UCLA Olga Radko Endowed Math Circle

ORMC Meetings Archive • Fall 2007–Summer 2022

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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
Summer 2021 quarter // Filter groups by:
6/27/2021

Welcome to Summer ORMC! This Sunday, we will start by exploring various exciting ciphers!

Handouts: Ceasar Disk

Welcome to Summer ORMC! This Sunday, we will start by exploring various exciting ciphers!

Handouts: Ceasar Disk

For our first class we work on problems involving modular arithmetic.

Handouts: Modular Arithmetic
Handouts: Week 1 Solutions | Week 1 Handout | Week 1 Hw
7/4/2021

We will resume our selection of topics next week. We have a few problems for you to solve if you didn't complete them with your instructor last week.

Handouts: Homework
7/11/2021

This week, we'll continue with our exploration of ciphers by reviewing the reverse, Caesar, and Polybius Ciphers. We'll also learn about the Pigpen and Rail Fence Cipher.

Handouts: Rail Fence Cipher Template

This week, we'll continue with our exploration of ciphers by reviewing the reverse, Caesar, and Polybius Ciphers. We'll also learn about the Pigpen and Rail Fence Cipher.

Handouts: Rail Fence Cipher Template

This Sunday we introduce ourselves to ideas in graph theory. We also include solutions to those general problems from the 27th of June.

Handouts: Graph Theory Early Introduction | General Problem Solutions for Modular Arithmetic
Handouts: Week 3 Solutions | Week 3 Handout | Week 3 Hw
7/18/2021

We'll work through the student-generated codes and learn about the Pigpen and Rail Fence Cipher.

Handouts: Rail Fence Cipher Template

We'll work through the student-generated codes and learn about the Pigpen and Rail Fence Cipher.

Handouts: Rail Fence Cipher Template

We finish our graph theory handout from last week, and begin with knights and knaves.

Handouts: knights and knaves
Handouts: Week 4 Handout | Week 4 Solutions | Week 4 Hw
7/25/2021

This week, we'll finish lesson 2 by practicing with the Rail Fence Ciphers. Afterward, we'll begin Lesson 3 by doing a recap of everything we've learned so far.

This week, we'll finish lesson 2 by practicing with the Rail Fence Ciphers. Afterward, we'll begin Lesson 3 by doing a recap of everything we've learned so far.

We introduce some ideas in probability!

Handouts: Probability1_2
Handouts: Week 5 Handout | Week 5 Solutions
8/1/2021

This Sunday, we'll review the problems from the quiz, finish up Lesson 3, and, if we have extra time, jump over to Lesson 10 to explore the puzzling island of Knights and Liars.

This Sunday, we'll review the problems from the quiz, finish up Lesson 3, and, if we have extra time, jump over to Lesson 10 to explore the puzzling island of Knights and Liars.

This Sunday we continue our introduction in probability.

Handouts: Probability II
Handouts: Week 6 Handout | Week 6 Solutions | Week 6 Hw
8/8/2021

This week, we'll review the homework problems from Lesson 3 and begin Lesson 10, which focuses on Knights and Liars.

This week, we'll review the homework problems from Lesson 3 and begin Lesson 10, which focuses on Knights and Liars.

We work on some fractions and decimals problems this Sunday.

Handouts: FractionsDecimals
Handouts: Week 7 Handout | Week 7 Solutions | Week 7 Hw
8/15/2021

This Sunday, we'll work through the final problems in Lesson 10: Knights and Liars

Handouts: Solutions_Math_Kangaroo

This Sunday, we'll work through the final problems in Lesson 10: Knights and Liars.

Handouts: Solutions_Math_Kangaroo

We will have a math dominoes competition based on what we've learned this season.

Handouts: Game Problems | Game Answers
Fall 2021 quarter // Filter groups by:
10/3/2021

We will solve some cool math puzzles to warm up for the year.

Handouts: Handout

We will solve some cool math puzzles to warm up for the year.

We will introduce definitions in the hopes of constructing the shortest possible string of 0s and 1s that contains all possible codes of a certain length.

Handouts: Combinatorics on Words

We kick off the year by discussing some interesting questions about words! This is a two-week topic.

Handouts:

We explore combinatorial game theory, and discover a new system of numbers.

Handouts: Nimbers_Handout

We will review binary numbers based on chapters 20 and 21 from the book.

Handouts: Introduction to Geometry - Lesson 1

We will start off the quarter by introducing several motivating examples in geometry.

Handouts: Geometry 1

We start this week at 4pm. All enrolled families should already have received an email from Doug with the Zoom link and materials. Note that we are NOT posting materials publicly this year, because we do not have copyright permission to do so. If you did not receive Doug's email, please contact Oleg to confirm your registration.

We started the year with a fun competition/icebreaker! Students were assigned different groups for different parts of the competition, which were themed around algebra, arithmetic/number theory, geometry, and combinatorics/probability respectively.

Handouts: Problems and Answer Key
Handouts:
Handouts: W1 Problems | W1 Solutions
10/10/2021

We will study the consequences of basic similar triangles properties

Handouts: Handout

We will study the consequences of basic similar triangles properties

Handouts:

We will complete our study of de Bruijn and Sturmian words.

Handouts: Combinatorics on Words

The handout is the same as last time.

We continue studying game theory and nimbers.

We will cover Chapters 22 and 23 from the book, including a brief review of Roman numerals. We will not be doing Quiz 6.

New Zoom link this week! Check email

Ch. 23 of the ORMC Workbook

Handouts: Introduction to Geometry - Lesson 1 | Introduction to Geometry - Lesson 2

We will continue to go through the same handout from last time.

Problem solving with an assortment of different of topics

Handouts:
Handouts: Handout
Handouts:
Handouts: W2 Problems | W2 Solutions
10/17/2021

Understanding planetary habitability is key to understanding how and why life developed on Earth as well as whether life is present on planets that orbit different stars (exoplanets). Whether a planet could be habitable is determined primarily by the planet's climate. This lecture will address insights we've gained from studying Earth's climate and how those have been used to make predictions about which exoplanets might be habitable, and how astronomical observations indicate the possibility of new climatic regimes not found on modern Earth. Finally, the lecture will cover some questions about the future of humanity and the Fermi paradox.

Dorian Abbot is an Associate Professor of Geophysical Sciences at the University of Chicago. In his research he uses mathematical and computational models to understand and explain fundamental problems in Earth and Planetary Sciences. Professor Abbot has also worked on problems related to climate, paleoclimate, the cryosphere, planetary habitability, and exoplanets. Recently he's been focusing on terrestrial exoplanets and habitability. He has an undergraduate degree in physics and a PhD in applied math, both from Harvard University.

Understanding planetary habitability is key to understanding how and why life developed on Earth as well as whether life is present on planets that orbit different stars (exoplanets). Whether a planet could be habitable is determined primarily by the planet's climate. This lecture will address insights we've gained from studying Earth's climate and how those have been used to make predictions about which exoplanets might be habitable, and how astronomical observations indicate the possibility of new climatic regimes not found on modern Earth. Finally, the lecture will cover some questions about the future of humanity and the Fermi paradox.

Dorian Abbot is an Associate Professor of Geophysical Sciences at the University of Chicago. In his research he uses mathematical and computational models to understand and explain fundamental problems in Earth and Planetary Sciences. Professor Abbot has also worked on problems related to climate, paleoclimate, the cryosphere, planetary habitability, and exoplanets. Recently he's been focusing on terrestrial exoplanets and habitability. He has an undergraduate degree in physics and a PhD in applied math, both from Harvard University.

Understanding planetary habitability is key to understanding how and why life developed on Earth as well as whether life is present on planets that orbit different stars (exoplanets). Whether a planet could be habitable is determined primarily by the planet's climate. This lecture will address insights we've gained from studying Earth's climate and how those have been used to make predictions about which exoplanets might be habitable, and how astronomical observations indicate the possibility of new climatic regimes not found on modern Earth. Finally, the lecture will cover some questions about the future of humanity and the Fermi paradox.

Dorian Abbot is an Associate Professor of Geophysical Sciences at the University of Chicago. In his research he uses mathematical and computational models to understand and explain fundamental problems in Earth and Planetary Sciences. Professor Abbot has also worked on problems related to climate, paleoclimate, the cryosphere, planetary habitability, and exoplanets. Recently he's been focusing on terrestrial exoplanets and habitability. He has an undergraduate degree in physics and a PhD in applied math, both from Harvard University.

Understanding planetary habitability is key to understanding how and why life developed on Earth as well as whether life is present on planets that orbit different stars (exoplanets). Whether a planet could be habitable is determined primarily by the planet's climate. This lecture will address insights we've gained from studying Earth's climate and how those have been used to make predictions about which exoplanets might be habitable, and how astronomical observations indicate the possibility of new climatic regimes not found on modern Earth. Finally, the lecture will cover some questions about the future of humanity and the Fermi paradox.

Dorian Abbot is an Associate Professor of Geophysical Sciences at the University of Chicago. In his research he uses mathematical and computational models to understand and explain fundamental problems in Earth and Planetary Sciences. Professor Abbot has also worked on problems related to climate, paleoclimate, the cryosphere, planetary habitability, and exoplanets. Recently he's been focusing on terrestrial exoplanets and habitability. He has an undergraduate degree in physics and a PhD in applied math, both from Harvard University.

Understanding planetary habitability is key to understanding how and why life developed on Earth as well as whether life is present on planets that orbit different stars (exoplanets). Whether a planet could be habitable is determined primarily by the planet's climate. This lecture will address insights we've gained from studying Earth's climate and how those have been used to make predictions about which exoplanets might be habitable, and how astronomical observations indicate the possibility of new climatic regimes not found on modern Earth. Finally, the lecture will cover some questions about the future of humanity and the Fermi paradox.

Dorian Abbot is an Associate Professor of Geophysical Sciences at the University of Chicago. In his research he uses mathematical and computational models to understand and explain fundamental problems in Earth and Planetary Sciences. Professor Abbot has also worked on problems related to climate, paleoclimate, the cryosphere, planetary habitability, and exoplanets. Recently he's been focusing on terrestrial exoplanets and habitability. He has an undergraduate degree in physics and a PhD in applied math, both from Harvard University.

In this class, we will finish comparing binary digits and decimal digits (Chapter 23), and start discussing parity (oddness and even-ness of numbers, Chapter 24). On the way we will find time for a brief review of Roman numerals.

Handouts: Introduction to Geometry - Lesson 3 | Introduction to Geometry - Lesson 2

We will continue the first handout, starting with straight lines and symmetries.

We will complete studying chapter 2 of the book. Then students will take quiz 1. Then, if time permits, we will begin studying chapter 3.

We will complete studying chapter 2 of the book. Then students will take quiz 1. Then, if time permits, we will begin studying chapter 3.

We are back this week, ready to tackle Chapter Two of our geometry book. Looking forward to seeing everyone!

Handouts: Handout
Handouts:
Handouts: W3 Problems
10/24/2021
Handouts: Handout

We continue our study of similar triangles.

Handouts: Handout

Nim is a simple combinatorial game in which players take a certain number of elements from a pile. The last person to take an item is the winner. We will play games of Nim with multiple setups in order to determine winning strategies. Eventually, we will define a number system based on Nim.

Handouts: Nimbers I

Nim is a simple combinatorial game in which players take a certain number of elements from a pile. The last person to take an item is the winner. We will play games of Nim with multiple setups in order to determine winning strategies. Eventually, we will define a number system based on Nim.

Handouts:

We explore multiplication algorithms and the complex plane, and encounter the discrete Fourier Transform.

Handouts: Problems

We will do Problem 23.21 as a warm up exercise, and then continue to Lesson 24, which is about Odd and Even numbers.

Handouts: Triangle Congruence Proof Review Packet.pdf

We will finish discussing the first handout, connecting algebra with geometry, and potentially cover space-filling curves.

Handouts: Handout
Handouts:
Handouts: W4 Problems | W4 Solutions
10/31/2021

We have a game! Bring your warrior spirit!

Handouts: Game questions

We have fun competition/game week for Halloween!

Handouts:

Nim is a simple combinatorial game in which players take a certain number of elements from a pile. The last person to take an item is the winner. We will play games of Nim with multiple setups in order to determine winning strategies. Eventually, we will define a number system based on Nim.

Handouts: Nimbers II

We continue our exploration of Nim and devise a strategy for general Nim!

Handouts:

We continue discussing polynomial multiplication and the Fast Fourier Transform.

Handouts: Bonus_Problems

We will review last week's homework and then continue to explore parity -- the idea of odd and even numbers -- following Lesson 25 within our workbooks.

Handouts: Homework Packet | Fun lesson from today
Handouts:
Handouts: Handout
Handouts:
Handouts: W5 Problems | W5 Solutions
11/7/2021

We will play with frieze patterns, featured in this Numberphile video

Handouts: Handout

An introduction on Frieze patterns

Handouts: Handout
Handouts: Competition Problems

This week we'll split into teams and do math competitions.

Handouts:

August and Lydia will tell us about their summer research projects, and then we will have a competition.

Handouts: Competition_Problems

We will study lesson 26, in which we learn to use binary decompositions to perform a magic trick. From there we will review how to use the Russian abacus to represent, add and subtract multi-digit numbers.

Handouts: Homework assigned: Practice quiz | Homework due: Triangle Congruence Review | Extra challenge problems

We will start the second handout by discussing angles and triangles.

Handouts: I2G2

Continuing with our geometry book as we are finishing off Chapter 3, we will skip Chapter 4 and continue with Chapter 5.

Handouts: Handout
Handouts:
Handouts: W6 Problems | W6 Solutions
11/14/2021

We will study what is called "general topology" and is a subject usually taught as an upper-division course to math majors.

Handouts: Handout

An introduction to Topology using set theory as our base.

Handouts: handout

We will introduce dynamical systems with a look at logistic maps.

Handouts: Dynamical Systems I

We take a look at discrete dynamical systems, and how a particular dynamical system known as the logistic map leads to the mathematics of chaos.

Handouts:

We compare different voting systems and discover why it's so difficult to design a good one.

Handouts: Problems

We will cover lesson 27, and practice our magic trick. Then we will review using the abacus to calculate sums and differences (from Lesson 15 and 16).

Class Plan:

We continue our study of geometry. We will review the students' practice quizzes to see what areas we may need to review. If the students do not need review, we will move on to teaching the Pythagorean theorem.

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

Practice quiz below.

Homework Assigned:

  • Please re-read pages 1 through 12 of the "Introduction to Geometry: Lesson 1" packet to review euclidean geometry definitions. The students do not have to do the problems in this packet.
  • Please read and attempt the questions on pages 8 through 11 of the "Introduction to Geometry: Lesson 3" packet. Again, these proofs will be challenging so it is okay if the students do not complete the proofs. They should give the problems their time and effort of course, though.

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: Reading assigned | Homework assigned | Homework due: Practice Quiz

Triangle congruence, right angles, and perpendicular lines.

Handouts: I2G3 | I2G2
Handouts: Handout
Handouts:
Handouts: W7 Problems | W7 Solutions
11/21/2021

We revisit induction and if time allows go to the formalism of Peano axioms

Handouts: Handout

We will study the concept of mathematical induction as well as the Peano Axiom.

Handouts: handout

We will continue our study of dynamical systems by connecting logistic maps to the Mandelbrot set.

Handouts: Dynamical Systems II

We will continue our study of dynamical systems by connecting logistic maps to the Mandelbrot set.

Handouts:
Handouts: Bonus_Problems

In this class, taught by guest instructor Professor Kim, students will learn how to add and subtract binary numbers by modifying their abaci.

Handouts: Homework due | Reading due
Handouts: I2G3

Give quiz #3 and review the homework problems from the lesson.

Give quiz #3 and review the homework problems from the lesson.

Handouts: Handout
Handouts:
Handouts: W8 Problems
11/28/2021

There is no class on November 28tth, 2021. We wish everyone a happy Thanksgiving break!

12/5/2021

We have a game to mark the end of the quarter

We will be playing our end of quarter game.

Handouts: handout
Handouts: Competition Problems

We'll do a competition. It will be the last meeting of 2021.

Handouts:

We will finish up discussion of adding and subtracting binary numbers, and then take a recap quiz on binary numbers, odd and evens and Roman numerals. We will then discuss Chapter 29; using binary numbers to represent letters and characters. Finally we will learn how to play two mathematical games.

Class Plan:

We continue studying the Pythagorean theorem. This is the last class of the Fall session!

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

  • The student should read as far as they can starting on page 8 of the "Introduction to Geometry: Lesson 3" packet. On each page, the student should make a serious effort to solve the proofs on their own. Again, these proofs will be challenging so it is okay if the students do not complete the proofs.

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: Homework Due: Introduction to Geometry Lesson 3

Applications of triangle congruence, Pythagorean theorem.

Handouts: I2G3

We will be looking at the volume of the partition that makes up the house and using building blocks to construct the house to correspond to the partition.

We will be looking at the volume of the partition that makes up the house and using building blocks to construct the house to correspond to the partition.

Handouts:
Winter 2022 quarter // Filter groups by:
1/9/2022

We continue our work with the Peano axioms and induction handout.

Handouts: Handout

Induction and the Peano axiom.

Handouts:

We will discuss spanning trees of graphs, and a variety of methods to count how many of them they are.

Handouts:

We will attempt to naively count the number of spanning trees in a graph.

Handouts: Spanning Trees
Handouts: Problems

We will review Chapter 30, the Moebius strip, as well as doing some problems that review some of the materials that we covered in the last quarter.

Class Plan:

We begin the quarter continuing our study of geometry. We introduce the notion of parallel lines. Please download and print out the packet below.

Zoom Information:

This class and the January 16th class will be held online via zoom. We will announce soon if classes in the following weeks will be online as well. Here is the Zoom info for our recurring meeting room:

https://ucla.zoom.us/j/7568441046?pwd=cjh1MWVWc1FKTVpWYk1nMGtsVUZ2dz09

Meeting ID: 756 844 1046

Passcode: Beg2A-Geo

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

None.

Homework Assigned:

No homework will be collected. We have attached a pdf of review questions of last quarter's material for students who wish to review.

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: Fall Quarter Review Questions | Introduction to Geometry - Lesson 4

We will start this quarter by discussing parallel lines.

Handouts: I2G4
Handouts: Handout
Handouts:
Handouts: W1-mod | W1 Solutions
1/14/2022
Handouts:
1/16/2022

We study Cauchy induction, a beautiful modification of the usual induction. If traditional induction goes forward one step at a time, Cauchy jumps from n to 2n and then goes backward if he misses the needed number.

Handouts: Handout

We'll be considering a souped up version of mathematial induction.

Handouts:

We will wrap up our discussion on spanning trees and ways of counting them.

We will introduce two methods for computing the number of spanning trees in a graph: deletion-contraction and the miraculous Matrix Tree Theorem. We will need to take a detour to the land of matrices for the second method.

Handouts: Spanning Trees

We will cover Chapter 31, which introduces coordinates for the line and plane. Time permitting, we will do a review of Roman numerals.

Class Plan:

We continue studying parallel lines in the Euclidean plane. Please download and print out the Introduction to Geometry - Lesson 4 packet below.

Zoom Information:

This class will be held online via zoom. We will announce soon if classes in the following weeks will be online as well. Here is the Zoom info for our recurring meeting room:

https://ucla.zoom.us/j/7568441046?pwd=cjh1MWVWc1FKTVpWYk1nMGtsVUZ2dz09

Meeting ID: 756 844 1046

Passcode: Beg2A-Geo

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

None.

Homework Assigned:

We ask that all students read through pages 6 through 8 of the Introduction to Geometry - Lesson 4 packet (attached below). We also ask that the students attempt Problems 8 and 9.

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: Introduction to Geometry - Lesson 4
Handouts: I2G4
Handouts: Handout
Handouts:
Handouts: W2 | W2_sols
1/21/2022
Handouts:
1/23/2022

Josephus and his forty soldiers were trapped in a cave. This means that there was a total of 41 fighters in the circle. Let us number 1 the first fighter to raise his sword, let us number 2 the fighter to his right, etc. The goal of this lesson is to solve the following two problems.

Problem 1 What was the position of Josephus in the circle?

Problem 2 Suppose that there are n soldiers, including Josephus, in the cave. What should the position of Josephus be in order for him to stay alive?

Handouts: Handout

This week we will study the story of Jesephus, a Roman general and later historian.

Handouts:

We will be discussing the Peano Axioms and how we can rigorously define numbers and arithmetic.

Handouts:

Peano axioms provide a rigorous foundation for the natural numbers and arithmetic. We will list the axioms and develop competing systems for the counting numbers.

Handouts: Peano Axioms
Handouts: Problems

We will review the rules of Roman numerals, and do some problems associated with them. Then we will form small groups to learn a mathematical game and its winning strategy.

Class Plan:

We begin studying the applications of geometry to the sciences! Please download and print out the Vector Geometry - Lesson 1 packet below.

Zoom Information:

This class will be held online via zoom. Here is the Zoom info for our recurring meeting room:

https://ucla.zoom.us/j/7568441046?pwd=cjh1MWVWc1FKTVpWYk1nMGtsVUZ2dz09

Meeting ID: 756 844 1046

Passcode: Beg2A-Geo

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

We ask that all students read through pages 6 through 8 of the Introduction to Geometry - Lesson 4 packet. We also ask that the students attempt Problems 8 and 9.

Homework Assigned:

We ask that students read pages 5 and 6, and attempt problem 3 in the Vector Geometry - Lesson 1 packet. We will be reviewing pages 3 and 4 of the packet next lesson, as some students expressed confusion. However, these pages are not strictly necessary for the students to complete the homework. As always, we will review the homework with the students next lesson to ensure their understanding.

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: Introduction to Geometry - Lesson 4 | Vector Geometry - Lesson 1

We will begin the study of vector geometry in Euclidean space, applying the geometrical knowledge we have learned.

Handouts: Vector Geometry Handout 1
Handouts: Handout | Solutions
Handouts:
Handouts: W3 Problems | W3 sols
1/28/2022
Handouts:
1/30/2022

We again solve problems regarding the angles in the circle. This is the theme uniquely rich with nice problems.

Handouts: Handout

This week, we'll study some elementary Euclidean geometry about angles.

Handouts: handout

We will be finishing up our investigation of number systems and the Peano Axioms.

Handouts:

Peano axioms provide a rigorous foundation for the natural numbers and arithmetic. We will list the axioms and develop competing systems for the counting numbers. Can we make it all the way to the rational numbers with only a handful of axioms?

Handouts: Peano Axioms
Handouts: Bonus_Problems

In this lesson we will cover Chapter 32, where we finally discover why our book has a picture of a dragon on the front cover.

Class Plan:

We continue studying vector geometry. Please download and print out the Vector Geometry - Lesson 1 packet below.

Zoom Information:

This class will be held online via zoom. Here is the Zoom info for our recurring meeting room:

https://ucla.zoom.us/j/7568441046?pwd=cjh1MWVWc1FKTVpWYk1nMGtsVUZ2dz09

Meeting ID: 756 844 1046

Passcode: Beg2A-Geo

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

We ask that students read pages 5 and 6, and attempt problem 3 in the Vector Geometry - Lesson 1 packet. We will be reviewing pages 3 and 4 of the packet next lesson, as some students expressed confusion. However, these pages are not strictly necessary for the students to complete the homework. As always, we will review the homework with the students next lesson to ensure their understanding.

Homework Assigned:

We ask that students read and attempt all problems on pages 7 through 9 in the Vector Geometry - Lesson 1 packet.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: Vector Geometry - Lesson 1

We will continue the discussion of the first vector geometry handout from last time.

Handouts: Vector Geometry Handout 1
Handouts: Handout | Solutions
Handouts:
Handouts: W4 Problems | W4 Solutions
2/4/2022
Handouts:
2/6/2022

This time we have a game with our usual rules

Handouts: Game

Today we'll have a competition.

To celebrate our return to in-person, we'll have a competition day with some problems relevant to the last 4 weeks, as well as a potpourri of miscellaneous problems.

Handouts: Competition I
Handouts: Problems | Bonus Problems

We will finish Chapter 32, and work on selected problems from Chapter 33.

Class Plan:

We continue studying vector geometry. Please download and print out the Vector Geometry - Lesson 1 packet below.

Location and Time:

This class will be held in person from 4 - 6 pm at Mathematical Sciences 6221.

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

We ask that students read and attempt all problems on pages 7 through 9 in the Vector Geometry - Lesson 1 packet. As always, we will review the homework with the students next lesson to ensure their understanding.

Homework Assigned:

We ask that students complete the Vector Geometry - Lesson 1 packet. Most students should have already completed the packet in lecture or potentially have one or two more pages left.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: Vector Geometry - Lesson 1
Handouts: Vector Geometry Handout 2
Handouts: |
Handouts: W5 Problems | W5 Solutions
2/11/2022
Handouts: | Bonus Handout
2/13/2022

The first hour will be a lecture by our instructor Natalie and me about hat puzzles. We invited other groups to listen. In the second hour, we will do the attached worksheet on hat puzzles.

Handouts: Handout

Guest lecture

Handouts:

Nikita and Natalie give a guest lecture on their recent research, and we solve some hat problems!

Math Circle will be 12-2 pm. Copy and paste the following Zoom link in a new tab.

https://ucla.zoom.us/j/99144292918?pwd=VWpRY01BbDdzT09qaTRPUFV4eTMyUT09

We will hear a lecture from Nikita and Natalie about their results on infinite hat puzzles.

Handouts: Hat Puzzles | Hat Puzzles Slides

Math Circle's own Natalie Deering and Nikita Gladkov have solved a fun problem about the combinatorics of ordinal numbers, and will present their findings!

Handouts: Problems

We will start to discuss how to use ciphers to make secret messages.

Class Plan:

We continue studying vector geometry. We will complete Vector Geometry - Lesson 1 and begin Vector Geometry - Lesson 2.

Location and Time:

This class will be held in person from 12 - 2 pm at Mathematical Sciences 5117 as it is Superbowl Sunday.

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

We ask that students complete the Vector Geometry - Lesson 1 packet. Most students should have already completed the packet in lecture or potentially have one or two more pages left.

Homework Assigned:

There will be homework due by the February 27th class. We ask that students complete problems 1, 2, 3, 11, and 12 in the Vector Geometry - Lesson 2 packet. The material in-between problems 3 and 11 (page 4 through the top of page 9) will be covered in class as it is quite difficult. The students do not need any of that material to answer the problems assigned for homework.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: Vector Geometry - Lesson 2 | Vector Geometry - Lesson 1
Handouts: Vector Geometry Handout 2 | Vector Geometry Handout 3
Handouts: Handout | Solutions
Handouts: Worksheet
2/15/2022
Handouts: Handout | Bonus Exercises
2/20/2022

There is no class on February 20th, 2021. We wish everyone a Happy Presidents' day!

2/22/2022
Handouts:
2/27/2022

We discuss the ways to prove that some numbers are irrational

Handouts: Handout

Definitions and basics of irrationals.

Handouts:

We will be investigating irrational numbers, including ways to prove a number is irrational, and some interesting applications.

Handouts:

We introduce both algebraic and analytic methods for detecting irrational numbers.

Handouts: Irrational Numbers
Handouts:

We will try to crack each other's codes from last class. We will then study the fencepost cipher, which rearranges letters in a much more complicated way than the reversal cipher that we met in the last class.

Class Plan:

We continue working through the Vector Geometry - Lesson 2 packet.

Location and Time:

This class will be held in person from 4 - 6 pm at Mathematical Sciences 6221.

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

We ask that the students complete problems 1, 2, 3, 11, and 12 in the Vector Geometry - Lesson 2 packet.

Homework Assigned:

None.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: Vector Geometry - Lesson 2

In this handout, we will see how using gridlines makes vector geometry computations much easier, with hidden relations to algebra.

Handouts: Vector Geometry Handout 3
Handouts: |
Handouts: W6 Problems | W6 Solutions
3/1/2022
Handouts:
3/5/2022
3/6/2022

We continue the last week handout about proving irrationality of certain numbers

Handouts: Handout
Handouts:

We will continue our exploration of irrational numbers.

Handouts:

We will figure out just how many irrational numbers there are by studying Cantor's diagonal argument.

Handouts: Irrational and Algebraic Numbers

We will finish our discussion of the rail fence cipher, then do a quiz on ciphers (decoding and encoding, but not having to break any coded messages). We conclude with some number problems inspired by what we have learned about anagramming and coding messages.

Class Plan:

We continue working through the Vector Geometry - Lesson 2 packet.

Location and Time:

This class will be held in person from 4 - 6 pm at Mathematical Sciences 6221.

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

There is no homework due.

Homework Assigned:

We are not assigning any homework before the lesson as the proofs are highly nontrivial. If the students were confused by last class’ material, we recommend re-reading pages 9-12 of the previous Vector Geometry - Lesson 1 packet in preparation for this upcoming class.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: Vector Geometry - Lesson 2

We continue working on the handout last time.

Handouts: Vector Geometry Handout 3
Handouts:
Handouts:
3/13/2022

End of the quarter game

Handouts: Game
Handouts:

For our last meeting of the quarter, we will be having another competition!

Handouts: Competition II
Handouts: Problems

We will introduce functions as machines that turn inputs into outputs. A new handout will be provided in class.

Class Plan:

We finish working through the Vector Geometry - Lesson 2 packet.

Location and Time:

This class will be held in person from 4 - 6 pm at Mathematical Sciences 6221.

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

There is no homework due.

Homework Assigned:

No homework assigned.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: Vector Geometry - Lesson 2

We aim to finish the last vector geometry handout of the quarter.

Handouts:
Spring 2022 quarter // Filter groups by:
4/3/2022

We solve problems leading to information theory.

This handout is inspired by the video by 3Blue1Brown on solving wordle using information theory. youtu.be/v68zYyaEmEA


Handouts: Handout
Handouts:

We will be looking at beautiful wallpapers and the mathematics behind their symmetries.

The study of symmetries is at the heart of mathematics. A particularly interesting and complete example is that of wallpaper. We will define the main types of wallpaper symmetries including reflections, rotations, and glide reflections.

Handouts: Wallpaper Symmetries

We will build a model of hyperbolic space!

Handouts: Problems

We will finish up our discussion of functions, with some more examples, as well learning the proper mathematical notations for writing down the action of a function.

Class Plan:

We transition to studying computer science and logic!

Location and Time:

This class will be held in person from 4 - 6 pm at Mathematical Sciences 6221.

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

There is vector review homework due on Sunday, April 9th. Please complete Vector Geometry - Lesson 3.

Homework Assigned:

As many students will be missing one or two lessons due to spring break, we have compiled all logic lessons into one large packet labeled Logic Gates - Five Lessons Compiled attached below. This way, any students missing the following lessons will have easy access to any material they miss, rather than the instructors emailing each parent individually. Our homework and class plan is as follows:

  • Students complete up to page 24 (Lessons 1-3) before the April 17 Lesson
  • Students complete the remainder of the packet (Lessons 4-5) before the April 24 lesson.

Our classes up until the April 24 packet will consist of covering this compiled packet, at the above described pace.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: Vector Geometry - Lesson 3 | Logic Gates - Five Lessons Compiled

We will start off this quarter by discussing some "logic puzzles." They introduce important principles in (mathematical) logic and even find applications in modern computers.

Handouts: Logic 1
Handouts: Solutions | Handout
Handouts:
Handouts: W1 Problems
4/5/2022
Handouts:
4/10/2022

We will build a model of hyperbolic space!

Special thanks to Professor Frank Sottile for recommending these activities to us.

The material for these activities can be found at https://www.math.tamu.edu/~sottile/research/stories/hyperbolic_football/

Handouts: Handout

Euclidean geometry is the study of geometry on a flat plane. It can be regarded as a realization of a certain set of axioms. Hyperbolic geometry is the study of geometry on a negatively curved surfaces; it has a set of axioms different from those of the Euclidean geometry.

Handouts:

We will be constructing the Hyperbolic Soccer Ball and studying its geometry! Please bring the following items with you: scissors, transparent scotch tape, protractors, and ruler.

In small groups, we will build hyperbolic soccer balls in order to learn about the geometry of non-Euclidean spaces.

Handouts: Hyperbolic Soccer Ball

We will develop and study different types of binary codes that detect when a user has made an error. These will include ISBN, repeating codes, Hamming's square code, and Hamming's [7,4]-code. We will also be able to compare the efficiency of these codes.

Handouts: Problems1 | Problems2

We will review the homework problems from Chapters 5 and 6. Then we will start a discussion of 3D geometry and using projections to represent 3D shapes. Students will each need 16 cube shaped blocks, all of the same color.

Class Plan:

We transition to studying computer science and logic!

Location and Time:

This class will be held in person from 4 - 6 pm at Mathematical Sciences 6221.

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

There is vector review homework due on Sunday, April 9th. Please complete Vector Geometry - Lesson 3.

Homework Assigned:

As many students will be missing one or two lessons due to spring break, we have compiled all logic lessons into one large packet labeled Logic Gates - Five Lessons Compiled attached below. This way, any students missing the following lessons will have easy access to any material they miss, rather than the instructors emailing each parent individually. Our homework and class plan is as follows:

  • Students complete up to page 24 (Lessons 1-3) before the April 17 Lesson
  • Students complete the remainder of the packet (Lessons 4-5) before the April 24 lesson.

Our classes up until the April 24 packet will consist of covering this compiled packet, at the above described pace.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: Vector Geometry - Lesson 3 | Logic Gates - Five Lessons Compiled
Handouts: Logic 2 | Logic 3
Handouts: Handout | Solutions
Handouts:
Handouts:
4/17/2022

We are doing a well-tried handout on pigeonhole principle.

Handouts: Handout
Handouts:

We will be discussing the Millennium Problem P vs NP so that we can understand this problem and what makes it so difficult.

Handouts: |

We will outline the famous problem P vs NP. By the end of the session, we will prove P is contained in NP and introduce the proof technique of reduction.

Handouts: P vs NP

We will investigate the theory of special relativity.

We will continue our discussion of solid shapes and projection. You will need 27 single-color wooden cubes.

Class Plan:

We transition to studying computer science and logic!

Location and Time:

This class will be held in person from 4 - 6 pm at Mathematical Sciences 6221.

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

The students should have completed through page 24 (Lessons 1-3) of the Logic Gates - Five Lessons Compiled packet.

Homework Assigned:

The students should complete the entire Logic Gates - Five Lessons Compiled packet. If students finish early and would like extra practice, the Logic Gates - Continued packet is attached as an optional practice.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: Logic Gates - Five Lessons Compiled | Logic Gates - Continued
Handouts: Logic 3 | Logic 4 | Logic 5
Handouts:
Handouts:
4/19/2022
Handouts:
4/24/2022

We study the basic number theory needed for secure communication.

Handouts: Handout

This week we will study nubmer theory and its application in cryptography

Handouts:

Can you convince someone that you know something without telling them how they can figure it out themself? We will learn how to do this this week with something called a zero-knowledge proof.

A zero-knowledge proof is an interaction between two people: a verifier and a prover. The prover has the task of convincing the verifier of the validity of a claim without revealing any pertinent information about the proof. Zero-knowledge proofs are particularly useful in the world of computer science where we want to keep passwords and personal data safe.

Handouts: Zero Knowledge Proofs
Handouts: Problems

We will finish our unit on 3D geometry and building shapes with blocks. Time permitting we will then start on our new topic, which is logic. Be prepared to ask tricky questions, and get tricky answers in return!

Class Plan:

We complete studying logic gates. We offer the Logic Gates - Continued packet and a Math Kangaroo practice test for students who finish early.

Location and Time:

This class will be held in person from 4 - 6 pm at Mathematical Sciences 6221.

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

The students should have completed the Logic Gates - Five Lessons Compiled packet.

Homework Assigned:

None.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

Handouts: Logic Gates - Five Lessons Compiled | Logic Gates - Continued | Math Kangaroo 2007

We will continue to go through the previous handouts, in the hope of finishing the fifth handout by the end of class.

Handouts:
Handouts:
4/26/2022
Handouts:
5/1/2022

We have a game!

We will be having a competition!

Handouts: Competition I

We will finish our discussion of 3D shapes made with blocks and do a quiz about 3D shapes. Then we will begin a new chapter on logic. Time permitting, we will play a game involving reflection symmetries.

Class Plan:

We begin studying programming!

Location and Time:

This class will be held in person from 4 - 6 pm at Mathematical Sciences 6221.

Required Resources:

We ask that all students who can bring their own laptops and chargers. For students who are not able to, we will provide the proper materials.

Homework Due:

None.

Homework Assigned:

None.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

We will start introducing the basics of the programming language Python.

Handouts: Handout | Solutions
Handouts:
Handouts:
5/8/2022

We study the beginnings of calculus and the number e=2.71...

Handouts: Handout
Handouts:

We will be learning about the math of the stock market and finances!

Handouts:

We introduce the basic notions of options trading including call and put options, trading strategies, and arbitrage. We apply our knowledge to real-world trading scenarios.

Handouts: Financial Math

In this special class, Prof. Shanghua will teach us about mathematical games generally, and the strategies to win them. We will play games of chance, and then learn how to play (and in some configurations, to win), the game of Nim.

Class Plan:

We continue studying programming.

Location and Time:

This class will be held in person from 4 - 6 pm at Mathematical Sciences 6221.

Required Resources:

We ask that all students who can bring their own laptops and chargers. For students who are not able to, we will provide the proper materials.

To ensure a smooth class and prevent any technical difficulties, we ask that for all students who had trouble logging in last time to ensure they have a working account for this week. Students will need a Google account to access the Colab. We found that some students with school and/or age-restricted accounts were unable to gain access last time.

To check, please go to this link: tinyurl.com/ormcPythonIntro and attempt to run the first cell. If unsuccessful, we ask that the student create a personal account if possible.

Homework Due:

None.

Homework Assigned:

None.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

We will continue from last time: review Python workflow, and complete the exercises.

Handouts: Handout | Solutions
Handouts:
Handouts:
5/10/2022
Handouts:
5/15/2022

This lesson is going online because of COVID. We study binomial coefficients and Pascal triangle -- basic objects in combinatorics.

Handouts: Handout
Handouts:

We will be continuing our mathematical investigation of the stock market and finances.

We use the principle of no arbitrage to develop relationships among put and call pricing.

Handouts: Financial Math

We learn some Nash-style game theory.

Handouts:

We will continue our discussion of logic problems, introducing logic gates as a way to combine logical statements.

Class Plan:

We continue studying programming.

Location and Time:

This class will be held in person from 4 - 6 pm at Mathematical Sciences 6221.

Required Resources:

We ask that all students who can bring their own laptops and chargers. For students who are not able to, we will provide the proper materials.

To ensure a smooth class and prevent any technical difficulties, we ask that for all students who had trouble logging in last time to ensure they have a working account for this week. Students will need a Google account to access the Colab. We found that some students with school and/or age-restricted accounts were unable to gain access last time.

To check, please go to this link: tinyurl.com/ormcPythonIntro and attempt to run the first cell. If unsuccessful, we ask that the student create a personal account if possible.

Homework Due:

None.

Homework Assigned:

None.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

We will be practicing basic programming skills by doing problems from Project Euler.

Handouts:
Handouts:
5/22/2022

We introduce basic definitions of graph theory and work out some problems which don't require any background knowledge.

Handouts: Handout
Handouts:

We will be investigating the mathematics behind circuits!

We apply the theory of random walks on graphs to electrical circuits.

Handouts: Electrical Circuits and Random Walks

We introduce the basic notions of options trading including call and put options, trading strategies, and arbitrage. We apply our knowledge to real-world trading scenarios.

We will continue our study of mathematical logic, learning about how statements can be combined and modified using logical operations.

Class Plan:

We continue studying programming.

Location and Time:

This class will be held in person from 4 - 6 pm at Mathematical Sciences 6221.

Required Resources:

We ask that all students who can bring their own laptops and chargers. For students who are not able to, we will provide the proper materials.

To ensure a smooth class and prevent any technical difficulties, we ask that for all students who had trouble logging in last time to ensure they have a working account for this week. Students will need a Google account to access the Colab. We found that some students with school and/or age-restricted accounts were unable to gain access last time.

To check, please go to this link: tinyurl.com/ormcPythonIntro and attempt to run the first cell. If unsuccessful, we ask that the student create a personal account if possible.

Homework Due:

None.

Homework Assigned:

We ask every student to continue their exploration of the Turtle module in Python (https://tinyurl.com/ormcB2Aturtles), by creating their own drawing to be submitted. We will be anonymously voting on student submissions next class, as an informal programmatic art contest of sorts. For this purpose, we ask every student to create and save a drawing in the form of a screenshot. Their artwork, as well as the code that generated it, should be submitted to the following Google Form: https://forms.gle/nKvPjFWvvnyLJPKT6.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

We will start working with the Turtle package of Python, which allows one to draw figures (including fractals which are our end goal).

Handouts:
Handouts:
5/29/2022
6/5/2022

Dr. Terence Tao speaks about the cosmic distance ladder.

In this, last meeting of the year, we will finish our discussion of mathematical logic, by continuing with our analogy of logical operations and electrical circuits. There will be a short quiz.

We will conclude this class by revisiting recursion and drawing fractals.

6/6/2022

Class Plan:

We finish our study of programming. Thanks to everyone for the great year!

Location and Time:

This class will be held in person from 4 - 6 pm at Mathematical Sciences 6221.

Required Resources:

We ask that all students who can bring their own laptops and chargers. For students who are not able to, we will provide the proper materials.

Homework Due:

We ask every student to continue their exploration of the Turtle module in Python (https://tinyurl.com/ormcB2Aturtles), by creating their own drawing to be submitted. We will be anonymously voting on student submissions next class, as an informal programmatic art contest of sorts. For this purpose, we ask every student to create and save a drawing in the form of a screenshot. Their artwork, as well as the code that generated it, should be submitted to the following Google Form: https://forms.gle/nKvPjFWvvnyLJPKT6.

Homework Assigned:

None. Enjoy the summer break!

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!