UCLA Olga Radko Endowed Math Circle

ORMC Meetings Archive • Fall 2007–Spring 2023

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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
Summer 2022 quarter // Filter groups by:
6/26/2022

We will be kicking off our Summer with a dive into Binary Numbers!

Handouts: handout_1

Students will discuss an optical illusion, solve a warm-up problem having multiple solutions, and then study a bunch of problems on splitting the difference.

Students will discuss an optical illusion, solve a warm-up problem having multiple solutions, and then study a bunch of problems on splitting the difference.

Students will study the Polybius and Caesar cyphers.

Handouts: Caesar cypher template

Students will study the Polybius and Caesar cyphers.

Handouts: Ceasar cypher template

Students will play games counting stories and apartments in buildings.

Students will play games counting stories and apartments in buildings.

Students will try to solve the Instant Insanity puzzle as an introduction to graph theory.

Handouts: handout_1

Students will try to solve the Instant Insanity puzzle as an introduction to graph theory.

Handouts: handout_1

Students will study properties of vectors, constructing vectors with a compass and a ruler (straightedge).

Handouts: handout_1
7/10/2022

Students will study binary fractions, hexadecimal numbers, and relations between binary and hexadecimal numbers.

Handouts: handout_2

We will finish lesson 2, and solve the problems from lesson 3.

We will finish lesson 2 and solve the problems from lesson 3.

Students will warm up solving an anagram. Then they will study the pigpen and rail fence ciphers.

Students will warm up solving an anagram. Then they will study the pigpen and rail fence ciphers.

We will check the lesson 2 homework, including the crossing puzzle, and build more houses!

We will check the lesson 2 homework, including the crossing puzzle, and build more houses!

We will study various properties of graphs ending with Eulerian cycles and the famous Seven Bridges of Konigsberg problem.

Handouts: handout_2

We will study various properties of graphs ending with Eulerian cycles and the famous Seven Bridges of Konigsberg problem.

Handouts: handout_2

This week, we will continue our discussion of geometry and compass-ruler constructions.

Be sure to bring a compass!

Handouts: handout_2
7/17/2022

Students will begin studying knots and their invariants.

Handouts: handout 3

We will finish studying lesson 3 from the book and start lesson 4.

We will finish studying lesson 3 from the book and start lesson 4.

Students will take one last look at ciphers, solve fun problems of other types, and take a quiz on ciphers.

Handouts: Lesson 10

Students will take one last look at ciphers, solve fun problems of other types, and take a quiz on ciphers.

Handouts: Lesson 10

Students will play the lit windows game to learn that subtraction can be understood as removing a part from a whole.

Students will play the lit windows game to learn that subtraction can be understood as removing a part from a whole.

Students will continue the study of graph theory.

Handouts: handout 3

Students will continue the study of graph theory.

Handouts: handout 3

This week, we'll take a break from geometry and focus on combinatorics instead.

Handouts: handout 3
7/24/2022

Students will be introduced to mathematical induction and Peano Axioms to construct the Natural Numbers.

Handouts:

Students will solve fun problems on Roman numerals involving craft sticks.

Students will solve fun problems on Roman numerals involving craft sticks.

Students will continue their study of logic.

Students will continue their study of logic.

Students will finish studying lesson 3 and take quiz 2.

Students will finish studying lesson 3 and take quiz 2.

Students will continue their study of graph theory.

Handouts: handout 4

Students will continue their study of graph theory.

Handouts: handout 4

Student will apply their knowledge of enumerative combinatorics to figuring out probabilities of various events.

Handouts: Handout
7/31/2022

Students will continue knot theory and learn about some algebra behind knots.

Students will continue studying Roman numerals.

Students will continue studying Roman numerals.

Students will continue studying math logic.

Students will continue studying math logic.

Students will study chapter 4 of the BNP book.

Students will study chapter 4 of the BNP book.

Students will take a break from graph theory and solve fun logic puzzles.

Handouts: handout_5

Students will take a break from graph theory and solve fun logic puzzles.

Handouts: handout_5

This week, we will learn how to manipulate vectors, and we'll use them to solve a few problems.

We will also take a quick look at rational and irrational numbers.

Handouts: handout_5
8/7/2022

We will be finishing Peano Axioms that we started online.

Students will learn the rules of converting decimal numbers to Roman numerals.

Students will learn the rules of converting decimal numbers to Roman numerals.

Students will finish the Intro to Math Logic mini-course and take a quiz. If time permits, they will start a new topic, Lineland.

Students will finish the Intro to Math Logic mini-course and take a quiz. If time permits, they will start a new topic, Lineland.

Students will continue the study of the number line.

Students will continue the study of the number line.

Students will complete the previously studied handouts on Euler characteristic and logic puzzles.

Handouts: handout 6

Students will complete the previously studied handouts on Euler characteristic and logic puzzles.

Handouts: handout 6

We will continue our study of vectors, applying what we've learned to solve a few problems involving motion.

We'll also take a look at numbers in various bases.

Handouts: Newtonian Laws of Motion | Place-value numerals
8/14/2022

We will discuss the Chinese Remainder Theorem and how it can be used to solve systems of modular equations!

Students will take the first two quizzes in the book.

Students will take the first two quizzes in the book.

Students will continue studying various shapes intersecting lines and planes.

Students will continue studying various shapes intersecting lines and planes.

Students will study chapter 5 from the course book.

Students will study chapter 5 from the course book.

Students will apply their knowledge of graph theory, trees in particular, to solving a bunch of fun word problems.

Handouts: handout

Students will apply their knowledge of graph theory, trees in particular, to solving a bunch of fun word problems.

Handouts: handout

This week, we'll take a look at graphs and the variety of problems they help us understand.

Handouts: handout_7
8/21/2022

Students will learn basics of group theory and its applications.

Handouts: Groups and symmetry

Students will study chapter 9 from the book.

Students will study chapter 9 from the book.

Students may possibly start the next topic, Traveling on a Cube, if time permits.

Students may possibly start the next topic, Traveling on a Cube, if time permits.

Students will continue studying chapter 5 from the book.

Students will continue studying chapter 5 from the book.

Students will study a part of graph theory that shows how order emerges out of chaos.

Handouts: handout

Students will study a part of graph theory that shows how order emerges out of chaos.

Handouts:

This week, we'll continue our study of graph theory.

We'll also apply what we've learned to solve a fun puzzle.

Handouts: Handout
Fall 2022 quarter // Filter groups by:
8/28/2022

Students will end the Summer Session with a competition!

Today we'll learn to use the slide rule, a device that designed aircraft, sequenced DNA, and sent a man to space.

Handouts: Handout
9/25/2022
Handouts: Handout
Handouts:

We will play a game, called Estimathon (https://estimathon.com/), and start learning about Einstein's special relativity theory.

