ORMC Meetings Archive • Fall 2007–Spring 2024 For the current schedule, visit the Circle Calendar 2007–2008 2008–2009 2009–2010 2010–2011 2011–2012 2012–2013 2013–2014 2014–2015 2015–2016 2016–2017 2017–2018 2018–2019 2019–2020 2020–2021 2021–2022 2022–2023 2023–2024 Spring 2023 quarter // Filter groups by: Advanced 1A Advanced 1B Advanced 2 Advanced 3 AMC 10/12 A Training AMC 10/12 B Training AMC 8 Training Beginners 1A Beginners 1B Beginners 1C Beginners 2A Beginners 2B Chess club Intermediate 1A Intermediate 1B Intermediate 2A Intermediate 2B 6/4/2023

Handouts: Problems

Handouts: Rules | TeX archive | Solutions | Game dominoes

ARML-style end-of-year contest, with AMC problems to review topics we have discussed throughout the year

Handouts: worksheet | solutions(references) A contest in Olympiad format.

Handouts: EGMO | EGMO_solutions

We will do a little geometry practice to reinforce what we've learned in the past three lessons. We will take a quiz. Then we will learn to play some math-games.

The last meeting of the year! There will be a tournament with some prizes for the winners :)

Class Logistics:

We will meet from 4-6 pm at Math Sciences 6221

Class Plan:

We end the year with a fun competition!

Required Resources:

Pencil, eraser, and scratch paper.

Homework Due:

No homework

Homework Assigned:

No homework

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu or Naji Sarsam at najisarsam@g.ucla.edu if you have any questions, comments, or concerns!

Class Logistics:

We will meet from 4-6 pm at Math Sciences 6229

Class Plan:

We end the year with a fun competition!

Required Resources:

Pencil, eraser, and scratch paper.

Homework Due:

No homework

Homework Assigned:

No homework

Contact Information:

Handouts: Decryption I | Handout | Decryption II | 4-Coloring Graphs

Handouts: Summer 2023 quarter // Filter groups by: Advanced 1A Advanced 2A Beginners 1A Beginners 1B Beginners 2A Beginners 2B BNP A BNP B Intermediate 1A Intermediate 1B 6/25/2023

Handouts: Handout We review basic facts about real numbers. Conduit link: https://tinyurl.com/ORMCconduit

Handouts: Handout 1 Students will study chapter 12 from the course book.

Students will study chapter 12 from the course book.

Students will study the Polibius and Caesar ciphers.

Handouts: Caesar cipher template Students will study the Polibius and Caesar ciphers.

Handouts: Caesar cipher template Students will study the first two chapters of the coursebook.

Students will study the first two chapters of the coursebook.

Students will learn about binary numbers and complements, as well as their application to computer systems. By the end of the lesson, students should understand the fundamentals of the two's complement representation for signed binary numbers.

Handouts: | Solution Students will learn about binary numbers and complements, as well as their application to computer systems. By the end of the lesson, students should understand the fundamentals of the two's complement representation for signed binary numbers.

Handouts: | Solution 7/9/2023

Handouts: |

Handouts: Old handout, continued | New handout Students will study a few games as an intro to game theory.

Students will study a few games as an intro to game theory.

Students will study anagrams, the pigpen and rail fence ciphers.

Students will study anagrams, the pigpen and rail fence ciphers.

We will start with checking lesson 2 homework. It may take the entire class. If time permits, we will start lesson 3.

We will start with checking lesson 2 homework. It may take the entire class. If time permits, we will start lesson 3.

We will review the basics of boolean algebra.

Handouts: | Solution We will review the basics of Boolean algebra.

Handouts: Handout | Solution 7/16/2023

Handouts: We have seen the Archimedes' Axiom for real numbers. Now we will study the fields where it doesn't hold, so there are infinitesimal and unlimited numbers/

Students will play a few more games trying to figure out a winning strategy. Then they will take a quiz to assess their understanding of the covered material. If time permits, students will start chapter 19 from the course book.

Students will play a few more games trying to figure out a winning strategy. Then they will take a quiz to assess their understanding of the covered material. If time permits, students will start chapter 19 from the course book.

Students will study 3D solids and their 2D projections.

Students will study 3D solids and their 2D projections.

Finish up chapter 3, assign the second quiz.

Finish up chapter 3, assign the second quiz.

We will review Boolean algebra properties and apply them to logic problems.

Handouts: | Solution We will review Boolean algebra properties and apply them to logic problems.

Handouts: | Solution 7/23/2023

Handouts: Handout We see the hyperreals for the first time and prove their properties.

Handouts: Handout Students will study chapter 19 of the course book.

Students will study chapter 19 of the course book.

Students will be constructing all the 3D solids having given 2D projections.

Students will be constructing all the 3D solids having given 2D projections.

We will go over chapter 4.

We will go over chapter 4.

We will study Boolean algebra expressions in disjunctive normal form and use cubes of various dimensions to simplify them.

Handouts: | Solution We will study Boolean algebra expressions in disjunctive normal form and use cubes of various dimensions to simplify them.

Handouts: | Solution 7/30/2023

Handouts:

Handouts: Additional handout Students will study chapter 20 of the course book.

Students will study chapter 20 of the course book.

Students will study lesson 9 from the course book.

Students will study lesson 9 from the course book.

Finish chapter 5, take quiz 3.

