ORMC Meetings Archive • Fall 2007–Summer 2022

Search handouts:

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: AdvancedBeginners 1ABeginners 1BBeginners 2ABeginners 2BIntermediate 1Intermediate 2 6/27/2021 Beginners 1A [enter grade 2-3 in Fall]: Squares on a Chessboard Beginners 1B [enter grade 2-3 in Fall]: Squares on a Chessboard Beginners 2A [entering grades 4-5 in Fall]: Ciphers 1 Welcome to Summer ORMC! This Sunday, we will start by exploring various exciting ciphers!Handouts: Ceasar DiskBeginners 2B [entering grades 4-5 in Fall]: Ciphers 1 Welcome to Summer ORMC! This Sunday, we will start by exploring various exciting ciphers!Handouts: Ceasar DiskIntermediate 1 [grades 6-7 in Fall 2021]: Introduction to Modular Arithmetic For our first class we work on problems involving modular arithmetic.Handouts: Modular ArithmeticIntermediate 2 [grades 8-9 in Fall ]: Sets and Set Algebra Handouts: Week 1 Solutions | Week 1 Handout | Week 1 Hw 7/4/2021 Beginners 1A [enter grade 2-3 in Fall]: No Class: Happy Fourth of July! Beginners 1B [enter grade 2-3 in Fall]: No Class: Happy Fourth of July! Beginners 2A [entering grades 4-5 in Fall]: No Class (Independence Day) Beginners 2B [entering grades 4-5 in Fall]: No Class (Independence Day) Intermediate 1 [grades 6-7 in Fall 2021]: No Class (Independence Day) 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 Beginners 1A [enter grade 2-3 in Fall]: Chessboard Games Beginners 1B [enter grade 2-3 in Fall]: Chessboard Games Beginners 2A [entering grades 4-5 in Fall]: Ciphers 2 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 TemplateBeginners 2B [entering grades 4-5 in Fall]: Ciphers 2 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 TemplateIntermediate 1 [grades 6-7 in Fall 2021]: Introduction to Graph Theory! This Sunday we introduce ourselves to ideas in graph theory. We also include solutions to those general problems from the 27th of June.Intermediate 2 [grades 8-9 in Fall ]: Power Set and Cartesian Product Handouts: Week 3 Solutions | Week 3 Handout | Week 3 Hw 7/18/2021 Beginners 1A [enter grade 2-3 in Fall]: Chessboard Games Part 2 Beginners 1B [enter grade 2-3 in Fall]: Chessboard Games Part 2 Beginners 2A [entering grades 4-5 in Fall]: Ciphers 2 (Continued) We'll work through the student-generated codes and learn about the Pigpen and Rail Fence Cipher.Handouts: Rail Fence Cipher TemplateBeginners 2B [entering grades 4-5 in Fall]: Ciphers 2 (Continued) We'll work through the student-generated codes and learn about the Pigpen and Rail Fence Cipher.Handouts: Rail Fence Cipher TemplateIntermediate 1 [grades 6-7 in Fall 2021]: Knights and Knaves (and Finishing Graph Theory) We finish our graph theory handout from last week, and begin with knights and knaves.Handouts: knights and knavesIntermediate 2 [grades 8-9 in Fall ]: Functions Between Sets Handouts: Week 4 Handout | Week 4 Solutions | Week 4 Hw 7/25/2021 Beginners 1A [enter grade 2-3 in Fall]: Digits and Numbers Beginners 1B [enter grade 2-3 in Fall]: Digits and Numbers Beginners 2A [entering grades 4-5 in Fall]: Ciphers 2 (Continued) + Lesson 3 Recap 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. Beginners 2B [entering grades 4-5 in Fall]: Ciphers 2 (Continued) + Lesson 3 Recap 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. Intermediate 1 [grades 6-7 in Fall 2021]: Introduction to Probability We introduce some ideas in probability! Handouts: Probability1_2Intermediate 2 [grades 8-9 in Fall ]: Review Handouts: Week 5 Handout | Week 5 Solutions 8/1/2021 Beginners 1A [enter grade 2-3 in Fall]: Coordinates Beginners 1B [enter grade 2-3 in Fall]: Coordinates Beginners 2A [entering grades 4-5 in Fall]: Lesson 3 + 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. Beginners 2B [entering grades 4-5 in Fall]: Lesson 3 + 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. Intermediate 1 [grades 6-7 in Fall 2021]: Probability Continued This Sunday we continue our introduction in probability.Handouts: Probability IIIntermediate 2 [grades 8-9 in Fall ]: Compostion of Functions, Inverse Images, and Inverse Functions Handouts: Week 6 Handout | Week 6 Solutions | Week 6 Hw 8/8/2021 Beginners 1A [enter grade 2-3 in Fall]: How to Fight a Dragon Beginners 1B [enter grade 2-3 in Fall]: How to Fight a Dragon Beginners 2A [entering grades 4-5 in Fall]: Lesson 10: Knights and Liars This week, we'll review the homework problems from Lesson 3 and begin Lesson 10, which focuses on Knights and Liars.Beginners 2B [entering grades 4-5 in Fall]: Lesson 10: Knights and Liars This week, we'll review the homework problems from Lesson 3 and begin Lesson 10, which focuses on Knights and Liars.Intermediate 1 [grades 6-7 in Fall 2021]: Fractions and Decimals We work on some fractions and decimals problems this Sunday.Handouts: FractionsDecimalsIntermediate 2 [grades 8-9 in Fall ]: Cardinality of Sets Handouts: Week 7 Handout | Week 7 Solutions | Week 7 Hw 8/15/2021 Beginners 1A [enter grade 2-3 in Fall]: How to Fight a Dragon Part 2 Beginners 1B [enter grade 2-3 in Fall]: How to Fight a Dragon Part 2 Beginners 2A [entering grades 4-5 in Fall]: Logic Puzzles: Knights and Liars (Continued) This Sunday, we'll work through the final problems in Lesson 10: Knights and LiarsHandouts: Solutions_Math_KangarooBeginners 2B [entering grades 4-5 in Fall]: Logic Puzzles: Knights and Liars (Continued) This Sunday, we'll work through the final problems in Lesson 10: Knights and Liars.Handouts: Solutions_Math_KangarooIntermediate 1 [grades 6-7 in Fall 2021]: Math Dominoes! We will have a math dominoes competition based on what we've learned this season. Intermediate 2 [grades 8-9 in Fall ]: Game Week! Handouts: Game Problems | Game Answers Fall 2021 quarter // Filter groups by: Advanced 1AAdvanced 1BAdvanced 2AAdvanced 2BAdvanced 3AMC10/12 trainingBeginners 1ABeginners 1BBeginners 2ABeginners 2BBNP ABNP BIntermediate 1AIntermediate 1BIntermediate 2AIntermediate 2BOlympiads training 10/3/2021 Advanced 1A [gr. 7-11 in person]: Warm-up Puzzles We will solve some cool math puzzles to warm up for the year.Handouts: HandoutAdvanced 1B [gr. 7-11 remote]: Warm-up Puzzles We will solve some cool math puzzles to warm up for the year.Advanced 2A [gr. 9-11 in person]: Combinatorics on Words I 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 WordsAdvanced 2B [gr. 9-11 remote]: Combinatorics on Words We kick off the year by discussing some interesting questions about words! This is a two-week topic.Handouts: Advanced 3 [gr. 11-12 remote]: How to win Nim and related games We explore combinatorial game theory, and discover a new system of numbers.Handouts: Nimbers_HandoutAMC10/12 training: Algebraic Manipulation Beginners 1A [gr. 1-3 in person]: Review of binary numbers. We will review binary numbers based on chapters 20 and 21 from the book.Beginners 1B [gr. 1-3 remote]: Review of binary numbers. Beginners 2A [gr. 4-5 in person]: Fall - Euclidean Plane, Points, Distances Handouts: Introduction to Geometry - Lesson 1Beginners 2B [gr. 4-5 remote]: Introduction to Geometry 1 We will start off the quarter by introducing several motivating examples in geometry.Handouts: Geometry 1BNP A [K-1 in person]: Lesson 1 Counting Stories and Lesson 2 Parts of a Number BNP B [K-1 in person]: Lesson 1 Counting Stories and Lesson 2 Parts of a Number Intermediate 1A [gr. 5-7 in person]: Introduction to Geometric Thinking Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 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.Intermediate 2A [gr. 7-9 in person]: Week 1 Competition 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 KeyIntermediate 2B [gr. 7-9 remote]: Week 1 Handouts: Olympiads training: Bernoulli Polynomials and Summations Handouts: W1 Problems | W1 Solutions 10/10/2021 Advanced 1A [gr. 7-11 in person]: Similar triangles We will study the consequences of basic similar triangles propertiesHandouts: HandoutAdvanced 1B [gr. 7-11 remote]: Similar Triangles We will study the consequences of basic similar triangles propertiesHandouts: Advanced 2A [gr. 9-11 in person]: Combinatorics on Words II We will complete our study of de Bruijn and Sturmian words.Handouts: Combinatorics on WordsAdvanced 2B [gr. 9-11 remote]: Combinatorics on Words II The handout is the same as last time.Advanced 3 [gr. 11-12 remote]: How to win Nim and related games We continue studying game theory and nimbers.AMC10/12 training: Number Theory Beginners 1A [gr. 1-3 in person]: More binary numbers and place value We will cover Chapters 22 and 23 from the book, including a brief review of Roman numerals. We will not be doing Quiz 6.Beginners 1B [gr. 1-3 remote]: Decimal and Binary Numbers New Zoom link this week! Check emailCh. 23 of the ORMC WorkbookBeginners 2A [gr. 4-5 in person]: Fall - Angles Beginners 2B [gr. 4-5 remote]: Introduction to Geometry 1: Continued We will continue to go through the same handout from last time.BNP A [K-1 in person]: Continue with Lesson 2 Parts of a Number BNP B [K-1 in person]: Continue with Lesson 2 Parts of a Number Intermediate 1A [gr. 5-7 in person]: Math Wrangle Problem solving with an assortment of different of topicsIntermediate 1B [gr. 5-7 remote]: No class this Sunday. Please solve problems from the attached handout on your own. Handouts: Intermediate 2A [gr. 7-9 in person]: Binary Arithmetic and Truth Tables Handouts: HandoutIntermediate 2B [gr. 7-9 remote]: Week 2 Handouts: Olympiads training: Recursion (Combinatorial Point of View) Handouts: W2 Problems | W2 Solutions 10/17/2021 Advanced 1A [gr. 7-11 in person]: Public lecture: Climate and the Potential for Life on Other Planets 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.Advanced 1B [gr. 7-11 remote]: Public lecture: Climate and the Potential for Life on Other Planets 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.Advanced 2A [gr. 9-11 in person]: Climate and the Potential for Life on Other Planets 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.Advanced 2B [gr. 9-11 remote]: Public lecture: Climate and the Potential for Life on Other Planets 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.Advanced 3 [gr. 11-12 remote]: Public lecture: Climate and the Potential for Life on Other Planets 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.AMC10/12 training: Probability Beginners 1A [gr. 1-3 in person]: Binary numbers and parity 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.Beginners 1B [gr. 1-3 remote]: Ch. 24 & 25: Odd and Even Numbers Beginners 2A [gr. 4-5 in person]: Fall - Angles (Continued) Beginners 2B [gr. 4-5 remote]: Introduction to Geometry 1: Continued We will continue the first handout, starting with straight lines and symmetries.BNP A [K-1 in person]: Crossing puzzle and more partitions. 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. BNP B [K-1 in person]: Crossing puzzle and more partitions. 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. Intermediate 1A [gr. 5-7 in person]: Geometric Exploration: Angles and Triangle Inequality Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 2 We are back this week, ready to tackle Chapter Two of our geometry book. Looking forward to seeing everyone!Intermediate 2A [gr. 7-9 in person]: The Boolean Algebra and Logic Gates Handouts: HandoutIntermediate 2B [gr. 7-9 remote]: Week 3 Handouts: Olympiads training: Recursive Relations Handouts: W3 Problems 10/24/2021 Advanced 1A [gr. 7-11 in person]: More similar triangles Handouts: HandoutAdvanced 1B [gr. 7-11 remote]: More Similar triangles We continue our study of similar triangles.Handouts: HandoutAdvanced 2A [gr. 9-11 in person]: 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: Nimbers IAdvanced 2B [gr. 9-11 remote]: 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: Advanced 3 [gr. 11-12 remote]: The Fast Fourier Transform We explore multiplication algorithms and the complex plane, and encounter the discrete Fourier Transform.Handouts: ProblemsAMC10/12 training: Probability Beginners 1A [gr. 1-3 in person]: Lesson 24 - Odds and Evens We will do Problem 23.21 as a warm up exercise, and then continue to Lesson 24, which is about Odd and Even numbers.Beginners 1B [gr. 1-3 remote]: Magic! With Binary Numbers, Ch. 26 & 27 Beginners 2A [gr. 4-5 in person]: Fall - Triangles Beginners 2B [gr. 4-5 remote]: Introduction to Geometry 1: Finishing up We will finish discussing the first handout, connecting algebra with geometry, and potentially cover space-filling curves.BNP A [K-1 in person]: Lesson 3 Partitions and Subtraction BNP B [K-1 in person]: Lesson 3 Partitions and Subtraction Intermediate 1A [gr. 5-7 in person]: Triangle Inequality (Chapter 3) Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 3 Intermediate 2A [gr. 7-9 in person]: Disjunctive Normal Forms and Geometry of Cubes Handouts: HandoutIntermediate 2B [gr. 7-9 remote]: Week 4 Handouts: Olympiads training: Inequalities I: AM-GM Handouts: W4 Problems | W4 Solutions 10/31/2021 Advanced 1A [gr. 7-11 in person]: Game We have a game! Bring your warrior spirit!Handouts: Game questionsAdvanced 1B [gr. 7-11 remote]: Game day We have fun competition/game week for Halloween!Handouts: Advanced 2A [gr. 9-11 in person]: Nimbers II 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 IIAdvanced 2B [gr. 9-11 remote]: Nimbers II We continue our exploration of Nim and devise a strategy for general Nim!Handouts: Advanced 3 [gr. 11-12 remote]: The Fast Fourier Transform We continue discussing polynomial multiplication and the Fast Fourier Transform.Handouts: Bonus_ProblemsAMC10/12 training: Polynomials Beginners 1A [gr. 1-3 in person]: More on odd and even numbers 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.Beginners 1B [gr. 1-3 remote]: Finish Up Binary Magic & Begin Ch. 28: Adding and Subtracting Binary Numbers Beginners 2A [gr. 4-5 in person]: Fall - Cryptarithms (Halloween Lesson) Handouts: Homework Packet | Fun lesson from todayBeginners 2B [gr. 4-5 remote]: Halloween Special Event: Cryptarithms Handouts: BNP A [K-1 in person]: Lesson 4 The Number Line BNP B [K-1 in person]: Lesson 4 The Number Line Intermediate 1A [gr. 5-7 in person]: Continuation of Triangle Inequality Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 4 Intermediate 2A [gr. 7-9 in person]: Combinatorics and Permutations Handouts: HandoutIntermediate 2B [gr. 7-9 remote]: Week 5 Handouts: Olympiads training: Inequalities II: AM-GM continued and Inequality Intervals Handouts: W5 Problems | W5 Solutions 11/7/2021 Advanced 1A [gr. 7-11 in person]: Friezes We will play with frieze patterns, featured in this Numberphile videoHandouts: HandoutAdvanced 1B [gr. 7-11 remote]: Frieze Patterns An introduction on Frieze patternsHandouts: HandoutAdvanced 2A [gr. 9-11 in person]: Competition I Handouts: Competition ProblemsAdvanced 2B [gr. 9-11 remote]: Competition This week we'll split into teams and do math competitions.Handouts: Advanced 3 [gr. 11-12 remote]: Research Presentations and Competition August and Lydia will tell us about their summer research projects, and then we will have a competition.Handouts: Competition_ProblemsAMC10/12 training: Functions Beginners 1A [gr. 1-3 in person]: Lesson 26 - A Binary Numbers Magic Trick / Abacus Review 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.Beginners 1B [gr. 1-3 remote]: Ch. 28: Adding and Subtracting Binary Numbers and Review Games! Beginners 2A [gr. 4-5 in person]: Fall - Triangles (Continued) Beginners 2B [gr. 4-5 remote]: Introduction to Geometry 2 We will start the second handout by discussing angles and triangles.Handouts: I2G2BNP A [K-1 in person]: Correct Lesson 4 homework and begin Lesson 5 Digits and Numbers BNP B [K-1 in person]: Correct Lesson 4 homework and begin Lesson 5 Digits and Numbers Intermediate 1A [gr. 5-7 in person]: Congruent Figures Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 5 Continuing with our geometry book as we are finishing off Chapter 3, we will skip Chapter 4 and continue with Chapter 5.Intermediate 2A [gr. 7-9 in person]: Combinatorics and Permutations 2 Handouts: HandoutIntermediate 2B [gr. 7-9 remote]: Week 6 Handouts: Olympiads training: Inequalities III: Cauchy-Schwartz Handouts: W6 Problems | W6 Solutions 11/14/2021 Advanced 1A [gr. 7-11 in person]: Topology We will study what is called "general topology" and is a subject usually taught as an upper-division course to math majors.Handouts: HandoutAdvanced 1B [gr. 7-11 remote]: Set Topology An introduction to Topology using set theory as our base.Handouts: handoutAdvanced 2A [gr. 9-11 in person]: Dynamical Systems I We will introduce dynamical systems with a look at logistic maps.Handouts: Dynamical Systems IAdvanced 2B [gr. 9-11 remote]: 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: Advanced 3 [gr. 11-12 remote]: Voting Theory We compare different voting systems and discover why it's so difficult to design a good one.Handouts: ProblemsAMC10/12 training: AMC 10/12 A Review Beginners 1A [gr. 1-3 in person]: Finishing the binary numbers magic trick and a review of the abacus 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).Beginners 1B [gr. 1-3 remote]: Recap & Quiz Beginners 2A [gr. 4-5 in person]: Fall - Review Exam, Triangles (Continued) 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!Beginners 2B [gr. 4-5 remote]: Introduction to Geometry 2 & 3 Triangle congruence, right angles, and perpendicular lines.Handouts: I2G3 | I2G2BNP A [K-1 in person]: Continue with Lesson 5 Digits and Numbers BNP B [K-1 in person]: Continue with Lesson 5 Digits and Numbers Intermediate 1A [gr. 5-7 in person]: Continuing Triangle Congruence Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 6 Intermediate 2A [gr. 7-9 in person]: Complex Numbers and Geometry Handouts: HandoutIntermediate 2B [gr. 7-9 remote]: Week 7 Handouts: Olympiads training: Equations Handouts: W7 Problems | W7 Solutions 11/21/2021 Advanced 1A [gr. 7-11 in person]: Induction We revisit induction and if time allows go to the formalism of Peano axiomsHandouts: HandoutAdvanced 1B [gr. 7-11 remote]: Induction, Peano Axioms We will study the concept of mathematical induction as well as the Peano Axiom.Handouts: handoutAdvanced 2A [gr. 9-11 in person]: Dynamical Systems II We will continue our study of dynamical systems by connecting logistic maps to the Mandelbrot set.Handouts: Dynamical Systems IIAdvanced 2B [gr. 9-11 remote]: Dynamical Systems II We will continue our study of dynamical systems by connecting logistic maps to the Mandelbrot set.Handouts: Advanced 3 [gr. 11-12 remote]: Voting Theory Handouts: Bonus_ProblemsAMC10/12 training: AMC 10/12 B Review Beginners 1A [gr. 1-3 in person]: Chapter 28 - Adding and subtracting binary numbers In this class, taught by guest instructor Professor Kim, students will learn how to add and subtract binary numbers by modifying their abaci.Beginners 1B [gr. 1-3 remote]: Coordinates Beginners 2A [gr. 4-5 in person]: Fall - Pythagorean Theorem Handouts: Homework due | Reading dueBeginners 2B [gr. 4-5 remote]: Introduction to Geometry 3 Handouts: I2G3BNP A [K-1 in person]: Lesson 5 Digits and Numbers & Quiz #3 Give quiz #3 and review the homework problems from the lesson.BNP B [K-1 in person]: Lesson 5 Digits and Numbers & Quiz #3 Give quiz #3 and review the homework problems from the lesson.Intermediate 1A [gr. 5-7 in person]: Isosceles Triangles and Beginning Circles Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 7 Intermediate 2A [gr. 7-9 in person]: Complex Numbers and Geometry 2 Handouts: HandoutIntermediate 2B [gr. 7-9 remote]: Week 8 Handouts: Olympiads training: Equations II Handouts: W8 Problems 11/28/2021 Advanced 3 [gr. 11-12 remote]: NO MEETING: Thanksgiving Break AMC10/12 training: No Class Today: Thanksgiving Break Beginners 1B [gr. 1-3 remote]: NO CLASS: Thanksgiving Holiday Beginners 2A [gr. 4-5 in person]: Fall - Class Suspended (Thanksgiving Break) There is no class on November 28tth, 2021. We wish everyone a happy Thanksgiving break! 12/5/2021 Advanced 1A [gr. 7-11 in person]: Game We have a game to mark the end of the quarterAdvanced 1B [gr. 7-11 remote]: Game We will be playing our end of quarter game.Handouts: handoutAdvanced 2A [gr. 9-11 in person]: Competition II Handouts: Competition ProblemsAdvanced 2B [gr. 9-11 remote]: Competition We'll do a competition. It will be the last meeting of 2021.Advanced 3 [gr. 11-12 remote]: Competition Handouts: AMC10/12 training: Sequences and Series Beginners 1A [gr. 1-3 in person]: Chapter 29 - ASCII coding and quiz 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.Beginners 1B [gr. 1-3 remote]: Beginners 1B: Finish Up Making Heads and Tails of Dragons + Quarter Recap Beginners 2A [gr. 4-5 in person]: Fall - Pythagorean Theorem (Continued) 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!Beginners 2B [gr. 4-5 remote]: Introduction to Geometry 3 Applications of triangle congruence, Pythagorean theorem.Handouts: I2G3BNP A [K-1 in person]: Lesson 6 Young Diagrams 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.BNP B [K-1 in person]: Lesson 6 Young Diagrams 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.Intermediate 1A [gr. 5-7 in person]: Final Meeting! Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 8 Intermediate 2A [gr. 7-9 in person]: Week 10 Competition Intermediate 2B [gr. 7-9 remote]: Week 10 Handouts: Olympiads training: Coloring & Tiling Winter 2022 quarter // Filter groups by: Advanced 1AAdvanced 1BAdvanced 2AAdvanced 2BAdvanced 3AMC10/12 trainingBeginner/Intermediate Chess trainingBeginners 1ABeginners 1BBeginners 2ABeginners 2BBNP ABNP BIntermediate 1AIntermediate 1BIntermediate 2AIntermediate 2BIntermediate/Advanced Chess trainingOlympiads training 1/9/2022 Advanced 1A [gr. 7-11 in person]: Induction We continue our work with the Peano axioms and induction handout.Handouts: HandoutAdvanced 1B [gr. 7-11 remote]: The Peano Axiom Induction and the Peano axiom.Handouts: Advanced 2A [gr. 9-11 in person]: Spanning Trees and Kirchhoff's Matrix Tree Theorem We will discuss spanning trees of graphs, and a variety of methods to count how many of them they are.Handouts: Advanced 2B [gr. 9-11 remote]: Spanning Trees and Kirchhoff's Matrix Tree Theorem I We will attempt to naively count the number of spanning trees in a graph.Handouts: Spanning TreesAdvanced 3 [gr. 11-12 in person]: Spanning Trees and Kirchhoff's Tree Theorem Handouts: ProblemsAMC10/12 training: Piecewise Functions Beginners 1A [gr. 1-3 in person]: Chapter 30 -- Moebius strip 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.Beginners 1B [gr. 1-3 remote]: Finish Book 1 & Begin Ciphers 1 Beginners 2A [gr. 4-5 in person]: Winter - Parallel Lines 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=cjh1MWVWc1FKTVpWYk1nMGtsVUZ2dz09Meeting ID: 756 844 1046Passcode: Beg2A-GeoRequired 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!Beginners 2B [gr. 4-5 remote]: Introduction to Geometry 4 We will start this quarter by discussing parallel lines.Handouts: I2G4Intermediate 1A [gr. 5-7 in person]: Chapter 9: Quadrilaterals & Parallel Lines Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 9 Intermediate 2A [gr. 7-9 in person]: Euclidean Algorithm I Handouts: HandoutIntermediate 2B [gr. 7-9 remote]: 22W Week 1 Handouts: Olympiads training: Modular Arithmetic I and Divisibility Rules Handouts: W1-mod | W1 Solutions 1/14/2022 Intermediate/Advanced Chess training: Week 1: Diagnostic Handouts: 1/16/2022 Advanced 1A [gr. 7-11 in person]: Cauchy induction 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: HandoutAdvanced 1B [gr. 7-11 remote]: Cauchy Induction and Inequalities We'll be considering a souped up version of mathematial induction.Handouts: Advanced 2A [gr. 9-11 in person]: Spanning Trees and Kirchhoff's Matrix Tree Theorem II We will wrap up our discussion on spanning trees and ways of counting them. Advanced 2B [gr. 9-11 remote]: Spanning Trees and Kirchhoff's Matrix Tree Theorem II 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 TreesAdvanced 3 [gr. 11-12 in person]: Spanning Trees and Kirchhoff's Tree Theorem AMC10/12 training: Circles Beginners 1A [gr. 1-3 in person]: Chapter 31 -- Introduction to coordinates We will cover Chapter 31, which introduces coordinates for the line and plane. Time permitting, we will do a review of Roman numerals.Beginners 1B [gr. 1-3 remote]: More Ciphers! Beginners 2A [gr. 4-5 in person]: Winter - Parallel Lines (Continued) 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=cjh1MWVWc1FKTVpWYk1nMGtsVUZ2dz09Meeting ID: 756 844 1046Passcode: Beg2A-GeoRequired 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 4Beginners 2B [gr. 4-5 remote]: Introduction to Geometry 4: Continued Handouts: I2G4Intermediate 1A [gr. 5-7 in person]: Chapter 9: Part II Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 10 Intermediate 2A [gr. 7-9 in person]: Euclidean Algorithm II Handouts: HandoutIntermediate 2B [gr. 7-9 remote]: 22W Week 2 Handouts: Olympiads training: Fermat's Thm Handouts: W2 | W2_sols 1/21/2022 Intermediate/Advanced Chess training: Week 2: Forks Handouts: 1/23/2022 Advanced 1A [gr. 7-11 in person]: Josephus problem 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: HandoutAdvanced 1B [gr. 7-11 remote]: Josephus This week we will study the story of Jesephus, a Roman general and later historian.Handouts: Advanced 2A [gr. 9-11 in person]: Peano Axioms We will be discussing the Peano Axioms and how we can rigorously define numbers and arithmetic.Handouts: Advanced 2B [gr. 9-11 remote]: Peano Axioms I 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 AxiomsAdvanced 3 [gr. 11-12 in person]: 3D Geometry with Quaternions Handouts: ProblemsAMC10/12 training: Quadratics & Factoring Beginners 1A [gr. 1-3 in person]: Review of Roman numerals and Mathematical Games 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.Beginners 1B [gr. 1-3 remote]: Finish Ciphers & Quiz Beginners 2A [gr. 4-5 in person]: Winter - Vectors 1 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=cjh1MWVWc1FKTVpWYk1nMGtsVUZ2dz09Meeting ID: 756 844 1046Passcode: Beg2A-GeoRequired 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!Beginners 2B [gr. 4-5 remote]: Vector Geometry 1 We will begin the study of vector geometry in Euclidean space, applying the geometrical knowledge we have learned.Handouts: Vector Geometry Handout 1BNP A [K-1 remotely]: Lesson 7 Harder Subtraction Problems BNP B [K-1 remotely]: Lesson 7 Harder Subtraction Problems Intermediate 1A [gr. 5-7 in person]: Continuation of Chapter 9 and part of Chapter 10 Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 11 Intermediate 2A [gr. 7-9 in person]: Graph Theory 1 Handouts: Handout | SolutionsIntermediate 2B [gr. 7-9 remote]: 22W Week 3 Handouts: Olympiads training: Modular Arithmetic III: Euler's Thm Handouts: W3 Problems | W3 sols 1/28/2022 Intermediate/Advanced Chess training: Week 3: Pins & Skewers Handouts: 1/30/2022 Advanced 1A [gr. 7-11 in person]: Inscribed angles We again solve problems regarding the angles in the circle. This is the theme uniquely rich with nice problems.Handouts: HandoutAdvanced 1B [gr. 7-11 remote]: Elementary Euclidean Geometry This week, we'll study some elementary Euclidean geometry about angles.Handouts: handoutAdvanced 2A [gr. 9-11 in person]: Peano Axioms II We will be finishing up our investigation of number systems and the Peano Axioms.Handouts: Advanced 2B [gr. 9-11 remote]: Peano Axioms II 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 AxiomsAdvanced 3 [gr. 11-12 in person]: 3D Geometry with Quaternions Handouts: Bonus_ProblemsAMC10/12 training: Prime Decomposition Beginners 1A [gr. 1-3 in person]: Chapter 32 - Fighting dragons 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.Beginners 1B [gr. 1-3 remote]: Math Kangaroo Competition Prep Beginners 2A [gr. 4-5 in person]: Winter - Vectors 1 (Continued) 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=cjh1MWVWc1FKTVpWYk1nMGtsVUZ2dz09Meeting ID: 756 844 1046Passcode: Beg2A-GeoRequired 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 1Beginners 2B [gr. 4-5 remote]: Vector Geometry 1: Continued We will continue the discussion of the first vector geometry handout from last time.Handouts: Vector Geometry Handout 1BNP A [K-1 remotely]: Lesson 8 Even and Odd Numbers BNP B [K-1 remotely]: Lesson 8 Even and Odd Numbers Intermediate 1A [gr. 5-7 in person]: Chapter 10: Right Triangles Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 12 Intermediate 2A [gr. 7-9 in person]: Graph Theory II Handouts: Handout | SolutionsIntermediate 2B [gr. 7-9 remote]: 22W Week 4 Handouts: Olympiads training: Euler's Phi Function Handouts: W4 Problems | W4 Solutions 2/4/2022 Intermediate/Advanced Chess training: Week 4: Discovered Attack Handouts: 2/6/2022 Advanced 1A [gr. 7-11 in person]: Game This time we have a game with our usual rulesHandouts: GameAdvanced 1B [gr. 7-11 remote]: Competition Today we'll have a competition.Advanced 2A [gr. 9-11 in person]: 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.Advanced 2B [gr. 9-11 remote]: Competition I Handouts: Competition IAdvanced 3 [gr. 11-12 in person]: Competition Handouts: Problems | Bonus ProblemsAMC10/12 training: Similar Triangles Beginners 1A [gr. 1-3 in person]: Math Adventures Level 1, Finale We will finish Chapter 32, and work on selected problems from Chapter 33.Beginners 1B [gr. 1-3 remote]: Math Kangaroo Continued Beginners 2A [gr. 4-5 in person]: Winter - Vectors 1 (Continued) 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 1Beginners 2B [gr. 4-5 remote]: Vector Geometry 2 Handouts: Vector Geometry Handout 2BNP A [K-1 remotely]: Lesson 9 Properties of Odd and Even Numbers BNP B [K-1 remotely]: Lesson 9 Properties of Odd and Even Numbers Intermediate 1A [gr. 5-7 in person]: Chapter 11: Parallelograms (+ End of Chapter 10) Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 13 Intermediate 2A [gr. 7-9 in person]: Polynomials 1 Intermediate 2B [gr. 7-9 remote]: 22W Week 5 Handouts: | Olympiads training: Primes & Remaining Problems Handouts: W5 Problems | W5 Solutions 2/11/2022 Intermediate/Advanced Chess training: Week 5: Deflection & Attraction Handouts: | Bonus Handout 2/13/2022 Advanced 1A [gr. 7-11 in person]: Hat puzzles 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: HandoutAdvanced 1B [gr. 7-11 remote]: Guest Lecture Guest lectureHandouts: Advanced 2A [gr. 9-11 in person]: Guest Lecture Nikita and Natalie give a guest lecture on their recent research, and we solve some hat problems!Advanced 2B [gr. 9-11 remote]: Infinite Hat Puzzles 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=VWpRY01BbDdzT09qaTRPUFV4eTMyUT09We will hear a lecture from Nikita and Natalie about their results on infinite hat puzzles.Handouts: Hat Puzzles | Hat Puzzles SlidesAdvanced 3 [gr. 11-12 in person]: Guest Lecture: A Fun Problem About the Combinatorics of Ordinals 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: ProblemsAMC10/12 training: No class: enjoy the Super Bowl! Beginners 1A [gr. 1-3 in person]: Introduction to ciphers and secret messages We will start to discuss how to use ciphers to make secret messages.Beginners 1B [gr. 1-3 remote]: Introduction to Functions (Ch. 3 & 4) Beginners 2A [gr. 4-5 in person]: Winter - Vectors 2 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!Beginners 2B [gr. 4-5 remote]: Vector Geometry 2: Wrapping up BNP A [K-1 remotely]: Lesson 9 continued with Properties of Odd and Even Numbers BNP B [K-1 remotely]: Lesson 9 continued with Properties with Odd and Even Numbers Intermediate 1A [gr. 5-7 in person]: Chapter 12: Rectangles, Rhombuses, and Squares oh my! (Early Start) Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 14 Intermediate 2A [gr. 7-9 in person]: Polynomials 2 Handouts: Handout | SolutionsIntermediate 2B [gr. 7-9 remote]: 22W Week 6 Handouts: Worksheet 2/15/2022 Intermediate/Advanced Chess training: Week 6: Mixed Exercises Handouts: Handout | Bonus Exercises 2/20/2022 Advanced 1A [gr. 7-11 in person]: No Class Today! President's Day Beginners 2A [gr. 4-5 in person]: Winter - Class Suspended (Presidents' Day) There is no class on February 20th, 2021. We wish everyone a Happy Presidents' day!Intermediate 1A [gr. 5-7 in person]: No Meeting (President's Day) 2/22/2022 Intermediate/Advanced Chess training: Week 7: More Mixed Exercises Handouts: 2/27/2022 Advanced 1A [gr. 7-11 in person]: Irrational numbers We discuss the ways to prove that some numbers are irrationalHandouts: HandoutAdvanced 1B [gr. 7-11 remote]: Irrational numbers Definitions and basics of irrationals.Handouts: Advanced 2A [gr. 9-11 in person]: Irrational Numbers We will be investigating irrational numbers, including ways to prove a number is irrational, and some interesting applications.Handouts: Advanced 2B [gr. 9-11 remote]: Irrational Numbers We introduce both algebraic and analytic methods for detecting irrational numbers.Handouts: Irrational NumbersAdvanced 3 [gr. 11-12 in person]: Martingales Handouts: AMC10/12 training: Geometric Probability Beginners 1A [gr. 1-3 in person]: Cipers II 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.Beginners 1B [gr. 1-3 remote]: Functions Continued (Chapter 5) Beginners 2A [gr. 4-5 in person]: Winter - Vectors 2 (Continued) 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 2Beginners 2B [gr. 4-5 remote]: Vector Geometry 3 In this handout, we will see how using gridlines makes vector geometry computations much easier, with hidden relations to algebra. Handouts: Vector Geometry Handout 3BNP A [K-1 remotely]: Lesson 10 Commutativity of Addition BNP B [K-1 remotely]: Lesson 10 Commutativity of Addition Intermediate 1A [gr. 5-7 in person]: Cartesian Graphing Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 15 Intermediate 2A [gr. 7-9 in person]: Group Theory 1 Intermediate 2B [gr. 7-9 remote]: 22W Week 8 Handouts: | Olympiads training: Modular Arithmetic IV Handouts: W6 Problems | W6 Solutions 3/1/2022 Intermediate/Advanced Chess training: Week 8: White to Play and Mate in 2 Handouts: 3/5/2022 Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 16 3/6/2022 Advanced 1A [gr. 7-11 in person]: Irrational numbers 2 We continue the last week handout about proving irrationality of certain numbersHandouts: HandoutAdvanced 1B [gr. 7-11 remote]: Algebraic and Transcendental Numbers Handouts: Advanced 2A [gr. 9-11 in person]: Irrational Numbers II We will continue our exploration of irrational numbers.Handouts: Advanced 2B [gr. 9-11 remote]: Irrational and Algebraic Number We will figure out just how many irrational numbers there are by studying Cantor's diagonal argument.Handouts: Irrational and Algebraic NumbersAdvanced 3 [gr. 11-12 in person]: Martingales (cont.) AMC10/12 training: AM-GM Inequality Beginners 1A [gr. 1-3 in person]: Finishing ciphers and quiz 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.Beginners 1B [gr. 1-3 remote]: Functions Part III: Ch. 6 Beginners 2A [gr. 4-5 in person]: Winter - Vectors 2 (Continued) 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 2Beginners 2B [gr. 4-5 remote]: Vector Geometry 3: Continued We continue working on the handout last time.Handouts: Vector Geometry Handout 3BNP A [K-1 remotely]: Cont. Lesson 10 Commutativity of Addition BNP B [K-1 remotely]: Cont. Lesson 10 Commutativity of Addition Intermediate 1A [gr. 5-7 in person]: Equilateral Triangles Intermediate 2A [gr. 7-9 in person]: Group Theory 2 Intermediate 2B [gr. 7-9 remote]: 22W Week 9 Handouts: Olympiads training: Mods and Equations Handouts: 3/13/2022 Advanced 1A [gr. 7-11 in person]: Game End of the quarter gameHandouts: GameAdvanced 1B [gr. 7-11 remote]: Competition Handouts: Advanced 2A [gr. 9-11 in person]: Competition II For our last meeting of the quarter, we will be having another competition!Advanced 2B [gr. 9-11 remote]: Competition Handouts: Competition IIAdvanced 3 [gr. 11-12 in person]: Competition Handouts: ProblemsAMC10/12 training: Recursion Beginners 1A [gr. 1-3 in person]: Chapter 4; Introduction to functions We will introduce functions as machines that turn inputs into outputs. A new handout will be provided in class.Beginners 1B [gr. 1-3 remote]: Functions Quiz & Egyptian Multiplication Beginners 2A [gr. 4-5 in person]: Winter - Vectors 2 (Continued) 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 2Beginners 2B [gr. 4-5 remote]: Vector Geometry 3: Wrapping up We aim to finish the last vector geometry handout of the quarter.BNP A [K-1 remotely]: Review Lesson 10 Homework - Commutativity of Addition BNP B [K-1 remotely]: Review Lesson 10 Homework - Commutativity of Addition Intermediate 1A [gr. 5-7 in person]: More Triangles! Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 17 Intermediate 2A [gr. 7-9 in person]: Winter Competition Intermediate 2B [gr. 7-9 remote]: 22W Week 10 Handouts: Olympiads training: Quadratic Residues Spring 2022 quarter // Filter groups by: Advanced 1AAdvanced 1BAdvanced 2AAdvanced 2BAdvanced 3AMC10/12 trainingBeginner/Intermediate Chess trainingBeginners 1ABeginners 1BBeginners 2ABeginners 2BBNP ABNP BIntermediate 1AIntermediate 1BIntermediate 2AIntermediate 2BIntermediate/Advanced Chess trainingOlympiads training 4/3/2022 Advanced 1A [gr. 7-11 in person]: Information theory We solve problems leading to information theory.This handout is inspired by the video by 3Blue1Brown on solving wordle using information theory. youtu.be/v68zYyaEmEAHandouts: HandoutAdvanced 1B [gr. 7-11 in person]: Information Theory Handouts: Advanced 2A [gr. 9-11 in person]: Wallpaper Symmetries We will be looking at beautiful wallpapers and the mathematics behind their symmetries.Advanced 2B [gr. 9-11 in person]: Wallpaper 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 SymmetriesAdvanced 3 [gr. 11-12 in person]: The Hyperbolic Football We will build a model of hyperbolic space!Handouts: ProblemsAMC10/12 training: Binomial Theorem Beginners 1A [gr. 1-3 in person]: Lessons 5 and 6, Finishing up functions 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.Beginners 1B [gr. 1-3 remote]: First Meeting of Spring Quarter Beginners 2A [gr. 4-5 in person]: Spring - Logic Gates 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 LessonStudents 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!Beginners 2B [gr. 4-5 remote]: Logic 1 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 1BNP A [K-1 in person]: Lesson 11 Adding More Than Two Numbers BNP B [K-1 in person]: Lesson 11 Adding More Than Two Numbers Intermediate 1A [gr. 5-7 in person]: Chapter 15: Midsegment of a Triangle Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 18 Intermediate 2A [gr. 7-9 in person]: Polynomials 3 Handouts: Solutions | HandoutIntermediate 2B [gr. 7-9 remote]: 22S Week 1 Handouts: Olympiads training: Geometry: Similarity and Triangles Handouts: W1 Problems 4/5/2022 Intermediate/Advanced Chess training: Weeks 1-2: Endgame Tactics Handouts: 4/10/2022 Advanced 1A [gr. 7-11 in person]: Hyperbolic soccer ball 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: HandoutAdvanced 1B [gr. 7-11 in person]: Hyperbolic Geometry 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: Advanced 2A [gr. 9-11 in person]: Hyperbolic Soccer Ball 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.Advanced 2B [gr. 9-11 in person]: Hyperbolic Soccer Ball In small groups, we will build hyperbolic soccer balls in order to learn about the geometry of non-Euclidean spaces.Handouts: Hyperbolic Soccer BallAdvanced 3 [gr. 11-12 in person]: Smart Codes 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 | Problems2AMC10/12 training: Similar Triangles Beginners 1A [gr. 1-3 in person]: Chapter 7 - 3D geometry 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.Beginners 1B [gr. 1-3 remote]: Functions and Sets Beginners 2A [gr. 4-5 in person]: Spring - Logic Gates (Continued) 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 LessonStudents 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!Beginners 2B [gr. 4-5 remote]: Logic 2: Truth Functions; AND Operation Handouts: Logic 2 | Logic 3BNP A [K-1 in person]: Lesson 12 Operations BNP B [K-1 in person]: Lesson 12 Operations Intermediate 1A [gr. 5-7 in person]: Chapters: 16 & 18: Intercepts and Inequalities Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 19 Intermediate 2A [gr. 7-9 in person]: Polynomials Continued Handouts: Handout | SolutionsIntermediate 2B [gr. 7-9 remote]: 22S Week 2 Handouts: Olympiads training: Geometry: Similarity and Triangles II Handouts: 4/17/2022 Advanced 1A [gr. 7-11 in person]: Pigeonhole principle We are doing a well-tried handout on pigeonhole principle.Handouts: HandoutAdvanced 1B [gr. 7-11 in person]: Pigeonhole Handouts: Advanced 2A [gr. 9-11 in person]: P vs NP We will be discussing the Millennium Problem P vs NP so that we can understand this problem and what makes it so difficult.Handouts: | Advanced 2B [gr. 9-11 in person]: P vs NP 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 NPAdvanced 3 [gr. 11-12 in person]: Special Relativity We will investigate the theory of special relativity.AMC10/12 training: Pythagorean Theorem Beginners 1A [gr. 1-3 in person]: Chapter 8 - More solids We will continue our discussion of solid shapes and projection. You will need 27 single-color wooden cubes.Beginners 1B [gr. 1-3 remote]: 3D Geometry: Bring Cubes! Beginners 2A [gr. 4-5 in person]: Spring - Logic Gates (Continued) 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!Beginners 2B [gr. 4-5 remote]: Logic 3: OR, NOT, Boolean Algebra Handouts: Logic 3 | Logic 4 | Logic 5BNP A [K-1 in person]: Lesson 13 Compositions of Operations and Commutativity BNP B [K-1 in person]: Lesson 13 Compositions of Operations and Commutativity Intermediate 1A [gr. 5-7 in person]: Lesson 13 Compositions of Operations and Commutativity Intermediate 1A [gr. 5-7 in person]: Chapter 19: Symmetry Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 20 Intermediate 2A [gr. 7-9 in person]: Introduction to Algorithms Intermediate 2B [gr. 7-9 remote]: 22S Week 3 Handouts: Olympiads training: Geometry: Similarity and Triangles II - Continue to the remaining problems in W2 Handouts: 4/19/2022 Intermediate/Advanced Chess training: Week 3: Endgame Studies Handouts: 4/24/2022 Advanced 1A [gr. 7-11 in person]: Cryptography We study the basic number theory needed for secure communication.Handouts: HandoutAdvanced 1B [gr. 7-11 in person]: Cryptography This week we will study nubmer theory and its application in cryptographyHandouts: Advanced 2A [gr. 9-11 in person]: Zero Knowledge Proof 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.Advanced 2B [gr. 9-11 in person]: Zero Knowledge Proofs 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 ProofsAdvanced 3 [gr. 11-12 in person]: Electric Circuits and Random Walks Handouts: ProblemsAMC10/12 training: Volume Beginners 1A [gr. 1-3 in person]: Chapters 9 and 10a 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!Beginners 1B [gr. 1-3 remote]: Lesson 8 And 9 Beginners 2A [gr. 4-5 in person]: Spring - Logic Gates (Continued) 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!Beginners 2B [gr. 4-5 remote]: Logic 4: Wrapping up We will continue to go through the previous handouts, in the hope of finishing the fifth handout by the end of class.BNP A [K-1 in person]: Lesson 13 Compositions of Operations and Commutativity BNP B [K-1 in person]: Lesson 13 Compositions of Operations and Commutativity Intermediate 1A [gr. 5-7 in person]: More Symmetry! Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 21 Intermediate 2A [gr. 7-9 in person]: Algorithms Continued Intermediate 2B [gr. 7-9 remote]: 22S Week 4 Handouts: Olympiads training: Geometry: Triangles III Handouts: 4/26/2022 Intermediate/Advanced Chess training: Week 4-5: Candidate Moves Handouts: 5/1/2022 Advanced 1A [gr. 7-11 in person]: Game We have a game!Advanced 1B [gr. 7-11 in person]: Competition Advanced 2A [gr. 9-11 in person]: Competition We will be having a competition!Advanced 2B [gr. 9-11 in person]: Competition I Handouts: Competition IAdvanced 3 [gr. 11-12 in person]: Electric Circuits and Random Walks 2 AMC10/12 training: Advanced Algebraic Manipluations Beginners 1A [gr. 1-3 in person]: Chapter 10 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.Beginners 1B [gr. 1-3 remote]: Quiz and Lesson 10 Beginners 2A [gr. 4-5 in person]: Spring - Intro to Python 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!Beginners 2B [gr. 4-5 remote]: Python Programming We will start introducing the basics of the programming language Python. BNP A [K-1 in person]: Continue with Lesson 13 Compositions of Operations and Commutativity BNP B [K-1 in person]: Continue with lesson 13 Compositions of Operations and Commutativity Intermediate 1A [gr. 5-7 in person]: Chapter 20: Pivoting to a new kind of symmetry Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 22 Intermediate 2A [gr. 7-9 in person]: Game Theory I Handouts: Handout | SolutionsIntermediate 2B [gr. 7-9 remote]: 22S Week 5 Handouts: Olympiads training: Cyclic Quadrilaterals Handouts: 5/8/2022 Advanced 1A [gr. 7-11 in person]: e We study the beginnings of calculus and the number e=2.71...Handouts: HandoutAdvanced 1B [gr. 7-11 in person]: The number e Handouts: Advanced 2A [gr. 9-11 in person]: Financial Math We will be learning about the math of the stock market and finances!Handouts: Advanced 2B [gr. 9-11 in person]: Financial Math I 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 Advanced 3 [gr. 11-12 in person]: Electric Circuits and Random Walks 3 AMC10/12 training: Exponents & Logarithms Beginners 1A [gr. 1-3 in person]: The game of Nim 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. Beginners 1B [gr. 1-3 remote]: Ch. 11: Logic Beginners 2A [gr. 4-5 in person]: Spring - Intro to Python (continued) 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!Beginners 2B [gr. 4-5 remote]: Python Programming 2 We will continue from last time: review Python workflow, and complete the exercises.BNP A [K-1 in person]: Lesson 14 Inverse Operations BNP B [K-1 in person]: Lesson 14 Inverse Operations Intermediate 1A [gr. 5-7 in person]: Chapter 21: Angles in a Circle Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 23 Intermediate 2A [gr. 7-9 in person]: Game Theory II Handouts: Handout | SolutionsIntermediate 2B [gr. 7-9 remote]: 22S Week 6 Handouts: Olympiads training: Geometry: Radial Axis Handouts: 5/10/2022 Intermediate/Advanced Chess training: Week 6: Attacking the King Handouts: 5/15/2022 Advanced 1A [gr. 7-11 in person]: Combinatorics This lesson is going online because of COVID. We study binomial coefficients and Pascal triangle -- basic objects in combinatorics.Handouts: HandoutAdvanced 1B [gr. 7-11 in person]: Combinatorics Handouts: Advanced 2A [gr. 9-11 in person]: Financial Math II We will be continuing our mathematical investigation of the stock market and finances.Advanced 2B [gr. 9-11 in person]: Financial Math II We use the principle of no arbitrage to develop relationships among put and call pricing.Handouts: Financial Math Advanced 3 [gr. 11-12 in person]: Game Theory We learn some Nash-style game theory.Handouts: AMC10/12 training: Curved Surfaces Beginners 1A [gr. 1-3 in person]: Chapter 11 - More knights and liars, logic We will continue our discussion of logic problems, introducing logic gates as a way to combine logical statements.Beginners 1B [gr. 1-3 remote]: Lesson 12 and 13: The Or Operation and Logic continued. Beginners 2A [gr. 4-5 in person]: Spring - Intro to Python (continued) 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!Beginners 2B [gr. 4-5 remote]: Python Programming Continued We will be practicing basic programming skills by doing problems from Project Euler.BNP A [K-1 in person]: Continue with Lesson 14 Inverse Operation BNP B [K-1 in person]: Continue with Lesson 14 Inverse Operation Intermediate 1A [gr. 5-7 in person]: Chapter 21 & 22 Angles & Tangents Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 24 Intermediate 2A [gr. 7-9 in person]: More Number Theory Intermediate 2B [gr. 7-9 remote]: 22S Week 7 Handouts: Olympiads training: Geometry: Radial Axis Continued Handouts: 5/22/2022 Advanced 1A [gr. 7-11 in person]: Graph theory We introduce basic definitions of graph theory and work out some problems which don't require any background knowledge.Handouts: HandoutAdvanced 1B [gr. 7-11 in person]: Graph Theory Handouts: Advanced 2A [gr. 9-11 in person]: Electric Circuits and Random Walks We will be investigating the mathematics behind circuits!Advanced 2B [gr. 9-11 in person]: Electrical Circuits and Random Walks We apply the theory of random walks on graphs to electrical circuits.Handouts: Electrical Circuits and Random WalksAdvanced 3 [gr. 11-12 in person]: Financial Math 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.AMC10/12 training: Bayes'Theorem Beginners 1A [gr. 1-3 in person]: Chapter 12 and 13a - mathematical logic We will continue our study of mathematical logic, learning about how statements can be combined and modified using logical operations.Beginners 1B [gr. 1-3 remote]: Chapter 14 & 15 Beginners 2A [gr. 4-5 in person]: Spring - Intro to Python (Continued) 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!Beginners 2B [gr. 4-5 remote]: Python Programming: Drawing with Turtle We will start working with the Turtle package of Python, which allows one to draw figures (including fractals which are our end goal).BNP A [K-1 in person]: Lesson 15 Plane Reflections and Other Symmetries and Quiz 8 BNP B [K-1 in person]: Lesson 15 Plane Reflections and Other Symmetries and Quiz 8 Intermediate 1A [gr. 5-7 in person]: Chapter 22 Tangents part II Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 25 Intermediate 2A [gr. 7-9 in person]: Quadratic Reciprocity II Intermediate 2B [gr. 7-9 remote]: Handouts: Olympiads training: Cyclic Quadrilaterals Continued Handouts: 5/29/2022 Intermediate 1A [gr. 5-7 in person]: NO MEETING (Memorial Day) 6/5/2022 Advanced 1A [gr. 7-11 in person]: Game Advanced 1B [gr. 7-11 in person]: Competition Advanced 2B [gr. 9-11 in person]: Guest Lecture Dr. Terence Tao speaks about the cosmic distance ladder. Beginners 1A [gr. 1-3 in person]: Final Meeting -- Chapter 13b and 14 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.Beginners 1B [gr. 1-3 remote]: Final Meeting: Quiz 4 and Review Games Beginners 2B [gr. 4-5 remote]: Python Programming: Recursion and Fractals We will conclude this class by revisiting recursion and drawing fractals.BNP A [K-1 in person]: Review Quiz #8, Fun with Math Puzzles BNP B [K-1 in person]: Review Quiz #8, Fun With Math Puzzles Intermediate 1A [gr. 5-7 in person]: Last Class Wrapup! Intermediate 1B [gr. 5-7 remote]: Intro to Geometry by A. Shen, Lesson 26 Intermediate 2A [gr. 7-9 in person]: Spring competition Olympiads training: Mixed Problems for the last day. 6/6/2022 Beginners 2A [gr. 4-5 in person]: Spring - Intro to Python (Continued) 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!