Handouts: Einstein Special Relativity | Estimathon Game

We will play a game, called Estimathon (https://estimathon.com/), and start learning about Einstein's special relativity theory.

Handouts: Handout source | Estimathon | Estimathon answers | Handout | Handout with solutions

Students will start building their understanding of algebraic structures, from magams to groups.

Handouts: Handout 1 - From Magma to Groups | Quaternions

Introduction to ACM 10/12-level. Algebra techniques including: factoring, equations and systems of equations, functions and recursive functions, and logarithms.

Handouts: Week 1 Worksheet | Week 1 Exercises Solutions

Students will take a diagnostic test, made of fun problems by AoPS.

Handouts: AMC 8 2017

Students will work on a Math Kangaroo test for grades 3-4.

We will cover Chapter 15 -- exploring how objects in a higher number of dimensions look when projected into a smaller number.

We will cover Chapter 15 -- exploring how objects in a higher number of dimensions look when projected into a smaller number.

Quarter Goals:

  • Learn basics of modular arithmetic
  • Learn fundamentals of python programming
  • Practice employing programming to solve difficult math problems

Class Logistics:

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

Class Plan:

Hello everyone! We begin this quarter by briefly studying modular arithmetic. This will serve as a warmup for the type of coding challenges we plan to tackle in Python. The lecture materials will be posted after class.

Required Resources:

A pencil, eraser.

Homework Due:

None

Homework Assigned:

Please complete up to section 2 (pages 1 - 14) in the packet attached below. This packet was handed out during the lecture. We will review the homework next lecture.

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!

Handouts: Modular Arithmetic Packet

We begin this quarter by briefly studying modular arithmetic. This will serve as a warmup for the type of coding challenges we plan to tackle in Python.

Handouts: Handout

Students will learn the game of Nim, and how to always win!

Handouts:

Students will learn the game of Nim, and how to always win!

Handouts: Nim Handout
Handouts:
10/2/2022
Handouts: Handout
Handouts:

We continue the last handout on relativity. Please, bring it with you.

Handouts: Handout

This week we continued studying Algebraic Structures to get into the concept of Groups.

Handouts: Handout 1 - From Magma to Groups

Divisibility rules, basic modular arithmetic, and well-known modular arithmetic techniques and theorems

Handouts: Week 2 Worksheet | Week 2 Exercises Solutions

This week we started with combinatorics for our in-depth concept training for the AMC 8. We worked on problems from past AMC 8 tests during group work.

Handouts: | Answers

Last class, we started solving the 2013 Math Kangaroo packet for grades 3 and 4. Next class, we will spend the earlier half of the class discussing several hard problems from the packet and use our remaining time to work on a new packet.

We will continue with our study of the mathematics of projection. This week we will study Flatland -- a 2D world, in which 3D shapes appear in projected form.

We will cover Flatland, in which 3-dimensional objects are projected into a 2d space over time. Handouts will be released shortly.

Quarter Goals:

  • Learn basics of modular arithmetic
  • Learn fundamentals of python programming
  • Practice employing programming to solve difficult math problems

Class Logistics:

We will meet from 4-5 pm (only 1 hour lecture due to fundraising event aftewrard) at Math Sciences 6221

Class Plan:

We continue our study of modular arithmetic

Required Resources:

A pencil, eraser.

Homework Due:

Please complete up to section 2 (pages 1 - 14) in the packet attached below. This packet was handed out during the lecture. We will review the homework next lecture.

Please also fill out the following google form by October 5th so that we can prepare for our future python lessons: http://tiny.cc/intermediate1_CS.

Homework Assigned:

None.

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!

Handouts: Modular Arithmetic

We will continue working on the modular arithmetic handout from the previous week.

Students will continue learning about the game of Nim!

Students will learn the game of Nim, and how to always win!

Handouts:
10/3/2022

We continue having fun around Einstein's special relativity. This time we discuss time dilation

10/9/2022
Handouts: Handout | Solutions
Handouts: Handout | Solutions

This week we will discuss length contraction in ESP theory. Please keep having fun

Handouts: handout | solutions

This week we will discuss length contraction in ESP theory.

Handouts: handout | solutions

This week we will study Symmetry Groups of regular polygons and platonic solids.

Handouts: Handout 2: Symmetry Groups

More AMC techniques in number theory, including prime factorizations, the euclidean algorithm, and the chinese remainder theorem

Handouts: Week 3 Worksheet Solns | Week 3 Worksheet | Week 3 Modular Exponent Solns
Handouts: Practice Questions | Handout

Last class (10/2), we worked on a new Math Kangaroo packet. Next class, we will start by discussing the more challenging problems from the previous class and use our remaining time to work on a new packet.

We will do a recap of lineland and flatland, including a short quiz. Then we will start the next topic, which is inverse operations.

Quarter Goals:

  • Learn basics of modular arithmetic
  • Learn fundamentals of python programming
  • Practice employing programming to solve difficult math problems

Class Logistics:

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

Class Plan:

We finish our study of modular arithmetic and move on to the basics of python! We begin by studying data types and variables.

Required Resources:

A computer with mouse and charger being optional

Homework Due:

None.

Homework Assigned:

None.

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!

We will begin Python programming this week. Please bring laptops to class and ensure you have a Google account that can access and run Colab notebooks.

Beginner Notebook

Advanced Notebook

Students will learn how to optimise geometric constructions, such as finding the largest area of an object with fixed perimetre.

Handouts:

Students will learn the fundamentals of basic optimization problems.

Handouts:
Handouts:
10/16/2022

There are many ways to characterize integers: primes versus composite, abundant versus deficient, even naughty versus nice. We will focus on the second of these, trying to make sense of the question, “what’s the probability an integer is abundant?” Exploring this question will compel us to think deeply about primes, and a menagerie of Greek letters, and even the question of naughty versus nice.

There are many ways to characterize integers: primes versus composite, abundant versus deficient, even naughty versus nice. We will focus on the second of these, trying to make sense of the question, “what’s the probability an integer is abundant?” Exploring this question will compel us to think deeply about primes, and a menagerie of Greek letters, and even the question of naughty versus nice.

There are many ways to characterize integers: primes versus composite, abundant versus deficient, even naughty versus nice. We will focus on the second of these, trying to make sense of the question, “what’s the probability an integer is abundant?” Exploring this question will compel us to think deeply about primes, and a menagerie of Greek letters, and even the question of naughty versus nice.

There are many ways to characterize integers: primes versus composite, abundant versus deficient, even naughty versus nice. We will focus on the second of these, trying to make sense of the question, “what’s the probability an integer is abundant?” Exploring this question will compel us to think deeply about primes, and a menagerie of Greek letters, and even the question of naughty versus nice.

There are many ways to characterize integers: primes versus composite, abundant versus deficient, even naughty versus nice. We will focus on the second of these, trying to make sense of the question, “what’s the probability an integer is abundant?” Exploring this question will compel us to think deeply about primes, and a menagerie of Greek letters, and even the question of naughty versus nice.

Basic combinatorics topics, including permutations, combinations, complementary counting, and stars-and-bars

Handouts: Week 4 Worksheet | Week 4 Worksheet Solutions
Handouts: Problems | Handout

In our last class, we discussed some tricky questions from the second MK packet. Then, we spent the remainder of our time discussing the first two problems on a new MK packet. Next class, instead of completing the packet in its entirety, we will be discussing individual questions after allotting time for the students to discuss with their group mates.

We will discuss the book Flatland. Then we will finish Chapter 18, on inverting operations. If we have time, we start a new Chapter on geodesics (shortest paths) on the cube.

Quarter Goals:

  • Learn basics of modular arithmetic
  • Learn fundamentals of python programming
  • Practice employing programming to solve difficult math problems

Class Logistics:

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

Class Plan:

We continue our study of Python. We continue studying data types and introduce control flow.

Required Resources:

A computer with mouse and charger being optional

Homework Due:

None.

Homework Assigned:

Homework 1 multiple choice sheet.

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!

This week we will cover if-else statements and for loops.

Beginner Notebook

Advanced Notebook

Handouts: Homework

Students will learn the basics of probability, including conditionals.

Students will study chapter 11, Conditional Probability, from the book Intermediate Counting and Probability by AoPS.

https://drive.google.com/drive/folders/1G1AH8RT6kd46WimDh-6yccsNmms68Qz-?usp=sharing

Handouts:
10/23/2022
Handouts: Handout | Solutions
Handouts: Handout | Solutions

Students will study possibly the most important 20th century computer, the slide rule.

Handouts: Slide-rule - handout

We will learn to use the slide rule to calculate

Handouts: Handout | Slide rule

During this lecture, we will learn about a group associated to the Rubik's cube. We will study this group to understand how and why the cube can be solved.

Handouts: Handout 3 - Rubik's cubes

More topics in combinatorics and probability, including inclusion-exclusion, geometric probability, and binomial coefficient identities and formulas.

Handouts: Week 5 Worksheet | Week 5 Solutions
Handouts: Practice Questions | Packet

Last class, we continued with Math Kangaroo training. We will no longer be doing Math Kangaroo training for our upcoming class and will instead be starting our workbook. Please do not forget to purchase and bring the "From Optical Illusions to Fight Dragons" workbook.

In this class we will study geodesics, also known as shortest paths. In most of our experience shortest paths are straight lines. Given any 2 points there is exactly one shortest path between them. But there are spaces in which shortest paths look very different and for which two point may have two very different shortest paths between them (Ch. 19).

We will cover the topic of shortest paths on a geometric figure.

Quarter Goals:

  • Learn basics of modular arithmetic
  • Learn fundamentals of python programming
  • Practice employing programming to solve difficult math problems

Class Logistics:

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

Class Plan:

We continue our study of Python.

Required Resources:

A computer with mouse and charger being optional

Homework Due:

Homework 1 multiple choice worksheet

Homework Assigned:

Homework 2 multiple choice worksheet

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!

This week we will go into more depth on looping, including while loops and nested loops, and also cover how to make interactive programs with user input.

Beginner Notebook

Advanced Notebook

Handouts: Homework
Handouts:
Handouts:
Handouts:
10/30/2022
Handouts: Handout | Solutions
Handouts:

This Sunday we will have a special Halloween estimathon and for the remaining time we will look at a worksheet on measurement errors.

Handouts: Estimathon | A study on measurement errors

We will have a game and a worksheet on measurement errors.

Handouts: Errors handout

In this lecture, we will keep discussing about the 3x3x3 Rubik's cube and we will introduce and discuss the 2x2x2 Rubik's cube.

Handouts: Handout 4
Handouts: Week 6 Worksheet | Week 6 Solutions

Finished up with geometry, so students should finish the practice/homework packet problems for homework and bring it back to class next week.

Handouts: Handout | Practice/Homework

Last class, we started the "From Optical Illusions to Fighting Dragons" workbook and completed chapter 1. Next class, we anticipate to complete chapter 2 by the end of our session.

We will review Chapter 19, on shortest paths on a cube that students were able to pre-study for homework. Then we will cover Chapter 20, which is a review of both topics. There will be a short quiz. Time permitting, we will start to look at Egyptian multiplication.

Quarter Goals:

  • Learn basics of modular arithmetic
  • Learn fundamentals of python programming
  • Practice employing programming to solve difficult math problems

Class Logistics:

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

Class Plan:

We continue our study of Python.

Required Resources:

A computer with mouse and charger being optional

Homework Due:

Homework 2 multiple choice worksheet

Homework Assigned:

Homework 3 multiple choice worksheet

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!

This week we will continue where we left off on last week's content.

Handouts: Homework

Students will learn to play and win a fun game called the 1-9 Game.

Handouts:
Handouts:
Handouts:
11/6/2022
Handouts: Handout
Handouts:

This Sunday we will look at certain optimization probles, which will include the minimization and maximization of area, distance, or perimeter, given certain constraints, and properties of light.

Handouts:

We will study geometry problems asking to find minimums

Handouts: Handout

This week, we will introduce the concept of Fields and study some basic examples including the field of constructible real numbers.

Handouts: Handout 5
Handouts:
Handouts: Handout

Last class, we finished the second chapter of the workbook. We anticipate covering the third chapter by the end of this coming session. Please do not forget to bring your workbooks!

We will finish covering Egyptian multiplication.

Quarter Goals:

  • Learn basics of modular arithmetic
  • Learn fundamentals of python programming
  • Practice employing programming to solve difficult math problems

Class Logistics:

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

Class Plan:

We continue our study of Python.

Required Resources:

A computer with mouse and charger being optional

Homework Due:

Homework 3 multiple choice worksheet

Homework Assigned:

Homework 4

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!

This week we will finish our discussion of looping and user input.

Advanced Notebook

Handouts: Homework

Students will learn an important mathematical concept called induction, as well as a rigorous way to construct the natural numbers.

Handouts:
Handouts:
11/13/2022

Competition related to Group Theory and Fields Theory.

Handouts: Math Competition Exam 1 | Math Competition Exam 2

Enjoy Veteran's day weekend!

11/20/2022
Handouts: Handout | Solutions
Handouts: Handout | Solutions

Hello, this Sunday we will continue with optimization problems in a more geometrical context.

Handouts: Handout

We continue the same theme

Handouts: Handout
Handouts: Similar Triangles Handout

Answers are on last page of practice test

Handouts: Practice Test

Last two weeks, we finished the third chapter of the workbook and administered a small quiz for the students. Next class, we anticipate to cover all of the fourth chapter by the end of our session.

We will finish studying Chapter 22, revisiting binary numbers. For our class, it is not necessary for students to have studied this topic before in Beginners 1.

Quarter Goals:

  • Learn basics of modular arithmetic
  • Learn fundamentals of python programming
  • Practice employing programming to solve difficult math problems

Class Logistics:

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

Class Plan:

We continue our study of Python.

Required Resources:

A computer with mouse and charger being optional

Homework Due:

Homework 4 multiple choice worksheet

Homework Assigned:

None, although there is an optional practice problem sheet! The kids can do it to win points for the special lesson plan this upcoming class.

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!

This week we will review what we have covered over the course of the quarter and touch on some graph theory.

Students will continue learning about Peano Axioms and induction.

Handouts:
11/27/2022

We are thankful to all the parents and students!

12/4/2022
Handouts: Problems | Solutions

This class we will start studying ring theory.

Handouts: Handout 6

Discussion of piecewise functions, strategies for solving, and important piecewise functions like absolute value and floor. (Also reviewing Binomial Coefficients from previous weeks).

Handouts: Piecewise Functions Worksheet

Students will continue learning more about roman numerals and associated algorithms.

We follow Chapter 23, learning how to multiply numbers that are represented in binary form.

Quarter Goals:

  • Learn basics of modular arithmetic
  • Learn fundamentals of python programming
  • Practice employing programming to solve difficult math problems

Class Logistics:

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

Class Plan:

We have a fun end-of-year relay planned!

Required Resources:

Nothing!

Homework Due:

None, although there is an optional practice problem sheet! The kids can do it to win points for the special lesson plan this upcoming class.

Homework Assigned:

None, enjoy winter break!

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!

Handouts: Python Extra Practice (WIN SOME POINTS FOR YOUR TEAM!)

This week we will have a friendly team-based competition.

12/11/2022

We play a final game for the quarter

Winter 2023 quarter // Filter groups by:
1/8/2023

Students will learn set-theoretical foundations of probability and solve practice problems. Students will also have to save Alice and Bob from an evil dictator.

Handouts: Probability 1

Students will learn set-theoretical foundations of probability and solve practice problems. Students will also have to save Alice and Bob from an evil dictator.

Handouts: Probability 1

Students will study a beautiful and highly applicable part of graph theory.

Handouts: Network flows

This week we will discuss about polynomial rings and how the elements of these rings can be used to draw objects.

Handouts: Worksheet 7: Polynomial Rings | Solutions 7: Polynomial Rings

Circle geometry: including basics, inscribed angle theorem, power of a point, and incircles and circumcircles

Handouts: Circles 1 | Circles Solutions

Students will continue studying Roman numerals, including "move a stick" problems.

Multiplication is standardly introduced as repeated addition. In this lesson, students will learn that division can be introduced as repeated subtraction.

Multiplication is standardly introduced as repeated addition. In this lesson, students will learn that division can be introduced as repeated subtraction.

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We will introduce/play the card game SET and explain our goals for the quarter. Then we begin brainstorming about numbers and algebraic axioms.

Handouts will be posted after the lesson.

Required Resources:

Dr. Gleizer emailed the class parents regarding purchasing a copy of the card game SET. Please ask your child to bring it to class this week.

Have your children bring a pencil and eraser. No computers or associated accessories should be brought.

Homework Due:

None.

Homework Assigned:

Complete Handout 1, which is attached below as a PDF. Please note that this is a brainstorming worksheet. So, there are no right and wrong answers.

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!

Handouts: Algebra For SET Handout 1 - What Is a Number Part I

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We will introduce/play the card game SET and explain our goals for the quarter. Then we begin brainstorming about numbers and algebraic axioms.

Handouts will be posted after the lesson.

Required Resources:

Dr. Gleizer emailed the class parents regarding purchasing a copy of the card game SET. Please ask your child to bring it to class this week.

Have your children bring a pencil and eraser. No computers or associated accessories should be brought.

Homework Due:

None.

Homework Assigned:

TBA

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu or Siddarth Chalasani, darthsid2000@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: Algebra for SET. Handout 1.

Students will study a tricky combinatorial problem that is important in computer science and has deep historical roots.

Handouts: handout

Students will study a tricky combinatorial problem that is important in computer science and has deep historical roots.

Handouts: handout
Handouts: handout
1/15/2023
Handouts: Handout
Handouts: Handout

This week, we'll learn about a few error-correcting coding schemes.

If time permits, we'll try to use them to solve a hat puzzle.

Handouts: Handout

This week we will discuss the vanishing set of several polynomials in several variables.

Handouts: Worksheet 8 - Vanishing Sets and Ideals

More circles: triangle incircles, circumcircles, and cyclic quadrilaterals

Handouts: solutions | worksheet

Last class, we got through almost all of chapter 6 of the workbook. Next class, we will wrap up chapter 6 and start chapter 7.

We will do a short discussion of the relationship between ASCII coding and binary numbers. Then we will review some of the techniques from the last two classes (multiplication, division, binary). After a short quiz, we will do some Math Kangaroo problems if time allows.

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We dive deeper into the algebraic axioms of types of numbers on the real line.

We then cover examples of other objects which can be "added" together like numbers: symmetry groups.

Handouts will be posted after the lesson: Handout 1 was homework, Handout 2 and 3 were passed out in class.

Required Resources:

Have your children bring a pencil and eraser.

No computers or associated accessories should be brought.

The SET card game is not needed for this lesson.

Homework Due:

Handout 1, which is attached below as a PDF.

Homework Assigned:

Complete up to the second to last page of Handout 2, which is attached below as a PDF. Handout 3 is not due as 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!

Handouts: Algebra For SET Handout 1 - What Is a Number Part I | Algebra For SET Handout 2 - What Is a Number Part II | Algebra For SET Handout 3 - Symmetry Groups

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

Discuss solutions to handout 1 which was assigned as homework for the previous homework and begin a new handout as part 2 of abstract algebra.

Required Resources:

Have your children bring a pencil and eraser. No computers or associated accessories should be brought.

Homework Due:

Handout 1

Homework Assigned:

TBA

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu or Siddarth Chalasani, darthsid2000@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: Abstract Algebra III | Abstract Algebra II
Handouts:

Students will learn the basic principles of counting and be able to apply combinatorial arguments to solve probability problems.

Handouts: | Solutions
Handouts:
1/22/2023
Handouts: Handout | Solutions
Handouts: Handout | Solutions
Handouts: Handout

This week we will investigate the relation between affine varieties and ideals in polynomial rings.

Handouts: Worksheet 9: Affine Varieties

Basic Inequalities and solving strategies, AM-GM inequality, review of cyclic quadrilateral theorems from last week

Handouts: worksheet

Students signed up to take AMC 8 with ORMC will take the test in MS 5200 from 1:00 to 3:00 PM PST.

Last class, we were able to start chapter 7 of the workbook towards the end of class. Next class, we will take a short break from the workbook and work on some Math Kangaroo problems.

We will demonstrate and then learn a magic trick that use trinary representations to locate a card in a deck.

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We now study objects that have nice notions of addition and multiplication: fields. The primary examples we focus on are the modular finite fields.

Handouts will be posted after the lesson.

Required Resources:

Have your children bring a pencil and eraser.

No computers or associated accessories should be brought.

The SET card game is not needed for this lesson.

Homework Due:

Handout 2, which is attached below as a PDF.

Homework Assigned:

Completing Handout 5, which is attached below (and was also passed out in class).

Note that Handout 4 is a reference sheet that was also passed out in class. This reference sheet may be very helpful for the kids to finish their homeworl.

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!

Handouts: Algebra for SET Handout 2 - What is a Number Part II | Algebra for SET Handout 4 - Axioms Reference | Algebra for SET Handout 5 - Modular Arithmetic

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We now study objects that have nice notions of addition and multiplication: fields. The primary examples we focus on are the modular finite fields.

Handouts will be posted after the lesson.

Required Resources:

Have your children bring a pencil and eraser.

No computers or associated accessories should be brought.

The SET card game is not needed for this lesson.

Homework Due:

Handout 2, which is attached below as a PDF.

Homework Assigned:

TBA

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu or Siddarth Chalasani, darthsid2000@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: What is a number? Part II | Modular Arithmetic
Handouts:

Students will learn the basic principles of counting and be able to apply combinatorial arguments to solve probability problems.

Handouts:
Handouts:
1/29/2023
Handouts: Handout | Solutions
Handouts:

A DFA is defined as an abstract mathematical concept, but is often implemented in hardware and software for solving various specific problems, such as lexical analysis and pattern matching. For example, a DFA can model software that decides whether or not online user input such as email addresses is syntactically valid.
We will practice coming up with DFAs for different word problems and study their properties.

Handouts: Handout
Handouts: Worksheet 10: Affine Varieties I

Arithmetic and Geometric Sequences and Series, and Recursion

Handouts: Worksheet

Last class, we took a break from the workbook and worked on some Math Kangaroo problems. Next class, we will have a small quiz on what we have learned so far.

Students will continue practicing the trick and discussing the reason it works.

Students will continue practicing the trick and discussing the reason it works.

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We review the homework and finish our study of abstract fields.

We next study vector spaces, which are useful in mathematical modeling.

Handouts will be posted after the lesson (handouts 6 and 7 are not homework!)

Required Resources:

Have your children bring a pencil and eraser.

No computers or associated accessories should be brought.

The SET card game is not needed for this lesson.

Homework Due:

Completing Handout 5, which is attached below (and was also passed out in class).

Homework Assigned:

We ask that all the kids click on this Google notebook link and attempt the problems.

Please save a PDF of the kids work and submit this pdf to this submission form by February 5.

See email for technical details.

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!

Handouts: Algebra for SET Handout 5 - Modular Arithmetic | Algebra for SET Handout 6 - Abstract Fields | Algebra for SET Handout 7 - Vector Spaces

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We review the homework and finish our study of abstract fields.

We next study vector spaces, which are useful in mathematical modeling.

Handouts will be posted after the lesson.

Required Resources:

Have your children bring a pencil and eraser.

No computers or associated accessories should be brought.

The SET card game is not needed for this lesson.

Homework Due:

Completing Handout 5, which is attached below (and was also passed out in class).

Homework Assigned:

To be announced.

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu or Siddarth Chalasani, darthsid2000@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: Abstract Fields | Vector Spaces | Modular Arithmetic

Students will learn about permutations and basic group theory. We will use this theory to solve the 15 Puzzle.

Handouts:
Handouts:
2/5/2023
Handouts:

We will study the languages, recognized by DFAs. These languages are simple in some ways and are called "regular".

Handouts: Worksheet 11 : Affine Varieties II

AM-GM Review, complex number basics, DeMoivre's Theorem, roots of unity

Handouts: worksheet
Handouts: AMC 10 2003

Last class, we reviewed chapter 8 and finished quiz 2. Next class, we will be starting chapter 9 of the workbook.

Students will study the associative, commutative, and distributive properties of multiplication using both algebra and geometry.

We return to functions, using them, and operations involving fractions, to solve modeling problems and word problems.

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We finish our study of vector spaces and begin modeling the card game SET.

Handouts will be posted after the lesson

Required Resources:

Have your children bring a pencil and eraser.

No computers or associated accessories should be brought.

The SET card game is not needed for this lesson.

Homework Due:

We ask that all the kids click on this Google notebook link and attempt the problems.

Please save a PDF of the kids work and submit this pdf to this submission form by February 5.

See email for technical details.

Homework Assigned:

We have a second Python homework assignment due by February 19. Please do the following:

  • Click on this Google Colab notebook link,
  • Save a copy to the students’ personal google drive,
  • Have the students complete the notebook,
  • Save their work as a pdf to be submitted at this Google form

Instructions for submission are inside the notebook as well.

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!

Handouts: Algebra For SET Handout 7 - Vector Spaces | Algebra For SET Handout 8 - Modeling Set

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We finish our study of vector spaces and begin modeling the card game SET.

Handouts will be posted after the lesson

Required Resources:

Have your children bring a pencil and eraser.

No computers or associated accessories should be brought.

The SET card game is not needed for this lesson.

Homework Due:

We ask that all the kids click on this Google notebook link and attempt the problems.

Please save a PDF of the kids work and submit this pdf to this submission form by February 5.

See email for technical details.

Homework Assigned:

To be assigned

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu or Siddarth Chalasani, darthsid2000@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: Set Game Modeling | Vector Spaces
Handouts:
Handouts:
Handouts:
2/12/2023

We do have a second Python homework assignment due by February 19. Please do the following:

  • Click on this Google Colab notebook link,
  • Save a copy to the students’ personal google drive,
  • Have the students complete the notebook,
  • Save their work as a pdf to be submitted at this Google form

Instructions for submission are inside the notebook as well.

2/19/2023

The lecture outlines an approach to elementary geometry different from the standard compass-and-ruler constructions. If one uses origami instead, the resulting algebraic structure (Galois group) is more rich. In particular, some problems not solvable by means of compass-and-ruler constructions, like trisecting an angle, become solvable. The room for the lecture is MS 4000A.

Handouts: lecture notes

The lecture outlines an approach to elementary geometry different from the standard compass-and-ruler constructions. If one uses origami instead, the resulting algebraic structure (Galois group) is more rich. In particular, some problems not solvable by means of compass-and-ruler constructions, like trisecting an angle, become solvable. The room for the lecture is MS 4000A.

Handouts: lecture notes

The lecture outlines an approach to elementary geometry different from the standard compass-and-ruler constructions. If one uses origami instead, the resulting algebraic structure (Galois group) is more rich. In particular, some problems not solvable by means of compass-and-ruler constructions, like trisecting an angle, become solvable. The room for the lecture is MS 4000A.

Handouts: lecture notes

The lecture outlines an approach to elementary geometry different from the standard compass-and-ruler constructions. If one uses origami instead, the resulting algebraic structure (Galois group) is more rich. In particular, some problems not solvable by means of compass-and-ruler constructions, like trisecting an angle, become solvable. The room for the lecture is MS 4000A.

Handouts: lecture notes

review of topics from previous classes, including AM-GM and roots of unity. Also going over selected problems from this year's AIME.

Handouts: worksheet
Handouts:

Last class, we finished up chapter 9. Next class, we will start chapter 10 of the workbook.

We discussion arithmetic progressions and their sum formula.

We will talk about the definitions of arithmetic progressions and how to sum them up.

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We learn about functions and classes in Python, to efficiently program SET.

Required Resources:

Pencil, eraser, computers, and associated accessories should be brought.

The SET card game is not needed for this lesson.

Homework Due:

We have a second Python homework assignment due by February 19. Please do the following:

  • Click on this Google Colab notebook link,
  • Save a copy to the students’ personal google drive,
  • Have the students complete the notebook,
  • Save their work as a pdf to be submitted at this Google form

Instructions for submission are inside the notebook as well.

Homework Assigned:

  • If your child did not attend class last week, their homework is to work through as much of this Colab notebook about functions as possible.
    • We completely understand that this material may be challenging to get through independently. So, we have set aside time for review this upcoming Sunday.
    • Again, they should not feel rushed to finish the entire thing but instead, they should just try their best to do as much as they can. No stress!
  • If your child did attend class, please have them complete the following short Colab review notebook as homework.

Please note that we are not asking any students to complete both notebooks.

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!

Coding for SET - Functions and Classes I

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We learn about functions and classes in Python, to efficiently program SET.

The following notebook was used in class:

https://colab.research.google.com/drive/1paEMcuM8MsDnYcuOIL95vgXupWQ8XFUc?usp=sharing

Required Resources:

Pencil, eraser, computers, and associated accessories should be brought.

The SET card game is not needed for this lesson.

Homework Due:

We have a second Python homework assignment due by February 14 and a third Python notebook due by February 21. Please do the following:

Instructions for submission are in the emails sent.

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu or Siddarth Chalasani, darthsid2000@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: |

Students will continue to learn about the 15 Puzzle and will learn conditions under which it can be solved. We will also cover basic L1 geometry and solve interesting geometric problems.

Handouts:
Handouts:
2/26/2023
Handouts: Handout | Solutions
Handouts:
Handouts:

Trig Review, Stewart's Theorem, Mass Points

Handouts: worksheet
Handouts: Handout

Last class, we finished up to chapter 10 of the workbook. We will be doing a quick review before administering a short quiz for our next class.

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We learn about functions and classes in Python, to efficiently program SET.

Required Resources:

Pencil, eraser, computers, and associated accessories should be brought.

The SET card game is not needed for this lesson.

Homework Due:

  • If your child did not attend class last week, their homework is to work through as much of this Colab notebook about functions as possible.
    • We completely understand that this material may be challenging to get through independently. So, we have set aside time for review this upcoming Sunday.
    • Again, they should not feel rushed to finish the entire thing but instead, they should just try their best to do as much as they can. No stress!
  • If your child did attend class, please have them complete the following short Colab review notebook as homework.

Please note that we are not asking any students to complete both notebooks.

Homework Assigned:

None

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!

Coding for SET - Functions and Classes II

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We learn about classes in Python, to efficiently program SET.

Classes notebook used in class:

https://drive.google.com/file/d/1-yHpNq8-oH7JLhLQmZZvBmL8uXtOihEb/view?usp=sharing

Required Resources:

Pencil, eraser, computers, and associated accessories should be brought.

The SET card game is not needed for this lesson.

Homework Due:

Completing the functions notebook that was introduced in the last class:

https://colab.research.google.com/drive/1paEMcuM8MsDnYcuOIL95vgXupWQ8XFUc?usp=sharing

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu or Siddarth Chalasani, darthsid2000@g.ucla.edu if you have any questions, comments, or concerns!

Handouts:

Students will learn the mathematics behind games and optimal play over the course of the next two weeks. This will be a fun packet and accessible to everyone, but also contain several challenge problems in game theory.

Handouts:
Handouts:
3/5/2023
Handouts: Handout | Solutions
Handouts:
Handouts:

Cauchy-Schwarz Inequality, Mean Inequality Chain

Handouts: worksheet
Handouts:

Last week, we had a quick review section before taking a recap quiz of what we have learned so far. Next session, we will be working on the new lesson in Chapter 11 of the workbook.

We will start new materials on time. First we will talk about time zones and their relationships to the division of the Earth into meridians. Then, time permitting, we will start to talk about how to do calculations that involve time.

Handouts: handout

Students will first discuss homework from lesson 29, starting with the red pepper problem 29.4. Then, if time permits, they will begin reviewing lesson 27.

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We will review the general ideas and motivations behind functions and classes in Python.

Then we will brainstorm how one would program SET and we will finish by playing some fun games!

Next class will be a competition!

Required Resources:

Pencil, eraser, and the card game SET.

Homework Due:

None

Homework Assigned:

None

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!

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We will review the general ideas and motivations behind functions and classes in Python.

Then we will brainstorm how one would program SET and we will finish by playing some fun games!

Next class will be a competition!

Required Resources:

Pencil, eraser, and the card game SET.

Homework Due:

No homework. Students were required to submit their copy of the Classes notebook using the Google Form below:

https://forms.gle/qzY65kwaP2VXAsU67

Homework Assigned:

None

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu or Siddarth Chalasani, darthsid2000@g.ucla.edu if you have any questions, comments, or concerns!

Handouts:

Students will continue learning about more advanced concepts in game theory and build on what they learned last week.

Handouts:
Handouts:
3/12/2023
Handouts: Answers | Problems

We will celebrate the end of the quarter with a competition between the classes!

To celebrate the end of the quarter, we do our usual game!

Handouts: Problems

practice problems as a (fun) contest among groups of students!

Handouts: contest problems

Since this will be the last class of the quarter, we will take the time to properly finish up lesson 12 and play some ice breakers so that the students can get to know one another.

Students will start learning basics of mod n arithmetic, that of a circle divided into n equal parts.

Students will start learning basics of mod n arithmetic, that of a circle divided into n equal parts.

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

Today's class will be a fun competition for the kids to celebrate all of their hard work this quarter!

Required Resources:

Pencil, eraser, and the card game SET.

Homework Due:

None

Homework Assigned:

None

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!

Quarter Goals:

  • Learn the basics of abstract algebra
  • Model the card game SET with pure math and Python

Class Logistics:

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

Class Plan:

We will hold a math competition and then a set tournament for the last class.

Required Resources:

Pencil, eraser, and the card game SET.

Homework Due:

No homework.

Homework Assigned:

None

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu or Siddarth Chalasani, darthsid2000@g.ucla.edu if you have any questions, comments, or concerns!

Students will have a fun competition!

Spring 2023 quarter // Filter groups by:
4/2/2023
Handouts: Handout
Handouts:
Handouts:
Handouts:

Students will have a chance to work on the 2023 USAJMO and USAMO problems in class, and then we will discuss solutions.

Handouts: USAJMO/USAMO Problems

Students will have a chance to work on the 2023 USAJMO and USAMO problems in class, and then we will discuss solutions.

Handouts: USA(J)MO 2023 | Solutions to selected problems
Handouts: Practice Test

We will start off the spring quarter with chapter 13, Chessboard Games. Please prepare a transparent sheet protector and cut out the chessboard picture from the last few pages of the workbook for our next class.

We will continue to study the relationship between clocks and arithmetic. Time permitting, we may start our next topic, on the geometry of clocks.

Class Logistics:

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

Class Plan:

We will learn about proof by induction by doing lots of practice problems!

Please see the handout from the lesson attached below.

Note that we will be covering this handout over multiple lessons.

Students are not expected to finish the whole handout in class;

instead, most students completed 1 to 4 problems, as we expected.

Required Resources:

Pencil, eraser, and scratch paper.

Homework Due:

None

Homework Assigned:

Although arithmetic/algebra is essential to prove statements “rigorously”, visual proofs are often more useful for building intuition.

The homework for this week is to watch the following two videos and relate them to problems from the handout.

Students should write down which problem in the handout each of these videos corresponds to, as well as how the two styles of proof differ in approach.

Please note that the handout is not due as homework, even for students who were absent last class.

Students who were absent are encouraged to read the first page of the handout and may attempt the problems if they want to.

We’ve included the following video as a guided solution to Problem 1: Proof by induction | Sequences, series and induction | Precalculus | Khan Academy

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!

Handouts: Induction Handout

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

Class Plan:

We will learn about proof by induction by doing lots of practice problems!

Required Resources:

Pencil, eraser, and scratch paper.

Homework Due:

None

Homework Assigned:

Watch the following two videos that prove problems 1 and 2 from the handout, and explain in a couple of sentences how these visual proofs relate to or differ from the algebraic proofs we saw in class:

https://www.youtube.com/watch?v=OJ_3QK7kck8

https://www.youtube.com/watch?v=9YpnoRkr4oQ

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu or Siddarth Chalasani, darthsid2000@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: Handout
Handouts:

Students will learn techniques for solving functional equations, a common topic in math competitions. Functional equations have applications to theoretical physics, financial markets, and more advanced mathematics.

Handouts:
4/9/2023
Handouts: Handout | Solutions
Handouts: Handout
Handouts: Handout
Handouts:

Introduction to graph theory, continuation of USA(J)MO exercises from last week

Handouts: worksheet

Introduction to graph theory.

Handouts: Graph Theory
Handouts:

The class will continue studying chapter 13.

In this class, which will take place over Zoom, we will finish up Clock Arithmetic Part 2, and begin Lesson 27 (Time and Angles).

Robert will be leading the chess club on this day.

Class Logistics:

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

Class Plan:

We will learn about proof by induction by doing lots of practice problems!

Please see the handout from the lesson attached below.

Note that we will be covering this handout over multiple lessons.

Students are not expected to finish the whole handout in class.

Required Resources:

Pencil, eraser, and scratch paper.

Homework Due:

Although arithmetic/algebra is essential to prove statements “rigorously”, visual proofs are often more useful for building intuition.

The homework for this week is to watch the following two videos and relate them to problems from the handout.

Students should write down which problem in the handout each of these videos corresponds to, as well as how the two styles of proof differ in approach.

Please note that the handout is not due as homework, even for students who were absent last class.

Students who were absent are encouraged to read the first page of the handout and may attempt the problems if they want to.

We’ve included the following video as a guided solution to Problem 1: Proof by induction | Sequences, series and induction | Precalculus | Khan Academy

Homework Assigned:

No homework, we will move on to a new topic next class!

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!

Handouts: Induction

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

Class Plan:

We will continue our discussion on proof by induction by looking at more visual examples, and then move on to proof by contradiction!

Required Resources:

Pencil, eraser, scratch paper, and last week's handout.

Homework Due:

A couple of sentences on how the algebraic proofs from last week are similar to or different from their corresponding visual proofs.

Homework Assigned:

No homework this week.

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu, or Siddarth Chalasani, darthsid2000@ucla.edu, if you have any questions, comments, or concerns!

Handouts: Handout

Students will continue learning techniques for solving functional equations, a common topic in math competitions. Functional equations have applications to theoretical physics, financial markets, and more advanced mathematics. Additional exercises will be available for those who would like them.

Handouts:
4/16/2023

A guest lecture by Dr. Zuming Feng, to be given in MS 4000 A.

A guest lecture by Dr. Zuming Feng, to be given in MS 4000 A.

A guest lecture by Dr. Zuming Feng, to be given in MS 4000 A.

A guest lecture by Dr. Zuming Feng, to be given in MS 4000 A.

More graph theory theorems and problems, including continuation of unfinished exercises from last week.

Handouts: worksheet

Continuation of the graph theory worksheet from last week.

Handouts: Graph Theory 2

We will review chapter 13. If time remains, students will take quiz 4.

We will finish our discussion of the relationship between angles and clocks (Lesson 27 - Angles and Time), and then revisit how angles and time on globes.

Class Logistics:

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

Class Plan:

We will now jump to graph theory with some fun practice problems!

The lesson handout is attached below.

Please note that it is not required for students to have completed the lesson in class or to complete it as homework.

We will continue working on this handout next lesson

Required Resources:

Pencil, eraser, and scratch paper.

Homework Due:

None.

Homework Assigned:

There is no required homework.

If students would like (especially absent ones), they can continue working through the lesson handout although, again, there is no expectation of students to do so.

Absent students will be allowed to start this packet from the very beginning next class, and should not worry about catching up.

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!

Handouts: Graph Theory Intro

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

Class Plan:

We will introduce graph theory.

Required Resources:

Pencil, eraser, and scratch paper.

Homework Due:

No homework due.

Homework Assigned:

No homework assigned.

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu, or Siddarth Chalasani, darthsid2000@ucla.edu, if you have any questions, comments, or concerns!

Handouts: Handout
Handouts:
Handouts:
4/23/2023
Handouts: Handout | Solutions
Handouts: Handout | Solutions
Handouts: Handout
Handouts:

Review of previously discussed topics, chicken mcnugget theorem, diophantine equations

Handouts: worksheet

We will go over the Chicken Nugget Problem and Diophantine equations.

Handouts: Number Theory

Students will need an abacus for this class with ten beads per wire.

After a short quiz on clock arithmetic, we will start studying Euclidean geometry.

Class Logistics:

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

Class Plan:

We will continue with the intro graph theory packet from last class, attached below.

Students who finish this packet will move on to packets about graph isomorphism and crossing number.

These extra packets are attached below; please note that they are not due as homework! Students will still be working through these packets in class.

Required Resources:

Pencil, eraser, and scratch paper.

Homework Due:

There is no required homework.

If students would like (especially absent ones), they can continue working through the lesson handout although, again, there is no expectation of students to do so.

Absent students will be allowed to start this packet from the very beginning next class, and should not worry about catching up.

Homework Assigned:

No homework and there is no expectation for absent students to complete any of the isomorphism or crossing packets.

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!

Handouts: Graph Theory Intro | Graph Isomorphism | Graph Crossings and Planarity

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

Class Plan:

We will continue our discussion on graph theory.

Required Resources:

Pencil, eraser, scratch paper, and last week's handout.

Homework Due:

No homework due.

Homework Assigned:

No homework assigned.

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu, or Siddarth Chalasani, darthsid2000@ucla.edu, if you have any questions, comments, or concerns!

Handouts: Handout
Handouts:
Handouts:
4/30/2023
Handouts: Handout | Solutions
Handouts: Handout
Handouts:

Focus on Pell Equations and methods of solving via continued fractions

Handouts: worksheet

Introduction to the method of continued fractions and solutions of Pell equations.

Handouts: Continued Fractions and Pell Equations

Students will need their workbooks, pencils and erasers, and an abacus for this class.

We will finish our discussion of systems of axioms. Then we will introduce Euclid's postulates for geometry.

Class Logistics:

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

Class Plan:

We will continue with the packets about graph isomorphism and crossing number, attached below.

Please note that these packets are not due as homework! Students will still be working through these packets in class.

Required Resources:

Pencil, eraser, and scratch paper.

Homework Due:

No homework and there is no expectation for absent students to complete any of the isomorphism or crossing packets.

Homework Assigned:

No homework and there is no expectation for absent students to complete any of the isomorphism or crossing packets.

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!

Handouts: Graph Isomorphism | Graph Crossing

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

Class Plan:

We will continue our discussion on graph theory.

Required Resources:

Pencil, eraser, scratch paper, and handouts from the last two weeks.

Homework Due:

No homework due.

Homework Assigned:

Attempt as much of the planar graphs handout as you can.

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu, or Siddarth Chalasani, darthsid2000@ucla.edu, if you have any questions, comments, or concerns!

Handouts: Handout
Handouts:

Students will learn the mathematical game theory behind the game Chomp.

Handouts:
5/7/2023
Handouts: Handout | Solutions
Handouts: Handout
Handouts:
Handouts: worksheet

Introduction to Pell's equations and strategies to solve Diophantine equations in general.

Handouts: Diophantine Equations

Students will need their textbook, abacus, pencil(s) and eraser(s) for this class.

We will begin learning Euclidean geometry, starting with Euclid's postulates.

Handouts: handout

Class Logistics:

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

Class Plan:

We will continue with the packets about graph isomorphism and crossing number, attached below.

Please note that these packets are not due as homework! Every student finished these in class.

Students who finish early will be given an extra fhands-on handout about drawing graphs on other surfaces!

Please note that this packet is not due as homework!

Required Resources:

Pencil, eraser, and scratch paper.

Homework Due:

No homework and there is no expectation for absent students to complete any of the isomorphism or crossing packets.

Homework Assigned:

No homework and there is no expectation for absent students to complete any of the class packets.

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!

Handouts: Graph Isomorphism | Graph Crossing Number | Graphs on Surfaces

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

Class Plan:

We will continue our discussion on graph theory.

Required Resources:

Pencil, eraser, scratch paper, and handouts from the last three weeks.

Homework Due:

Attempt the planar graphs handout from last week.

Homework Assigned:

No homework assigned.

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu, or Siddarth Chalasani, darthsid2000@ucla.edu, if you have any questions, comments, or concerns!

Handouts: Handout
Handouts:
Handouts:
5/14/2023
Handouts: Handout | Solutions
Handouts: Handout | Solutions
Handouts:
Handouts:

Introduction to arithmetic functions, a very important subject in number theory. Will cover basic properties, and famous examples

Handouts: worksheet

More exercises on Pell's equation. Introduction to some arithmetic functions.

Handouts: Handout

Having introduced our definitions in the last class, we will start to learn how to construct and compare triangles using only our straight edge and compasses.

Handouts: handout

Class Logistics:

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

Class Plan:

We move on from graph theory into a different hands-on topic: cryptography!

Students will practice writing secrete messages using various ciphers.

The packet for the class will be attached below after the lesson.

Required Resources:

Pencil, eraser, and scratch paper.

Homework Due:

No homework and there is no expectation for absent students to complete any of the prior class packets.

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!

Handouts: Cryptography 1

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

Class Plan:

We will introduce cryptography by exploring different types of ciphers.

Required Resources:

Pencil, eraser and scratch paper.

Homework Due:

No homework due.

Homework Assigned:

No homework assigned.

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu, or Siddarth Chalasani, darthsid2000@ucla.edu, if you have any questions, comments, or concerns!

Handouts: Handout
Handouts:
Handouts:
5/21/2023
Handouts: Handout | Solutions
Handouts: Handout

Geometry, using complex numbers

Handouts: worksheet

Introduction of complex number method in solving geometry problems.

Handouts: Complex Number Geometry

We will go back to roman numerals before starting a new topic. It would be helpful for children to review the rules for making roman numerals on pages 31-32.

Homework is to review quiz 5 with your children, correct all problems that they missed (if any), sign it and bring back to the next class. If you student has not taken it yet, please ask them to take it at home and bring to the next class (pages 291-292). 20 mins max, no assistance please

We will finish our introduction to Geometry, focusing on using our only available tools to recreate triangles with given dimensions or angle(s). We will practice making rigorous arguments about the properties of

Class Logistics:

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

Class Plan:

We continue studying cryptography.

The packet for the class will be attached below after the lesson.

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!

Handouts: RSA

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

Class Plan:

We will continue our discussion on cryptography by exploring simplified RSA encryption.

Required Resources:

Pencil, eraser, scratch paper and last week's handout.

Homework Due:

No homework due.

Homework Assigned:

No homework assigned.

Contact Information:

Please reach out to the instructors Anvesha Dutta, anveshadutta@g.ucla.edu, or Siddarth Chalasani, darthsid2000@ucla.edu, if you have any questions, comments, or concerns!

Handouts: Handout
Handouts:
5/28/2023

We wish all families a restful weekend and we thank all those who have served to defend the US

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: