities.

Aug

Session 11

Review

Wed Aug 11, 2021, 10:30 PM

Final Review -- Rapid-fire questions aimed to simulate real questions that will reinforce the many problem solving tactics we have learnt so far.
Time to be determined.

Aug

Session 12

AoPS Math

Thu Aug 12, 2021, 10:30 PM

Last Session of the Series -- Bring Your Own Questions, or join us for a problem solving session on difficult problems in the Intro to Counting and Probability book.

Public Discussion

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