Finish chapter 5, take quiz 3.

We will take a break from our normal material and have a fun competition.

Handouts: | Answer Key We will take a break from our normal material and have a fun competition.

Handouts: | Answer Key 8/6/2023 If more than n pigeons are placed in n pigeonholes, there must be at least one pigeonhole with more than one pigeon. This seemingly simple principle is instrumental in solving many rather hard combinatorial problems.

We will look at infinitesimal changes in the hyper-Euclidian plane and do the nonstandard trigonometry and geometry.

Handouts: Handout Students will study chapter 21 of the course book.

Students will study chapter 21 of the course book.

Students will pay a virtual visit to the Island of Knights and Liars. Students will have to solve logic puzzles based on the habits of the islanders.

Students will pay a virtual visit to the Island of Knights and Liars. Students will have to solve logic puzzles based on the habits of the islanders.

Discuss chapter 6, and if time permits start chapter 7.

Discuss chapter 6, and if time permits start chapter 7.

Students will start learning the theory of permutations. The goal of this mini-course is to understand when the famous puzzle is solvable and when it's not.

Handouts: | Answer Key Students will start learning the theory of permutations. The goal of this mini-course is to understand when the famous puzzle is solvable and when it's not.

Handouts: | Answer Key 8/13/2023

Handouts: handout | solutions We continue with the same topic

Handouts: Handout Students will study chapter 22 of the course book. If time remains, they will start chapter 23.

Students will study chapter 22 of the course book. If time remains, they will start chapter 23.

Students will learn the definition of a statement and how the AND operation acts on statements.

Students will learn the definition of a statement and how the AND operation acts on statements.

Review chapter 7, and take quiz 4.

Review chapter 7, and take quiz 4.

We will continue our study on the 15 puzzle, delving more into permutations and learning taxicab geometry.

Handouts: | Answer Key We will continue our study on the 15 puzzle, delving more into permutations and learning taxicab geometry.

Handouts: | Answer Key 8/20/2023

Handouts: Handout | Bonus problems

Summer 2023 quarter // Filter groups by: Advanced Beginners 1A Beginners 1B Beginners 2A Beginners 2B BNP A BNP B Intermediate 1A Intermediate 1B 8/27/2023

Students will study the Euler constant e and exponential functions.

Students will study chapter 23 of the course book.

Students will study chapter 23 of the course book.

Students will continue studying Boolean algebra.

Students will continue studying Boolean algebra.

Quiz 5, Chapter 9. We will finish the rest of the book!

Quiz 5, Chapter 9. We will finish the rest of the book!

We will learn basics of graph theory and consider various relevant theorems.

We will learn basics of graph theory and consider various relevant theorems.

Fall 2023 quarter // Filter groups by: Advanced 1A Advanced 1B Advanced 2 Advanced 3 AMC 10/12 AMC 8 Training Beginners 1A Beginners 1B Beginners 1C Beginners 2A Beginners 2B BNP A BNP B Chess club Intermediate 1A Intermediate 1B Intermediate 2A Intermediate 2B Olympiads 10/1/2023

Handouts: Handout | Solutions

Handouts: Handout | Solutions

Handouts: Handout. | Solution key.

Handouts: Problems Basics for the amc, with a focus on solving equations and important factoring identities

Handouts: worksheet | solutions

Handouts: Practice Test Students will review Roman numerals and then study lesson 18 from the course book.

Students will review Roman numerals and then study lesson 18 from the course book.

Students will review Roman numerals and then study lesson 18 from the course book.

Students will review clock arithmetic and learn the applications of mod 360 arithmetic to measuring angles and to timekeeping.

Students will review clock arithmetic and learn the applications of mod 360 arithmetic to measuring angles and to timekeeping.

Students will study lesson 1 and possibly lesson 2 of the course book.

Students will study lesson 1 and possibly lesson 2 of the course book.

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will warm up with some fun games and then introduce basic probability.

Required Resources:

Pencils, eraser, scratch paper and dice.

Homework Due:

N/A.

Homework Assigned:

Finish the handout (Problem 17 is optional).

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout We will warm up with some fun games and then introduce basic probability.

Homework: Finish the handout for week 1 (Problem 17 is optional).

Handouts: Handout for Week 1 | Optional Problems Students will start learning set theory.

Handouts:

Handouts: We'll do a variety of Olympiad problems to warm up for the year of problem-solving.

The problems will range in level, from practice problems through BAMO up to Putnam, so there should be something for everyone.

Handouts: 10/8/2023

Handouts: Handout | Solutions

Handouts: Solutions | Handout

Handouts:

Handouts: AMC basics involving functions: domain, range, graphing, inverses, recursive functions

Handouts: worksheet | solutions

Handouts: We will discuss chapter 19, which goes over the balance scale and problems relating to it.

We will talk about binary numbers and the balance scale. I will also review how to do addition and subtraction using an abacus.

We will discuss chapter 19, which goes over the balance scale and problems relating to it.

Students will review unit of measurements such as time and learning about coordinates on the globe

Students will learn about time's relationships with the globe, including time zones and more.

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will start with a review of basic probability from last week. We will then introduce combinatorics tools and apply them to calculate probabilities.

Required Resources:

Pencils, eraser and scratch paper.

Homework Due:

Finish last week’s handout (Problem 17 is optional).

Homework Assigned:

Attempt problems 1-12, 14, 16, 18, 20 and 21.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout We introduce the concepts of factorial, permutations, and binomial coefficients, as well as their application to calculating probabilities.

Homework: Problem 1-12, 14, 16, 18, 20 and 21 from the handout.

Handouts: Handout for Week 2 We are going to explore the concept of induction, and apply it to the tower of Hanoi. Further, we are going to talk about combinations, permutations, and binomial coefficients.

Handouts:

Handouts: We'll focus on writing clear proofs as we do problems from books and from a variety of actual Olympiads.

Handouts: Problems 10/15/2023

Handouts: Handout | Solutions

Handouts: Handout | Solutions

Handouts: |

Handouts: worksheet 3 basics of complex number arithmetic and geometry

Handouts: worksheet | solutions

Handouts: We will complete chapter 20.

We will finish Chapter 19 on pan balances, and begin Chapter 20, using the balance pans to introduce the idea of binary numbers.

We will complete chapter 20.

Students will learn about Earth's poles and practice calculating time based off Earth's movement.

Students will continue learning about the relationships between geometry and time, using real-world examples from around the globe.

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will start with a review of combinatorics from last week. We will then learn how to use combinatorics to calculate probabilities.

Required Resources:

Pencils, eraser, scratch paper and dice.

Homework Due:

Problems 1-12, 14, 16, 18, 20 and 21 from last week's handout.

Homework Assigned:

Problems 1-17 on the handout.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 3974.

Class Plan:

We will start with a review of combinatorics from last week. We will then learn how to use combinatorics to calculate probabilities.

Required Resources:

Pencils, eraser and scratch paper.

Homework Assigned (Due Oct 22):

Problem 1-17 on the handout below. Reading on the first half of Page 9 is optional.

Contact Information

Email zhenye@ucla.edu and will652397@gmail.com if you have any questions.

Handouts: Handout for Week 3 | Homework Solution We are going to explore many aspects and applications of induction, in divisibility problems, inequalities, visual and geometry problems, and puzzles.

Handouts:

Handouts: This week, we will solve competition problems with invariants.

When there is some repeated process, rather than studying what does change, we may want to look at what stays the same.

This allows us to make connections between the starting and ending positions, and we can rule out many possibilities this way.

Handouts: 10/22/2023

Handouts: Solutions | Handout

Handouts: Solutions | Handout

Handouts: |

Handouts:

Handouts: worksheet

Handouts: We will continue our journey in Binary Land, and cover chapter 21.

We will use the pan balance to motivate defining and working with binary numbers.

We will continue our journey in Binary Land, and cover chapter 21.

Students will use modular arithmetic to convert time on Planet Heptadium. In the second half of the class, will learn how to solve different types of cryptarithms.

Students will learn more about modular arithmetic through examples surrounding time in a world where people count mod seven.

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will explore some fun logic puzzles.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

Problems 1-17 from last week's handout.

Homework Assigned:

None.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 3974.

Class Plan:

We will explore some fun logic puzzles as well as some challenging mathematical games.

Required Resources:

Pencils, eraser and scratch paper.

Homework Assigned:

No homework this week.

Contact Information

Email zhenye@ucla.edu and will652397@gmail.com if you have any questions.

Handouts: Handout for Week 4

Handouts:

Handouts: We'll look at a few problems involving polynomials and the tricks to solve them.

Handouts: 10/29/2023

Handouts: Handout | Solutions

Handouts: Handout | Solutions

Handouts:

Handouts: Rings 1

Handouts: worksheet

Handouts: Students who have not already taken quiz 6 will take it, and then we will work on chapter 22.

We will follow Chapter 21, studying the method for writing numbers in binary form.

Students who have not already taken quiz 6 will take it, and then we will work on chapter 22.

Students will learn about prime numbers and practice using divisibility patterns.

Students will review previous concepts in Quiz 1 and learn how to solve Cryptarithms in this week's lesson.

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will explore problem solving through sample olympiad problems.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

None.

Homework Assigned:

Problems 1-8 on the handout.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 3974.

Class Plan:

We will do competition-type math problems and introduce some problem-solving techniques.

Required Resources:

Pencils, eraser and scratch paper.

Homework Assigned (Due Nov. 5):

Problem 1-8 on the handout.

Contact Information

Email zhenye@ucla.edu and will652397@gmail.com if you have any questions.

Handouts: Handout for Week 5 | Homework Solution We are going to take a look into the basics of error correcting codes. In other words, we are going to think of smart ways to encode and decode messages such that slight errors that may alter our message during transmission won't affect the receivers ability to interpret it.

Handouts:

Handouts: We consider some more techniques for working with polynomials, such as Vieta's Formulas and tools for working with irreducible polynomials.

Handouts: 11/5/2023

Handouts: Handout | Solutions

Handouts: Handout | Solutions

Handouts:

Handouts: Handouts: test

Handouts: We will finish chapter 23, and then start chapter 24.

We will finish chapter 23, and then start chapter 24.

Students will continue learning how to use Modular Arithmetic to solve ciphers as well as review divisibility rules from last week.

Students will learn about divisibility rules for numbers in base 10.

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will introduce sets and discuss their properties.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

Problems 1-8 on the previous week's handout.

Homework Assigned:

Finish this week's handout.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 3974.

Class Plan:

We will introduce the concept of sets and do some basic set theory.

Required Resources:

Pencils, eraser and scratch paper.

Homework Assigned (Due Nov. 19):

Finish all problems on the handout.

Contact Information

Email zhenye@ucla.edu and will652397@gmail.com if you have any questions.

Handouts: Handout for Week 6 | Solutions to Selected Problems We will look into some interesting graph theory problems, along with a surprising application.

Handouts:

Handouts: We will do competition problems using inequalities such as AM-GM and Cauchy-Schwarz.

Handouts: 11/19/2023 Students will be given a tour of the Airspace corporation. A quarterly guest lecture will be a part of the tour.

Students will be given a tour of the Airspace corporation. A quarterly guest lecture will be a part of the tour.

Students will be given a tour of the Airspace corporation. A quarterly guest lecture will be a part of the tour.

Students will be given a tour of the Airspace corporation. A quarterly guest lecture will be a part of the tour.

After finishing our review of Chapter 22 (counting triangles), we will work through Chapter 23 -- bits and digits.

Students will working on the Ciphers and Functions Packet.

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will continue our discussion of sets by introducing the notions of power sets and Cartesian products.

Required Resources:

Pencils, eraser, scratch paper, and handout from Week 5: Problem Solving.

Homework Due:

Previous week's handout.

Homework Assigned:

Finish this week's handout.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 3974.

Class Plan:

We will review the basic concepts of set theory, and introduce power set and Cartesian products.

Required Resources:

Pencils, eraser and scratch paper.

Homework Assigned (Due Dec. 3):

Finish the handout

Contact Information

Email zhenye@ucla.edu and will652397@gmail.com if you have any questions.

Handouts: Handout for Week 7 | Solutions to Selected Problems We are going to apply some of our Graph Theory skills to playing the games of Sim and Sprouts and solve related problems.

Handouts:

Handouts: 12/3/2023

Handouts: Handout | Solutions

Handouts: Handout | Solutions

Handouts:

Handouts: |

Handouts: worksheet

Handouts: We will review some counting problems. Then we will discuss the differences and similarities between decimal and binary numbers (Chapter 23).

Students will finish reviewing the previous week's handout and then complete a practice Math Kangaroo.

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will continue our discussion of sets by discussing functions between sets and cardinalities of finite and infinite sets.

Required Resources:

Pencils, eraser, scratch paper, and handout from Week 5: Problem Solving.

Homework Due:

Previous week's handout.

Homework Assigned:

Problems 1.1 to 1.9 and 1.12.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 3974.

Class Plan:

We will study functions between sets.

Required Resources:

Pencils, eraser and scratch paper.

Homework Assigned (Due Dec 10):

Finsh Problem 1.1 - 1.9 and 1.12 on the handout.

Contact Information

Email zhenye@ucla.edu and will652397@gmail.com if you have any questions.

Handouts:

Handouts:

Handouts: We will go over the basics of generating functions, and see how they can be used in olympiad problems about counting.

Handouts: 12/10/2023

Handouts: Problems

Handouts: Handout | Solutions

Handouts:

Handouts: worksheet

Handouts: Algebra | Geometry | Number Theory | Probability We will cover Chapter 24 (odd and even numbers). Students who finish the chapter will then play a mathematical game in pairs.

Students will play a review Jeapordy Game

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will have a fun competition to end the quarter!

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

Problems 1.1 to 1.9 and 1.12 on previous week's handout.

Homework Assigned:

None.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 3974.

Class Plan:

We will do an end-of-quarter competition.

Required Resources:

Pencils, eraser and scratch paper.

Homework Assigned:

None.

Contact Information

Email zhenye@ucla.edu and will652397@gmail.com if you have any questions.

Handouts:

Handouts:

Handouts: We'll continue thinking about generating functions, showing some more advanced techniques for particular competition problems.

Handouts: Winter 2024 quarter // Filter groups by: Advanced 1A Advanced 1B Advanced 2 Advanced 3 AMC 10/12 Training AMC 8 Training Beginners 1A Beginners 1B Beginners 1C Beginners 2A Beginners 2B BNP A BNP B Chess club Intermediate 1A Intermediate 1B Intermediate 2A Intermediate 2B Olympiads 1/7/2024

Handouts: Handout

Handouts: Handout

Handouts:

Handouts: Basics of trig functions, law of sines, law of cosines, stewart's theorem

Handouts: worksheet

Handouts: We will complete chapter 28.

We will finish our class on odds and evens (Chapter 25, with a review of 24.15), and then we will demonstrate some binary mathemagic!

We will complete chapter 28.

Students will begin studying the fundamental properties of geometry through introduction handouts.

Handouts: Students will review the fundamentals of geometry through two introduction handouts.

Handouts: Lesson packet

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will begin our exploration of Euclidean geometry.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

None.

Homework Assigned:

Section 1 on this week's handout.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 3974.

Class Plan:

We will introduce basic concepts in Euclidean geometry.

Required Resources:

Pencils, eraser and scratch paper.

Homework Assigned (Due 1/14):

Finish Section 1 (1.1 - 1.13) on the handout.

Contact Information

Email zhenye@ucla.edu and will652397@gmail.com if you have any questions.

Handouts: Handout for Week 1 | Solutions to Selected Problems

Handouts:

Handouts: We'll take a look at a variety of different combinatorics problems, from olympiad training books and actual competitions.

Handouts: 1/14/2024

Handouts: Handout

Handouts: Handout

Handouts:

Handouts: Using mass points method to solve 2D geometry problems

Handouts: worksheet

Handouts: We will take quiz 7, and then work on chapter 29 which focuses on a recap of previous material and understanding ascii tables.

We will cover the binary magic trick from Chapter 26 and 27.

We will take quiz 7, and then work on chapter 29 which focuses on a recap of previous material and understanding ascii tables.

Students will learn to utilize a ruler and compass to construct triangles and evaluate congruence proofs. They will also continuing focusing on rays and straight angles.

Handouts: Lesson 2 Students will learn to utilize a ruler and compass to construct triangles and evaluate congruence proofs.

Handouts: Previous Lesson | Lesson

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will continue our exploration of Euclidean geometry.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

Section 1 on last week's handout.

Homework Assigned:

Attempt all of this week's handout.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 3974.

Class Plan:

We will continue to do some Euclidean geometry, focusing on calculating angles and theorems on congruence triangles.

Required Resources:

Pencils, eraser and scratch paper.

Homework Assigned (Due 1/21):

Finish the worksheet up to Problem 3.7. If you have time, attempt Problem 3.8, 3.9, and 3.10.

Contact Information

Email zhenye@ucla.edu and will652397@gmail.com if you have any questions.

Handouts: Handout for Week 2 | Solutions to Selected Problems

Handouts:

Handouts: I've selected the easier half of this year's Putnam problems, and broken them into approachable pieces with some hints.

Handouts: 1/21/2024

Handouts: Warmup Problems | Worksheet | Solutions

Handouts: Solutions | Warmup | Handout

Handouts:

Handouts: Solving AMC problems using basic-intermediate concepts in number theory

Handouts: worksheet Students who have signed up to take the AMC 8 test with ORMC will take it in MS 5200 from 1:00 PM on.

We will finish chapter 29, then continue on to chapter 30.

We will finish the binary magic trick (Chapter 27), and start to think about how to make arithmetic work with binary numbers (Chapter 28).

We will finish chapter 29, then continue on to chapter 30.

Students will review the past geometry concepts ( rays, lines, and triangle constructions) through a test and begin learning about the Pythagorean Theorem.

Handouts: Students will review the previous lessons and take a quiz on geometric constructions.

Handouts: Practice Test

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will discuss the notion of area and perimeter.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

Attempt all of last week's handout.

Homework Assigned:

Attempt all problems until 3.13.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 3974.

Class Plan:

We will discuss the notion of area and perimeter.

Required Resources:

Pencils, eraser, ruler and scratch paper.

Homework Assigned (Due 1/28):

Finish the handout except for the challenge problems. Attempt the challenge problems if you have time.

Contact Information

Email zhenye@ucla.edu and will652397@gmail.com if you have any questions.

Handouts: Handout for Week 3 | Solutions to Selected Problems

Handouts:

Handouts: Inspired by a problem from last week's worksheet on the 2023 Putnam, this week we will be diving into uses of expected values in probability problems.

Handouts: 1/28/2024

Handouts: Solutions | Handout

Handouts: Solutions | Handout

Handouts:

Handouts: More topics in number theory: euclidean algorithm, chinese remainder theorem

Handouts: worksheet

Handouts: We will go over chapter 31.

The abacus will help us to visualize arithmetic -- addition and subtraction -- of binary numbers. At the end of the class, parents are invited in for a demonstration of the binary magic trick that students have been practicing.

We will go over chapter 31.

Students will use the triangle congruency postulates they have learned to prove different identities of a Rhombus and begin learning about the Pythagorean theorem.

Handouts: Students will continue building upon their knowledge of geometry by learning how to construct and utilize right angles and triangles.

Handouts: 01/28 Packet

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will discuss a non-Euclidean notion of distance and the corresponding geometry.

Required Resources:

Pencils, eraser, scratch paper and compass.

Homework Due:

Attempt all problems up to 3.13 on last week's handout.

Homework Assigned:

No homework.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 3974.

Class Plan:

We will introduce taxicab geometry, including taxicab distances and circles.

Required Resources:

Pencils, eraser, ruler and scratch paper.

Homework Assigned (Due 2/4):

Finish the handout.

Contact Information

Email zhenye@ucla.edu and will652397@gmail.com if you have any questions.

Handouts: Handout for Week 4

Handouts:

Handouts: We'll take a look at some interesting number theory problems from problem books and competitions.

Handouts: 2/4/2024

Handouts: Handout

Handouts: Handout

Handouts:

Handouts: Worksheet with mixed AMC 10 and 12 problems covering various topics that we have covered during the year up to this point

Handouts: worksheet

Handouts: We will finish our discussion of binary arithmetic (addition and subtraction, Chapter 28), and then look at how binary coding can be used to represent letters as well as numbers (ASCII, chapter 29). We will not have a quiz.

Students will continue learning about how to use right angles and triangle congruences to prove the Pythagorean Theorem. If there is time, they will begin learning about line segments in the Geometry Workbook.

Handouts: Students will continue learning about right triangles and The Pythagorean Theorem.

Handouts:

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will continue our exploration of taxicab geometry with a discussion on shapes.

Required Resources:

Pencils, eraser, scratch paper and compass.

Homework Due:

No homework.

Homework Assigned:

Attempt all of this week's handout.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 3974.

Class Plan:

We will continue on the theory of taxicab geometry, focusing on graphing conic curves.

Required Resources:

Pencils, eraser, ruler and scratch paper.

Homework Assigned:

TBD

Contact Information

Email zhenye@ucla.edu and will652397@gmail.com if you have any questions.

Handouts: Handout for Week 5

Handouts:

Handouts: This week, we will talk about combinatorial geometry.

We'll start with the classic Lazy Caterer's Problem and build up to harder problems about counting geometrical objects.

Handouts: 2/18/2024

Handouts: Handout | Solutions

Handouts: Handout

Handouts:

Handouts: Practice for AMC 10/12 -level counting techniques

Handouts: worksheet

Handouts: We will finish chapter 33, and complete the book!

We will study the differences between orientable and non-orientable surfaces. Students will make their own Mobius strips and study what happens when the strips are cut. We will follow Chapter 30 from the workbook. Students should each bring with them a pair of scissors that they are able to safely use.

We will finish chapter 33, and complete the book!

Students will continue learning about the Euclidean Plane, focusing on vectors and learning basic physic properties.

Handouts: Students will explore the properties of parallel lines and apply them to proofs.

Handouts: 02/18 Packet

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will explore the qualities of large numbers.

Required Resources:

Pencils, eraser, scratch paper and compass.

Homework Due:

All of the previously assigned handout

Homework Assigned:

Sections 1, 2 and 3 on this week's handout.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout

Handouts: Handout for Week 6 | Solutions to Selected Problems

Handouts:

Handouts: We use the complex plane interpretation to solve geometry problems using complex algebra.

Handouts: 2/25/2024

Handouts: Handout | Solutions

Handouts: Handout | Solutions

Handouts:

Handouts: More practice and review on important combinatorics techniques for the AMC 10/12

Handouts: worksheet

Handouts: We will finish chapter 33

We will start with a short quiz on binary numbers, odds and evens and the balance scale. Then we will start the topic of coordinates (Chapter 31).

We will finish chapter 33

Students will continue learning about vectors and begin doing vector algebra such as addition.

Handouts: Students will learn about the unique properties of vectors and why they are useful in geometric proofs.

Handouts: Handout | Problem 4 Solution

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will introduce the concept of a mathematical game and Nash equilibrium.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

Sections 1, 2 and 3 on the previous week's handout.

Homework Assigned:

Sections 1, 2 and 3 on this week's handout.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 3974.

Class Plan:

We will introduce mathematical game theory, including the concepts of Nash equilibrium, dominant strategies, and mixed strategies.

Required Resources:

Pencils, eraser, ruler and scratch paper.

Homework Assigned:

Finish Section 2 and 3 on the handout.

Contact Information

Email zhenye@ucla.edu and will652397@gmail.com if you have any questions.

Handouts: Handout for Week 7 | Solutions to Selected Problems

Handouts:

Handouts: We'll take a look at a particular kind of coordinate system based on triangles.

We'll then use these barycentric coordinates to prove theorems and solve competition problems based on triangles.

Handouts: 3/3/2024

Handouts: Handout | Solutions

Handouts: Handout | Solutions

Handouts:

Handouts: Winter Final Exam I | Winter Final Exam II Solving AMC 10/12 problems related to factoring, systems of equations, graphing, logarithms, and functions

Handouts: worksheet

Handouts: We will start the new book, packets will be provided.

We conclude our discussion of coordinate geometry

We will start the new book, packets will be provided.

Students will continue their handout from last week, solidifying their knowledge of vector addition and drawing them.

Handouts: Students will learn about linear combinations of vectors and how to utilize them.

Handouts:

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will solve some fun mathematical games.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

Sections 1, 2 and 3 on the previous week's handout.

Homework Assigned:

Section 1 on the this week's handout.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 3974.

Class Plan:

We will continue our exploration in mathematical game theory.

Required Resources:

Pencils, eraser, ruler and scratch paper.

Homework Assigned:

No homework this week.

Contact Information

Email zhenye@ucla.edu and will652397@gmail.com if you have any questions.

Handouts: Handout for Week 8 Probability and Statistics

In this class, students will use probability and statistics to determine whether they think that a popular Minecraft YouTuber cheated during his December 2020 speed-run of the game (as well as other fun problems!).

Handouts: Many combinatorial problems have the same solution - the Catalan numbers.

We will use some of these problems to practice bijective combinatorial proofs, and then apply those techniques to competition problems.

Handouts: Spring 2024 quarter // Filter groups by: Advanced 1A Advanced 1B Advanced 2 Advanced 3 AMC 10/12 Training AMC 8 Training Beginners 1A Beginners 1B Beginners 1C Beginners 2A Beginners 2B BNP A BNP B Chess club Intermediate 1A Intermediate 1B Intermediate 2A Intermediate 2B Olympiads 3/10/2024

Handouts: Handout

Handouts: Handout

Handouts: |

Handouts: Contest-style worksheet, including questions involving all topics covered up to this point in the class.

Handouts: individual round | relay round | team round

Handouts: Number Theory | Geometry | Combinatorics/Probability | Algebra We will work on the second packet.

We will review materials from Chapter 32. Then students will work on the review chapter (Chapter 33) in small groups.

We will work on the second packet.

Students will spend the last class of the quarter playing a jeopardy style review game on the topics covered this quarter.

Handouts:

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will have a fun competition to end the quarter!

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

Sections 1 on the previous week's handout.

Homework Assigned:

None.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 3974.

Class Plan:

We will do an end-of-quarter competition.

Required Resources:

Pencils, eraser and scratch paper.

Homework Assigned:

None.

Contact Information

Email zhenye@ucla.edu and will652397@gmail.com if you have any questions.

Handouts: Handouts:

Handouts: We'll prove some formulas for summing binomial coefficients, and use them to solve competition problems.

Handouts: 3/31/2024

Handouts: Handout | Solutions

Handouts: Handout | Solutions

Handouts:

Handouts: miscellaneous geometry practice from past amc 10/12 exams

Handouts: worksheet

Handouts: Welcome to Spring quarter! We will start chapter 3 of the book.

We will introduce the subject of ciphers and practice coding and decoding our own messages.

Welcome to Spring quarter! We will start chapter 3 of the book.

Students will review past vector concepts from last quarter: addition, subtraction, and resizing, and apply them into geometric proofs.

Handouts: More practice with vector addition, subtraction and scaling.

Handouts: Vectors and Physics 3

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will introduce the concepts of exponents and logarithms.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

None.

Homework Assigned:

None.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Introducing exponents and logarithms, understanding the relationship to one another, and preparing for financial interest calculations.

Handouts:

Handouts:

Handouts: We return to number theory, and solve some problems with factorization and gcds.

Handouts: 4/7/2024

Handouts: Handout

Handouts: Solutions | Handout

Handouts:

Handouts: Review of some important AMC 10/12 number theory concepts, with practice problems

Handouts: worksheet

Handouts: We will discuss functions. Chapter 4 of the book.

We will have a second lesson on ciphers.

We will discuss functions. Chapter 4 of the book.

Students will use their knowledge of vectors to learn about the Newtonian Laws of Motion.

Handouts:

Handouts: Vectors and Physics Packet

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will explore proof by induction.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

None.

Homework Assigned:

None.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Conceptual understanding of induction and problem-solving using inductive hypothesis.

Handouts:

Handouts:

Handouts: We'll pick up last week's theme of factorization, but instead of focusing on gcds, we focus on direct applications of unique factorization into primes.

Handouts: 4/14/2024

Handouts: Handout | Solutions

Handouts: Handout | Solutions

Handouts:

Handouts: Various AMC 10/12 problems, with a focus on algebra-related problems (polynomials, solving inequalities/equations/modular congruences, etc.)

Handouts: worksheet

Handouts: We will cover chapter 5 and go further in depth into functions.

We will review the materials on codes from the last two classes, and do a short quiz. Remember to bring your Cesar cipher disk to class!

We will cover chapter 5 and go further in depth into functions.

Students will continue to learn about the Newtons Three Laws of Motion, specifically focusing on the third law. They will complete practice problems about pulley systems.

Continuing the study of Newton's Laws in packet 4 (focusing on his 2nd and 3rd laws, along with practicing acceleration).

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will talk about investments and interest.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

None.

Homework Assigned:

None.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout A comprehensive introduction to financial literacy series, starting with the concept of investment, interest, and the time value of money.

Handouts:

Handouts:

Handouts: We will study multiplicative functions such as the sum-of-divisors function and Euler's totient function, and use them to solve Olympiad number theory problems.

Handouts: 4/21/2024

Handouts: Handout | Solutions

Handouts: Handout | Solutions

Handouts:

Handouts: Assorted AMC 10/12 combinatorics practice problems

Handouts: worksheet

Handouts: We will complete chapter 6, and then take the quiz 2.

We will continue our discussion of functions, with definitions and lots of examples.

We will complete chapter 6, and then take the quiz 2.

Students will go over the review packet in groups and then take a calmative test to gauge their understanding of the concepts

Handouts:

Handouts: Review Packet

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will talk about present value of money and discounting.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

None.

Homework Assigned:

Sections 1, 2 and 3 in this week's handout.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout An introduction to the concept of present value and discounting with a specific focus on present value calculations for annuities and perpetuities.

Handouts:

Handouts:

Handouts: We learn about vector spaces, and use dimensions of vector spaces to solve competition problems.

Handouts: 4/28/2024

Handouts: Handout

Handouts: Handout

Handouts: |

Handouts: AMC 10/12 trigonometry practice

Handouts: worksheet

Handouts: We will finish up our work on functions. Then, if time permits us to, we will start our next major topic, which is the study of 3D solids.

Handouts: Students reviewed their exam on Physics concepts and started a lesson on Barycentric Coordinates.

Handouts: Barycentric Coordinates

Class Logistics:

We will meet from 4 to 6 pm over Zoom: https://ucla.zoom.us/j/95659914795?pwd=U1dBVG4xNVpON1A0Yit4VG5rYlIzUT09.

Class Plan:

We will explore representing numbers using continued fractions.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

Sections 1, 2 and 3 in last week's handout.

Homework Assigned:

Section 1 on this week's handout.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout

Handouts: Topic: Intermediate 2A 4/28

Time: Apr 28, 2024 03:45 PM Pacific Time (US and Canada)

Join Zoom Meeting

https://ucla.zoom.us/j/92456640968?pwd=amhNajlSUXlES2V5cEZtSVg1akUvZz09

Meeting ID: 924 5664 0968

Passcode: 112358

Join by SIP

• 92456640968@zoomcrc.com

Handouts:

Handouts: | We pick up the linear algebra theme from last week. This time, will look at matrices, and the functions they define between vector spaces.

Handouts: Handout 5/5/2024

Today, we'll play with the LEAN proof assistant.

AMC 10/12 practice problems related to algebra

Handouts: worksheet

Handouts: Handout | Practice Problems we will finish chapter 8.

We will do a short quiz on functions, and begin the study of 3D geometry. Please bring blank cubes to class.

we will finish chapter 8.

Students will finish learning about balancing torque in the Barycentric packet and then begin the Geometry in Problems book.

Students played 5D chess against instructors and amongst each other.

Handouts: Barycentric Coordinates

Class Logistics:

We will meet from 4 to 6 pm over Zoom: https://ucla.zoom.us/j/99291091244?pwd=SzIwbFpuZmtqZVY4alZyc0VYUlpGdz09.

Class Plan:

We will explore an exciting variation of a classic game.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

Sections 1 in last week's handout.

Homework Assigned:

None.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

A variation on the classic game. We will meet from 4 to 6 pm over Zoom: https://ucla.zoom.us/j/99700609296?pwd=VW9ENW9GRkJPcENDV2J4Z1lINDBJQT09

Handouts:

Handouts: We will study operations called affine transformations, and use them to simplify competition problems in geometry.

Handouts: 5/12/2024

Handouts: Handout | Solutions

Handouts: Handout | Solutions

Handouts:

Handouts: More combinatorics practice

Handouts: worksheet

We will continue our study of 3D geometry, using projections to study more complicated constructions made from cubes. If the class is in person we will also do a short quiz to review our understanding of functions.

Students will play a unique game called 5D multi travel chess and solve puzzles in groups

Finishing the packet, along with additional problems to ensure comprehension.

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will have a review of basic probability concepts, followed by a discussion on conditional probability, independence and expectation.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

None.

Homework Assigned:

Finish all problems through Section 4 on this week's handout.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout An introduction to the fundamentals of probability theory alongside an exploration of how mathematical expectation connects to expected return in finance.

Handouts:

Handouts:

Handouts: We will solve problems with an evergreen Pigeonhole Principle.

Handouts: Handout 5/19/2024

Handouts: Handout | Solutions

Handouts: Handout | Solutions

Handouts:

We will finish up chapter 10

We will continue our discussion of 3D shapes, including shortest paths on 3D shapes. Time permitting we will have a short quiz on the material that we have covered so far.

We will finish up chapter 10

Students will continue to work through the book, working on mostly Chapter 1 problems.

As a final physics lesson for the quarter students covered momentum and kinetic energy, through a packet written by Kyle.

Handouts: Physics Review

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will start with a review on conditional probability, followed by an introduction to random walks and the Markov property. Finally, we will explore applications of the probability concepts we have studied to modern finance.

Required Resources:

Pencils, eraser, and scratch paper.

Homework Due:

Finish all problems through Section 4 on last week's handout.

Homework Assigned:

None.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

Handouts: Handout Start with a review on conditional probability, followed by an introduction to random walks and the Markov property. Continuing to explore various financial asset classes in Modern Finance.

Handouts: This week, we work on more combinatorial problems related to tilings.

Handouts: We see how trigonometric identities are useful in competition problems, including those featuring square roots, geometry, and telescoping sums.

Handouts: 5/26/2024 Memorial Day weekend, no Chess Club

6/2/2024 Prof. Rahul Roy from UCLA Physics Department will give a guest lecture in MS 4000 A, followed by Q&A. Then ORMC graduating seniors will get their diplomas and presents and possibly share their plans for the future.

Prof. Rahul Roy from UCLA Physics Department will give a guest lecture in MS 4000 A, followed by Q&A. Then ORMC graduating seniors will get their diplomas and presents and possibly share their plans for the future.

Prof. Rahul Roy from UCLA Physics Department will give a guest lecture in MS 4000 A, followed by Q&A. Then ORMC graduating seniors will get their diplomas and presents and possibly share their plans for the future.

Prof. Rahul Roy from UCLA Physics Department will give a guest lecture in MS 4000 A, followed by Q&A. Then ORMC graduating seniors will get their diplomas and presents and possibly share their plans for the future.

Students will compete in teams solving problems related to topics covered throughout the year

Handouts: worksheet

Final class of the quarter. Topic is TBD, but it will not be from the book.

Final class of the quarter. Topic is TBD, but it will not be from the book.

Students will play a review game for the last class of the Quarter

Class Logistics:

We will meet from 4 to 6 pm at Math Sciences 6221.

Class Plan:

We will end the quarter by playing some fun finance-related board games!

Required Resources:

None

Homework Due:

None

Homework Assigned:

None.

Contact Information:

Please reach out to Siddarth Chalasani at darthsid2000@ucla.edu if you have any questions, comments or concerns!

As we approach the end of the quarter, we will play the strategy board game "Acquire", immersing ourselves in the world of powerful real estate tycoons where players compete against each other in a gripping game of manipulation, mergers, and strategic stock trading.

We are going to be looking into the brilliant game of 5D chess by doing some puzzles and playing friendly matches.

We'll look at a variety of olympiad-style problems based on the simple premise of tiling a gridded shape with other gridded shapes.

Handouts: