# LAMC Meetings Archive • Fall 2007–Summer 2020

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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
 Fall 2019 quarter // Filter groups by: Advanced 1AAdvanced 1BAdvanced 2AAdvanced 2BAMC10/12 TrainingBeginners 1ABeginners 1BBeginners 2ABeginners 2BBNPBNP BridgeIntermediate 1AIntermediate 1BIntermediate 2AIntermediate 2BOlympiads 1Olympiads 2 10/6/2019 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Moscow Math Olympiad Warm-Up We start off the new year with some problems from the Moscow Math Olympiad.Handouts: HandoutAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Week 1: Moscow Math Olympiad Warm-Up We start off the new year with some problems from the Moscow Math Olympiad.Handouts: Week-1Advanced 2A [gr.11-12 (Adam, Matt)]: Wallpaper Symmetries What kinds of patterns can be used as wallpaper? What are their groups of symmetries, and how can we classify them? How many are there? We will attempt to answer some of these questions and learn how to use Thurston's "orbifold notation" for wallpaper patterns.Handouts: Wallpaper SymmetriesAdvanced 2B [gr.11-12 (Aaron, Harris)]: Gaussian Integers 1 Introduction to Gaussian integers, as well as prime and irreducible Gaussian integersHandouts: Gaussian Integers 1Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Ciphers 1 Did you ever want to communicate with your friends in a secret way that only those who knew the secret could understand? A cipher is a tool for writing and reading secret messages. We will study three ciphers this time: the reverse cipher, Polybius cipher, and Casear cipher. You will find a template for making a Caesar cipher disk at the link below. Handouts: Caesar cipher templateBeginners 1B [gr.2-3 (Oleg, 5pm)]: Ciphers 1 Did you ever want to communicate with your friends in a secret way that only those who knew the secret could understand? A cipher is a tool for writing and reading secret messages. We will study three ciphers this time: the reverse cipher, Polybius cipher, and Casear cipher. You will find a template for making a Caesar cipher disk at the link below. Handouts: Caesar cipher templateBeginners 2A [gr.3-4 (Doug, 3:45pm)]: Hats and Doors To start out the quarter, we will be developing logic skills by looking at problems with hats and doors. The goal of this handout is to learn how to make an assumption, test the assumption, and readjust the original assumption if necessary.Handouts: handout | solutionsBeginners 2B [gr.3-4 (TBA, 5pm)]: Hats and Doors To start out the quarter, we will be developing logic skills by looking at problems with hats and doors. The goal of this handout is to learn how to make an assumption, test the assumption, and readjust the original assumption if necessary.Handouts: handout | solutionsBNP [Breaking Numbers into Parts (Kindergarten)]: Welcome to BNP We will start the BNP curriculum.BNP Bridge [Only for students who finished BNP last year]: Problem Solving We will solve a variety of fun problems.Intermediate 1A [gr.5-6 (Preston, 4-6pm)]: Egyptian Fractions Today we will be looking at how to optimally divide cakes among any amount of people by using an ancient Egyptian technique of breaking fractions into their unit parts but doing so in a specific way, which we will work with and then prove to be optimal.Handouts: Egyptian Fractions 1Intermediate 1B [gr.5-6 (TBA, 4-6pm)]: Egyptian Fractions 1 Today we will be looking at how to optimally divide cakes among any amount of people by using an ancient Egyptian technique of breaking fractions into their unit parts but doing so in a specific way, which we will work with and then prove to be optimal. Handouts: Egyptian Fractions 1Intermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Algebra We will be starting off the new quarter with some algebra activities.Handouts: Handout | SolutionsIntermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: Algebra We will be starting off the new quarter with some algebra activities.Handouts: Handout | SolutionsOlympiads 1: Problems about Digits and Base Representations We will discuss a few properties concerning representations of nonnegative integers and rationals in a general base (such as divisibility criteria), and particularly in base 10. Then we will apply this knowledge to several Olympiad-type Number Theory problems.Handouts: Handout | Solutions 10/9/2019 AMC10/12 Training: AMC Exam We will go through a sample AMC exam from 2019. 10/13/2019 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Advanced 1A: Intro to Probability 1 We start off probability by introducing some set theory notation and defining sample spaces. Then we apply those to classical probability questions.Handouts: Handout | HomeworkAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Week 2: Intro to probability We start off probability by introducing some set theory notation and defining sample spaces. Then we apply those to classical probability questions.Handouts: Week-2 | Homework-2Advanced 2A [gr.11-12 (Adam, Matt)]: Wallpaper Symmetries II We will continue to answer some of the questions posed about wallpaper symmetries. For those that finish the worksheet on wallpaper symmetries, we started discussing the origins and early properties of the p-adic numbers.Advanced 2B [gr.11-12 (Aaron, Harris)]: Gaussian Integers 2 Characterization of which positive integers are sums of squaresHandouts: Gaussian Integers 2Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Ciphers 2 An anagram is a word or phrase formed by rearranging letters of another word or phrase. Most often, all the original letters are used once. For example, the words "silent" and "listen" form an anagram. This time, we will have anagrams for a warm-up and then study two ciphers: pigpen cipher and rail fence cipher. Beginners 1B [gr.2-3 (Oleg, 5pm)]: Ciphers 2 An anagram is a word or phrase formed by rearranging letters of another word or phrase. Most often, all the original letters are used once. For example, the words "silent" and "listen" form an anagram. This time, we will have anagrams for a warm-up and then study two ciphers: pigpen cipher and rail fence cipher. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Egyptian Multiplication An alternate method of multiplication based in binary numbers and the basic ideas of the distributive property.Handouts: Handout | solutionsBeginners 2B [gr.3-4 (TBA, 5pm)]: Egyptian Multiplication An alternate method of multiplication based in binary numbers and the basic ideas of the distributive property.Handouts: Handout | solutionsBNP [Breaking Numbers into Parts (Kindergarten)]: Chapter 2: Parts of a Number We will continue the BNP curriculum.BNP Bridge [Only for students who finished BNP last year]: Problem Solving We will solve a variety of fun problems.Intermediate 1A [gr.5-6 (Preston, 4-6pm)]: Egyptian fractions part II This week we continue from last week and try to prove a mathematical algorithm, which is a very important activity in mathematics.Handouts: Egyptian fractions 2Intermediate 1B [gr.5-6 (TBA, 4-6pm)]: Egyptian fractions part II This week we continue from last week and try to prove a mathematical algorithm, which is a very important activity in mathematics.Handouts: Egyptian fractions 2Intermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Tilings and Colorings We will discuss board-tiling problems-- is it possible to completely cover a region with a particular set of tiles without overlap? -- and interesting mathematical problems that arise from these puzzles.Handouts: HandoutIntermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: Tilings and Colorings We will discuss board-tiling problems-- is it possible to completely cover a region with a particular set of tiles without overlap? -- and interesting mathematical problems that arise from these puzzles.Handouts: HandoutOlympiads 1: Length and Areas in Olympiad Geometry We will solve a variety of geometry problems involving the computation of a length or an area, or using notions about areas to prove an identity. The problems range in difficulty from introductory to fairly challenging.Handouts: HandoutOlympiads 2: Induction and Bezout's Lemma We will go over these fundamental concepts and do a range of problems.Handouts: Handout 10/16/2019 AMC10/12 Training: AMC Exam, part 2 We'll continue going through the solutions for the 2019 AMC exams 10/20/2019 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Advanced 1A: Conditional Probability We continue our probability unit with a worksheet on Conditional Probability. This includes the Law of Total Probability and Bayes' Theorem.Handouts: Handout | HomeworkAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Week 3: Probability II We are continuing solving probability problems. The topics for this class are Conditional Probability, Law of Total Probability, Bayes' Rule.Handouts: Week-3 | Homework-3Advanced 2A [gr.11-12 (Adam, Matt)]: Frieze Patterns We will study the symmetries of frieze patterns, especially those of unimodular frieze patterns. We work toward an interesting result proved by Conway and Coxeter about polygonal structures in frieze patterns.Advanced 2B [gr.11-12 (Aaron, Harris)]: Frieze Patterns 1 We will study the symmetries of frieze patterns, especially those of unimodular frieze patterns. We work toward an interesting result proved by Conway and Coxeter about polygonal structures in frieze patterns.Handouts: Frieze Patterns 1Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Recap and quiz 1 We will finish the study of the rail fence cipher and take a quiz on ciphers. Remember, we do not quiz students, we quiz teachers. If you get a low grade, it means we didn't do a good job. Please study for the quiz - don't let us down! Beginners 1B [gr.2-3 (Oleg, 5pm)]: Recap and quiz 1 We will finish the study of the rail fence cipher and take a quiz on ciphers. Remember, we do not quiz students, we quiz teachers. If you get a low grade, it means we didn't do a good job. Please study for the quiz - don't let us down! Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Russian Peasant Math We will continue with different ways to multiplying 2 numbers. This week we will look at Russian Peasant Multiplication, which, surprisingly, has no relation to Russia or Peasants. However, this will be another good way to show the students how to write numbers as sum of powers of 2Handouts: handout | answersBeginners 2B [gr.3-4 (TBA, 5pm)]: Russian Peasant Math We will continue with different ways to multiplying 2 numbers. This week we will look at Russian Peasant Multiplication, which, surprisingly, has no relation to Russia or Peasants. However, this will be another good way to show the students how to write numbers as sum of powers of 2Handouts: handout | answersBNP [Breaking Numbers into Parts (Kindergarten)]: Chapter 3: Partitions and Subtraction We will continue the BNP curriculum.BNP Bridge [Only for students who finished BNP last year]: Problem Solving We will solve a variety of fun problems.Intermediate 1A [gr.5-6 (Preston, 4-6pm)]: Modular Arithmetic I This week we begin on a very very very important topic in mathematics; Modular Arithmetic. Although the importance of this topic is not fully realized until a course in Abstract Algebra, it is still a very important topic because it can instill an understanding that the mathematics or arithmetic that we see commonly is not the only way of operating and that mathematics can be far more general and far reaching. Handouts: Part 1Intermediate 1B [gr.5-6 (TBA, 4-6pm)]: Modular arithmetic This week we begin on a very very very important topic in mathematics; Modular Arithmetic. Although the importance of this topic is not fully realized until a course in Abstract Algebra, it is still a very important topic because it can instill an understanding that the mathematics or arithmetic that we see commonly is not the only way of operating and that mathematics can be far more general and far reaching. Handouts: Part 1Intermediate 2A [gr.7-8 (Hunter, 4-6pm)]: More Tilings and Some Algebra We will continue to expand on last week's topic of tilings.Handouts: Handout | SolutionsIntermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: More Tilings and Some Algebra We will continue to expand on last week's topic of tilings.Handouts: Handout | SolutionsOlympiads 1: Graphs and Trees We solve a couple of introductory problems to Graph Theory and several harder ones. The lesson spans over two weeks.Handouts: HandoutOlympiads 2: Fundamental Theorem of Arithmetic and Congruences Using unique factorization into primes and modular arithmetic to solve problems. 10/23/2019 AMC10/12 Training: Triangle and Circle Geometry We will go through geometry problems with related to triangles and circles in the context of AMC 10/27/2019 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Advanced 1A: Random Variables and Expected Value Our third week of probability includes a handout on random variables and expected value, as well as some more interesting conditional probability problems.Handouts: HandoutAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Week 4: Probability III Our third week of probability includes a handout on random variables and expected value, as well as some more interesting conditional probability problems.Handouts: Week-4Advanced 2A [gr.11-12 (Adam, Matt)]: Frieze Patterns II We continue our study of the symmetries of unimodular frieze patterns with some challenge problems. We introduce the result proved by Conway and Coxeter connecting polygonal triangulations to frieze patterns.Advanced 2B [gr.11-12 (Aaron, Harris)]: Frieze Patterns 2 We continue our study of the symmetries of unimodular frieze patterns with some challenge problems. We introduce the result proved by Conway and Coxeter connecting polygonal triangulations to frieze patterns.Handouts: Frieze Patterns 2Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Function machine We will take the first look at one of the most important concepts in mathematics, that of a function. Beginners 1B [gr.2-3 (Oleg, 5pm)]: Function machine We will take the first look at one of the most important concepts in mathematics, that of a function. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Bases and Exponents I This packet introduces the topic of exponents, some of their properties, and size comparison!Handouts: answers pgs 1-3 | handoutBeginners 2B [gr.3-4 (TBA, 5pm)]: Bases and Exponents I This packet introduces the topic of exponents, some of their properties, and size comparison!Handouts: answers pgs 1-3 | handoutBNP [Breaking Numbers into Parts (Kindergarten)]: Chapter 3: Partitions and Subtraction (cont.) We will continue the BNP curriculum.BNP Bridge [Only for students who finished BNP last year]: Math Kangaroo Practice We will solve problems from the Math Kangaroo grades 1-2 contest.Intermediate 1A [gr.5-6 (Preston, 4-6pm)]: Modular arithmetic part II A continuation of next week. Please use this week's sheet as a a set of problems that build stronger arithmetic skills and provide insight into other ways of "counting."Handouts: Part IIIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Modular arithmetic part II A continuation of next week. Please use this week's sheet as a a set of problems that build stronger arithmetic skills and provide insight into other ways of "counting."Handouts: Part IIIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Algebra and Remainders We will be working with some algebra problems this week.Handouts: Handout | SolutionsIntermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: Algebra and Remainders We will be working with some algebra problems this week.Handouts: Handout | SolutionsOlympiads 1: Graphs and Trees, Part 2 We continue the lesson from last week with a few Olympiad-type problems in Graph Theory.Handouts: HandoutOlympiads 2: Euler's Phi Function Euler's totient function and more number-theoretic functionsHandouts: Handout 10/30/2019 AMC10/12 Training: Polygon Geometry We will go through AMC geometry problems with the emphasis on polygons. 11/3/2019 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Graphs, Random Walks, and Electrical Circuits We will be working through a fun application of probability and graph theory to electrical circuits. No knowledge of physics is necessary, everything needed is contained in the handout.Handouts: HandoutAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Week 5: Random Walks and Electrical Circuits We will be working through a fun application of probability and graph theory to electrical circuits. No knowledge of physics is necessary, everything needed is contained in the handout.Handouts: Electrical-CircuitsAdvanced 2A [gr.11-12 (Adam, Matt)]: Formal Proof Writing We work in groups to write rigorous proofs of statements from number theory, graph theory, combinatorics, set theory and other topics.Handouts: Formal ProofsAdvanced 2B [gr.11-12 (Aaron, Harris)]: Formal Proofs 1 Introduction to formal proof writing. Sets, functions, basic combinatorics and number theory proofsHandouts: Proofs 1Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Mathematical notations for functions. (Nadya Kuzkina) Students will learn the y = f(x) notation. Beginners 1B [gr.2-3 (Oleg, 5pm)]: Mathematical notations for functions. (Nadya Kuzkina) Students will learn the y = f(x) notation. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Bases and Exponents I Cont. Continuing last week's handout!Handouts: handout | pg 4 answersBeginners 2B [gr.3-4 (TBA, 5pm)]: Bases and Exponents I cont. Continuing last week's handout!Handouts: pg 4 answers | handoutBNP [Breaking Numbers into Parts (Kindergarten)]: Chapter 4: The Number Line We will continue the BNP curriculum.BNP Bridge [Only for students who finished BNP last year]: Math Kangaroo Practice We will solve problems from the Math Kangaroo grades 1-2 contest.Intermediate 1A [gr.5-6 (Preston, 4-6pm)]: Logical Negations This week we are working with some logic problems in the guise of "real world" sentences. The hope is that students can see that a basic logical structure is embedded in common speech, and that logical structure is the basis for mathematics and is taken to its most pure form and to its greatest lengths. Please use these worksheets as a warm up for the logical skills needed for induction next week.Handouts: HandoutIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Logical Negations This week we are working with some logic problems in the guise of "real world" sentences. The hope is that students can see that a basic logical structure is embedded in common speech, and that logical structure is the basis for mathematics and is taken to its most pure form and to its greatest lengths. Please use these worksheets as a warm up for the logical skills needed for induction next week.Handouts: HandoutIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Remainders Continuing our work in algebra last week, we will look at remainders and divisibility.Handouts: Solutions | HandoutIntermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: Remainders Continuing our work in algebra last week, we will look at remainders and divisibility.Handouts: Solutions | HandoutOlympiads 1: Inequalities with Integers We discuss various techniques for solving problems involving integer inequalities, specific to Olympiad Number Theory.Handouts: HandoutOlympiads 2: Number Theory Problems NT problems including showing there are infinitely many 4k+1 primes.Handouts: Handout 11/6/2019 AMC10/12 Training: Trigonometry We will cover some of the applications of trigonometry in AMC. 11/10/2019 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Graphs, Random Walks, and Electrical Circuits Continued We dive further into the connection between random walks and electrical circuits, deriving series and parallel circuits. We then discuss electrical circuits on an integer lattice and its connection to Polya's problem.Handouts: HandoutAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Week 6: Electrical Circuits and Random Walks We dive further into the connection between random walks and electrical circuits, deriving series and parallel circuits. We then discuss electrical circuits on an integer lattice and its connection to Polya's problem.Handouts: Week-6-HandoutAdvanced 2A [gr.11-12 (Adam, Matt)]: Formal Proof Writing II We work in groups to write rigorous proofs of statements from number theory, graph theory, combinatorics, set theory and other topics.Handouts: Formal Proofs IIAdvanced 2B [gr.11-12 (Aaron, Harris)]: Formal Proofs 2 Introduction to formal proof writing. Sets, functions, basic combinatorics and number theory proofsHandouts: Proofs 2Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: More functions. (Nadya Kuzkina) We will continue studying functions. Beginners 1B [gr.2-3 (Oleg, 5pm)]: More functions. (Nadya Kuzkina) We will continue studying functions. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Beginners 2A: Bases and Exponents II Review what we learned about exponents and continue to build how to compare numbersHandouts: handout | solutions I | solutions IIBeginners 2B [gr.3-4 (TBA, 5pm)]: Bases and Exponents II Review what we learned about exponents and continue to build how to compare numbersHandouts: handout | solutions I | solutions IIBNP [Breaking Numbers into Parts (Kindergarten)]: Chapter 5: Digits and Numbers We will continue the BNP curriculum.BNP Bridge [Only for students who finished BNP last year]: Math Kangaroo Practice We will solve problems from the Math Kangaroo grades 1-2 contest.Intermediate 1A [gr.5-6 (Preston, 4-6pm)]: Induction (part 1) This week we are starting induction! If these problems are challenging (they most likely are) do not panic. These are meant to be attempted to the best of everyone's ability and asking questions is extremely encouraged. Handouts: InductionIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Induction part 1 This week we are starting induction! If these problems are challenging (they most likely are) do not panic. These are meant to be attempted to the best of everyone's ability and asking questions is extremely encouraged. Handouts: InductionIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Greatest Common Divisors We will continue our work in algebra with GCDs.Handouts: Handout | SolutionsIntermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: Greatest Common Divisors We will continue our work in algebra with GCDs.Handouts: Handout | SolutionsOlympiads 1: Inequalities with Integers, Part 2 We continue the lecture from last time, with a few additional Olympiad-type Number Theory problems.Handouts: HandoutOlympiads 2: Lifting the Exponent The useful Lifting the Exponent Lemma, which states that for odd prime p and m,n such that p|(m-n), vp(m^p-n^p) = vp(m-n)+1.Handouts: Handout | Solutions 11/17/2019 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Complex Numbers We start a new unit: Complex Numbers! We will see that while complex numbers might seem unnatural, they are actually extremely useful and can simplify problems that have seemingly nothing to do with the square root of -1.Handouts: HandoutAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Week 7: Complex Numbers We start a new unit: Complex Numbers! We will see that while complex numbers might seem unnatural, they are actually extremely useful and can simplify problems that have seemingly nothing to do with the square root of -1.Handouts: Week-7-HandoutAdvanced 2A [gr.11-12 (Adam, Matt)]: Olympiad Problems We work on Olympiad style problems about Combinatorics, Number Theory, Probability, Geometry, and basic Set and Function Theory.Handouts: Olympiad ProblemsAdvanced 2B [gr.11-12 (Aaron, Harris)]: Olympiad Style Problems 1 Handouts: Olympiad Style Problems 1 | SolutionsBeginners 1A [gr.2-3 (Oleg, 3:45pm)]: Recap and quiz 2. (Nadya Kuzkina) We will review functions. Then students will take quiz 2. Beginners 1B [gr.2-3 (Oleg, 5pm)]: Recap and quiz 2. (Nadya Kuzkina) We will review functions. Then students will take quiz 2. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Venn Diagrams A look at how we can organize multiple sets of objects/people/things using venn diagrams!Handouts: handout 1 | handout 2 | solutions 1 | solutions 2Beginners 2B [gr.3-4 (TBA, 5pm)]: Venn Diagrams A look at how we can organize multiple sets of objects/people/things using venn diagrams!Handouts: handout 1 | handout 2 | solutions 1 | solutions 2BNP [Breaking Numbers into Parts (Kindergarten)]: Chapter 5: Digits and Numbers (cont.) We will continue the BNP curriculum.BNP Bridge [Only for students who finished BNP last year]: Math Kangaroo Practice We will solve problems from the Math Kangaroo grades 1-2 contest.Intermediate 1A [gr.5-6 (Preston, 4-6pm)]: Induction Part II This week we are continuing on induction proofs. It is fully expected that these problems are challenging, but they are extremely important to attempt, not necessarily get correct. The point of these two weeks is to 1. prepare students for induction proofs (the basis of discrete math and many proofs about finite objects) and 2. to challenge them to see the power of mathematical logic to prove an infinite amount of statements in a finite time. Intermediate 1B [gr.5-6 (TBA, 4-6pm)]: Induction Part II This week we are continuing on induction proofs. It is fully expected that these problems are challenging, but they are extremely important to attempt, not necessarily get correct. The point of these two weeks is to 1. prepare students for induction proofs (the basis of discrete math and many proofs about finite objects) and 2. to challenge them to see the power of mathematical logic to prove an infinite amount of statements in a finite time.Intermediate 2A [gr.7-8 (Hunter, 4-6pm)]: The Euclidean Algorithm The Euclidean Algorithm is a way to find the greatest common divisor of two numbers. Using what we've learned in algebra in the past weeks, we will investigate how this method works.Handouts: Handout | SolutionsIntermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: The Euclidean Algorithm The Euclidean Algorithm is a way to find the greatest common divisor of two numbers. Using what we've learned in algebra in the past weeks, we will investigate how this method works.Handouts: Handout | SolutionsOlympiads 1: Geometric Combinatorics and Convexity We define convexity, convex hulls and triangulations, then solve a few Olympiad-type problems in Geometric Combinatorics.Handouts: HandoutOlympiads 2: Solving Diophantine Equations Techniques for solving equations with the constraint that the variables must take integer values.Handouts: Handout 11/20/2019 AMC10/12 Training: Number Theory We will go through AMC problems covering several sections of number theory 11/23/2019 Olympiads 1: Trigonometry in Olympiad Geometry We define and discuss basic concepts from trigonometry, including the law of sines and the law of cosines. We then apply these notions to solving several Olympiad-type geometry problems.Handouts: Handout 11/24/2019 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Complex Numbers II We will explore roots of unity and some geometric aspects of the complex numbers.Handouts: Notes | HandoutAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Week 8: Complex Numbers II We will explore roots of unity and some geometric aspects of the complex numbers.Handouts: Notes | Complex-Numbers-IIAdvanced 2A [gr.11-12 (Adam, Matt)]: Olympiad Problems II We do further Olympiad style problems about Combinatorics, Number Theory, Probability, Geometry, and basic Set and Function Theory.Advanced 2B [gr.11-12 (Aaron, Harris)]: Olympiad Style Problems 2 Handouts: Olympiad Style Problems 2 | Solutions | HintsBeginners 2A [gr.3-4 (Doug, 3:45pm)]: Similar Shapes and Gnomons This week we will be looking at what it means for shapes to be similar, as well as exploring how we can add on to a shape to create another that is similar to the original.Handouts: handout 1 | handout 2 | solutions 1 | solutions 2Beginners 2B [gr.3-4 (TBA, 5pm)]: Similar Shapes and Gnomons This week we will be looking at what it means for shapes to be similar, as well as exploring how we can add on to a shape to create another that is similar to the original.Handouts: handout 1 | handout 2 | solutions 1 | solutions 2BNP [Breaking Numbers into Parts (Kindergarten)]: Chapter 6: Young Diagrams We will continue the BNP curriculum.BNP Bridge [Only for students who finished BNP last year]: Math Kangaroo Practice We will solve problems from the Math Kangaroo grades 1-2 contest.Intermediate 1A [gr.5-6 (Preston, 4-6pm)]: Area and Perimeter This week we are working on finding the perimeter of some interesting shapes. These problems are designed to prepare students to quickly recognize the shapes they are looking at and how they can break them into easily solvable pieces. Handouts: WorksheetIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Perimeter fun This week we are working on finding the perimeter of some interesting shapes. These problems are designed to prepare students to quickly recognize the shapes they are looking at and how they can break them into easily solvable pieces. Handouts: Perimeter Intermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Euclid's Lemma Some more fun with algebra, primes, and GCDs!Handouts: Handout | SolutionsIntermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: Euclid's Lemma Some more fun with algebra, primes, and GCDs!Handouts: Handout | SolutionsOlympiads 2: Number Theory Contest Handouts: Handout 12/1/2019 Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Polygons and solids. (Nadya Kuzkina) First, students will learn basic facts about polygons. Then they will proceed to build some solids out of cubes and to draw their 2D projections. Beginners 1B [gr.2-3 (Oleg, 5pm)]: Polygons and solids. (Nadya Kuzkina) First, students will learn basic facts about polygons. Then they will proceed to build some solids out of cubes and to draw their 2D projections. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: No Meeting- Happy Thanksgiving!! Beginners 2B [gr.3-4 (TBA, 5pm)]: No Meeting- Happy Thanksgiving!! BNP [Breaking Numbers into Parts (Kindergarten)]: No class - Thanksgiving holiday BNP Bridge [Only for students who finished BNP last year]: No class - Thanksgiving holiday 12/8/2019 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Team Competition For the last meeting of the quarter we will split up into groups and compete!Advanced 1B [gr.9-10 (Anton, 4-6pm)]: Week 10: Game We're playing a traditional end-of quarter game.Advanced 2A [gr.11-12 (Adam, Matt)]: Final Meeting Handouts: Problems with SolutionsAdvanced 2B [gr.11-12 (Aaron, Harris)]: Competition Day with 2A A 2 hour long math competition against the other high school group!Handouts: Problems with SolutionsBeginners 1A [gr.2-3 (Oleg, 3:45pm)]: More solids. (Oleg Gleizer) In this class, students will draw 2D projections of more complicated solids. Beginners 1B [gr.2-3 (Oleg, 5pm)]: More solids. (Oleg Gleizer) In this class, students will draw 2D projections of more complicated solids. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Math Review For the last meeting of 2019, we will be playing a Math Review Game!Beginners 2B [gr.3-4 (TBA, 5pm)]: Math Review For the last meeting of 2019, we will be playing a math review game!BNP [Breaking Numbers into Parts (Kindergarten)]: Chapter 7: Harder Subtraction Problems We will continue the BNP curriculum.BNP Bridge [Only for students who finished BNP last year]: Math Kangaroo Practice We will solve problems from the Math Kangaroo grades 1-2 contest.Intermediate 1A [gr.5-6 (Preston, 4-6pm)]: Mathematical Dominoes (Game) This week we are playing a Math Circle classic! The rules are attached. Hope everyone has a great time :). Handouts: How to PlayIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Mathematical Dominoes (Game) This week we are playing a Math Circle classic! The rules are attached. Hope everyone has a great time :). Handouts: How to PlayIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Math Games We will finish out the quarter with some friendly competition! Intermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: Math Games We will finish out the quarter with some friendly competition! Olympiads 2: Winter Break Problemset Review of NT, review of counting and intro to combinatorial identities.Handouts: Handout Winter 2020 quarter // Filter groups by: Advanced 1AAdvanced 1BAdvanced 2AAdvanced 2BAMC10/12 TrainingBeginners 1ABeginners 1BBeginners 2ABeginners 2BBNPBNP BridgeIntermediate 1AIntermediate 1BIntermediate 2AIntermediate 2BOlympiads 1Olympiads 2 1/12/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Tropical Geometry I We start off the new (calendar) year with something you probably haven't seen before: tropical geometry. Throw out everything you know about addition and multiplication; we define new operations and explore polynomials under the new rules.Handouts: HandoutAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Week 1: Tropical Polynomials I We start off the new (calendar) year with something you probably haven't seen before: tropical polynomials. Throw out everything you know about addition and multiplication; we define new operations and explore polynomials under the new rules.Handouts: Tropical Polynomials | SolutionsAdvanced 2A [gr.11-12 (Adam, Matt)]: Taxicab Geometry We motivate the study of metrics by introducing the taxicab metric (the distance traveled by a taxi in a city with a grid layout). How would you define a circle, line segment between points, or a parabola with a new notion of distance?Advanced 2B [gr.11-12 (Aaron, Harris)]: Metrics 1 - Taxicab We introduce a new notion of distance - the taxicab metric. We investigate how geometry behaves with this new distance, and try to find similarities and differences between this and the Euclidean metric.Handouts: Metrics 1Beginners 1B [gr.2-3 (Oleg, 5pm)]: More Solids. (Oleg Gleizer) Students were asked to study the 8th packet, More Solids, during the Winter break. Since the packet is rather challenging for the age, we will through it class. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Auctions and Subtraction Games We started a warm-up discussing auction theory. We will begin our exploration of game theory by starting with the example of subtraction games of varying subtraction sets.Handouts: handout | solutionsBeginners 2B [gr.3-4 (TBA, 5pm)]: Auctions and Subtraction Games We started a warm-up discussing auction theory. We will begin our exploration of game theory by starting with the example of subtraction games of varying subtraction sets.Handouts: handout | solutionsIntermediate 1A [gr.5-6 (Preston, 4-6pm)]: Succesive Differences This week we will be looking at geometrical numbers and the successive difference found in the sequence of these numbers. Interestingly, these types of numbers have been studied for thousands of years ever sense the Ancient Greeks. These sorts of problems are very useful to build strategies for induction proofs and pattern spotting. Handouts: Worksheet | SolutionsIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Succesive Differences This week we will be looking at geometrical numbers and the successive difference found in the sequence of these numbers. Interestingly, these types of numbers have been studied for thousands of years ever sense the Ancient Greeks. These sorts of problems are very useful to build strategies for induction proofs and pattern spotting. Handouts: Worksheet | SolutionsIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Graphs and Geometry Welcome back to Math Circle! We will kick off the quarter with some applications of graphs and geometry.Handouts: Handout | Solutions | Homework | Homework SolutionsIntermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: Graphs and Geometry Welcome back to Math Circle! We will kick off the quarter with some applications of graphs and geometry.Handouts: Handout | SolutionsOlympiads 1: Problem Session 1 We state and prove Ceva's theorem, then solve a few Olympiad-type problems.Handouts: HandoutOlympiads 2: Counting and Pigeonhole Handouts: Handout 1/15/2020 AMC10/12 Training: Probability and statistics We will go through AMC problems related to statistics and probability theory 1/17/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Tropical Geometry II Handouts: Handout 1/19/2020 Advanced 1B [gr.9-10 (Anton, 4-6pm)]: Week 2: Tropical Polynomials II Handouts: Tropical Orthogonal RepresentationsAdvanced 2A [gr.11-12 (Adam, Matt)]: Metrics Using the taxicab metric as a guide, we define the general notion of metric and give numerous examples.Handouts: MetricsAdvanced 2B [gr.11-12 (Aaron, Harris)]: Metrics 2 - Sequences We continue our study of metrics, this time considering more abstract examples. We discuss sequences, and we learn that with regards to sequences, the taxicab metric and the Euclidean metric are equivalent.Handouts: Metrics 2Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Math Kangaroo preparation class. (Joshua Enwright) Students will solve problems from the 2014 Canadian Math Kangaroo test. Beginners 1B [gr.2-3 (Oleg, 5pm)]: Math Kangaroo preparation class. (Joshua Enwright) Students will solve problems from the 2014 Canadian Math Kangaroo test.Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Subtraction Games and More This week we started off class discussing "I cut you choose." We then continued will be continuing our discussion of subtraction games, in particular the Game 21. With 21 sticks, each player can either take away 1,2, or 3 sticks each turn, what is the winning strategy if you don't want to take the last stick? If you want to take the last one? How are these two related?Beginners 2B [gr.3-4 (TBA, 5pm)]: Subtraction Games and More This week we started off class discussing "I cut you choose." We then continued will be continuing our discussion of subtraction games, in particular the Game 21. With 21 sticks, each player can either take away 1,2, or 3 sticks each turn, what is the winning strategy if you don't want to take the last stick? If you want to take the last one? How are these two related? BNP Bridge [Only for students who finished BNP last year]: Homework HomeworkHandouts: Homework ProblemsIntermediate 1A [gr.5-6 (Preston, 4-6pm)]: Knights and Knaves This week we will be working on some very interesting logical problems. These sorts of problems, although not generalization to higher mathematical theory, are very useful in practicing mathematical logic and intuition.Handouts: Worksheet | SolutionsIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Knights and Knaves This week we will be working on some very interesting logical problems. These sorts of problems, although not generalization to higher mathematical theory, are very useful in practicing mathematical logic and intuition. Handouts: Worksheet | SolutionsIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Graphs and Geometry (II) More work with graphs and geometry.Handouts: Handout | SolutionsIntermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: Graphs and Geometry (II) More work with graphs and geometry.Handouts: Handout | SolutionsOlympiads 1: Practice Test 1 The students took a 2-hour long practice exam for BAMO-type competitions. There were 3 problems (in Geometry, Combinatorics and Number Theory).Handouts: HandoutOlympiads 2: Invariants and Monovariants Handouts: Handout 1/22/2020 AMC10/12 Training: Functions AMC problems related to high school level functions theory 1/26/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Infinity Part 1 In the first part of a two (or three) part series on cardinality, we deal with bijections and give a proper definition for the cardinality of a set. Handouts: Handout | HomeworkAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Infinity 1 In the first part of a 3-part series on cardinality, we deal with bijections and give a proper definition for the cardinality of a set.Handouts: Infinity-1 | HomeworkAdvanced 2A [gr.11-12 (Adam, Matt)]: Primes in Extensions of the Integers I We can extend the integers by including square roots of integers like -1 or 3. Can we predict which prime integers remain prime in the extension?Advanced 2B [gr.11-12 (Aaron, Harris)]: Prime Splitting 1 We can extend the integers by including square roots of integers like -1 or 3. Can we predict which prime integers remain prime in the extension?Handouts: Prime Splitting 1Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Left and Right, and Quiz 3. (Oleg Gleizer) First, we will go through a few problems from the 9th packet. Then students will take a quiz on polygons and solids. Then we will finish discussing the packet.Beginners 1B [gr.2-3 (Oleg, 5pm)]: Left and Right, and Quiz 3. (Oleg Gleizer) First, we will go through a few problems from the 9th packet. Then students will take a quiz on polygons and solids. Then we will finish discussing the packet.Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Math Kangaroo Practice This week, we will be preparing for the Math Kangaroo contest by working out various types of problems!Handouts: solutions | handoutsBeginners 2B [gr.3-4 (TBA, 5pm)]: Math Kangaroo Practice This week, we will be preparing for the Math Kangaroo contest by working out various types of problems!Handouts: handouts | solutionsIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Graphs and Geometry (III) More work with graph theory and geometry proofs.Handouts: Handout | SolutionsIntermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: Graphs and Geometry (III) More work with graph theory and geometry proofs.Handouts: Handout | SolutionsOlympiads 1: Problem Session 2 Today we discussed the solutions for Practice Exam 1, and then solved three other problems.Handouts: HandoutOlympiads 2: Combinatorics Problems Handouts: Handout | Solutions 1/29/2020 AMC10/12 Training: AMC Practice Exam We will go through an actual AMC test, and discuss some of the solutions 2/2/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Infinity Part 2 We continue with part 2 of our Infinity sequence. This time we define cardinality through injectivity and bijectivity. Handouts: Homework | HandoutAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Infinity 2 In the second part of the sequence, we explore more bijections and prove several surprising facts about the cardinalities about the naturals, integers, and the reals.Handouts: Infinity 2 | Homework Advanced 2A [gr.11-12 (Adam, Matt)]: Primes in Extensions of the Integers II Happy Groundhog Day! With the help of famous results about quadratic reciprocity we will classify primes in most quadratic extensions of the integers.Advanced 2B [gr.11-12 (Aaron, Harris)]: Prime Splitting 2 With the help of famous results about quadratic reciprocity we will classify primes in most quadratic extensions of the integers.Handouts: Primes Splitting 2Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Knights and Liars We will solve logic problems from the Knights and Liars packet. (Oleg Gleizer)Beginners 1B [gr.2-3 (Oleg, 5pm)]: Knights and Liars We will solve logic problems from the Knights and Liars packet. (Oleg Gleizer)Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Calendar Mathematics Intro: How many days are in a year? How are leap years counted? Why do we include every 400 years, but not 100, 200, or 300? Hint: a year is technically about 365.25 days - 11 minutes.In this handout we examine how to systematically perform calculations to find the day of the week (Sunday, Monday, Tuesday, etc.) a particular date is, e.g., your birthdayHandouts: handout | solutionsBeginners 2B [gr.3-4 (TBA, 5pm)]: Calendar Mathematics Intro: How many days are in a year? How are leap years counted? Why do we include every 400 years, but not 100, 200, or 300? Hint: a year is technically about 365.25 days - 11 minutes.In this handout we examine how to systematically perform calculations to find the day of the week (Sunday, Monday, Tuesday, etc.) a particular date is, e.g., your birthdayHandouts: handout | solutionsIntermediate 1A [gr.5-6 (Preston, 4-6pm)]: Math Kangaroo Practice This week we will be playing a game with the Math Kangaroo Practice tests. The Math Kangaroo is a math test for young mathematicians and is usually held in the middle of the year. The game we are playing this week will encourage team work, communication, and dieligent justification of answers.Handouts: Test 2013 | Test 1998Intermediate 1B [gr.5-6 (TBA, 4-6pm)]: Math Kangaroo Practice This week we will be playing a game with the Math Kangaroo Practice tests. The Math Kangaroo is a math test for young mathematicians and is usually held in the middle of the year. The game we are playing this week will encourage team work, communication, and dieligent justification of answers. Handouts: Test 2013 | Test 1998Intermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Graphs and Geometry (IV) More graphs and geometry.Handouts: Handout | Solutions | Homework | Homework SolutionsIntermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: Graphs and Geometry (IV) More graphs and geometry.Handouts: Handout | SolutionsOlympiads 1: Practice Test 2 The students took an Olympiad-style practice exam with 3 problems (in Geometry, Algebra, and Combinatorics).Handouts: HandoutOlympiads 2: Double Counting Handouts: Solutions | Handout 2/3/2020 Intermediate 1A [gr.5-6 (Preston, 4-6pm)]: Graph Theory This week we start on the topic of Graph Theory! This topic considers a particular object of mathematics, the Graph, which is defined by its vertices and the edges connecting them. We will be considering the degree of the vertices as well a particular type of Graph, the Bipartite Graph. Handouts: Graph Theory Sheet | Solutions 2/9/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Infinity Part 3 Handouts: HandoutAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Infinity 3 This week we are concluding our conversation about infinity with some more challenge problems on constructing bijections.We also look into some mathematical paradoxes related to infinity and not only.Handouts: Infinity-3Advanced 2A [gr.11-12 (Adam, Matt)]: Generating Functions We will introduce the generating function, a creative, combinatorial tool that can simply solve many interesting problems. By the end, we will have used generating functions to study the Fibonacci sequence, dice games, and ways to pay the unlucky cashier with coins.Advanced 2B [gr.11-12 (Aaron, Harris)]: Generating Functions We will introduce the generating function, a creative, combinatorial tool that can simply solve many interesting problems. By the end, we will have used generating functions to study the Fibonacci sequence, dice games, and ways to pay the unlucky cashier with coins.Handouts: Generating FunctionsBeginners 1A [gr.2-3 (Oleg, 3:45pm)]: The truth function and the AND operation. (Oleg Gleizer) Students will learn the notion of a statement, simple and composite, and how the truth function takes value on statements. Beginners 1B [gr.2-3 (Oleg, 5pm)]: The truth function and the AND operation. (Oleg Gleizer) Students will learn the notion of a statement, simple and composite, and how the truth function takes value on statements. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: More Math Kangaroo Practice! Warm-Up: What is the trick to square numbers ending with 5 and why does it work?More math kangaroo problems!Handouts: handouts | solutionsBeginners 2B [gr.3-4 (TBA, 5pm)]: More Math Kangaroo Practice! Warm-Up: What is the trick to square numbers ending with 5 and why does it work?More math kangaroo problems!Handouts: handout | solutionsIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Graph Theory This week we start on the topic of Graph Theory! This topic considers a particular object of mathematics, the Graph, which is defined by its vertices and the edges connecting them. We will be considering the degree of the vertices as well a particular type of Graph, the Bipartite Graph.Handouts: Solutions | Graph Theory SheetIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Graphs and Geometry (V) We will be finishing up our unit on graphs and geometry this week!Handouts: Homework | Handout | Solutions | Homework SolutionsIntermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: Graphs and Geometry (V) We will be finishing up our unit on graphs and geometry this week!Handouts: Handout | SolutionsOlympiads 1: Problem Session 3 Today we went through the solutions for the practice exam, and we solved a few extra problems in class.Next time there will be no class (on President's Day).Handouts: HandoutOlympiads 2: Algebra Review Handouts: Handout 2/16/2020 Advanced 1B [gr.9-10 (Anton, 4-6pm)]: No class! Beginners 2A [gr.3-4 (Doug, 3:45pm)]: No Meeting! Beginners 2B [gr.3-4 (TBA, 5pm)]: No Meeting! Intermediate 1A [gr.5-6 (Preston, 4-6pm)]: Some more graph theory Please use the worksheet from last week.This week we completed the rest of the Graph Theory packet, going over topics such as the coloring of a graph, which is the least number of colors required to fully "color" a graph. An interesting theory associated with this is that if one considers ANY map that separates the area into counties, states, cities, etc. then one can color that map with four colors such that no two adjacent counties, states, cities, etc. have the same color. This theorem was proved using computers!Handouts: Graph Theory Sheet | SolutionsIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Some more graph theory. Please use the worksheet from last week.Handouts: Graph Theory Sheet | SolutionsOlympiads 2: Geometry Review Handouts: Handout 2/23/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Point Mass Geometry Part 1 We start off our two week unit on Point Mass Geometry. This is a topic that lets you get the nice results of planar geometry without the tedious work!Handouts: Handout | SolutionsAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Point Mass Geometry We will learn a new method of solving geometry problems with assigning masses to points and using intuition from physics.Handouts: Handout | SolutionsAdvanced 2A [gr.11-12 (Adam, Matt)]: Measure and Probability I In the first week of a three week sequence, we introduce basic probability concepts such as conditional probability, Bayes' Rule, and tower propertyHandouts: Measure and Probability IAdvanced 2B [gr.11-12 (Aaron, Harris)]: Probability Measures 1 Handouts: Probability 1Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: The OR and negation operations. (Oleg Gleizer) We will continue studying the Mathematical Logic mini-course.Beginners 1B [gr.2-3 (Oleg, 5pm)]: The OR and negation operations. (Oleg Gleizer) We will continue studying the Mathematical Logic mini-course.Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Polyhedra Warm-Up: Multiply two-digit and three-digit numbers using the criss-cross method! It really reduces the amount of work required!Today we will be introducing the topic of Polyhedras and learning the terminology. Handouts: handout | solutionsBeginners 2B [gr.3-4 (TBA, 5pm)]: Polyhedra Warm-Up: Multiply two-digit and three-digit numbers using the criss-cross method! It really reduces the amount of work required!Today we will be introducing the topic of Polyhedras and learning the terminology. Handouts: handout | solutionsIntermediate 1A [gr.5-6 (Preston, 4-6pm)]: Instant Insanity Puzzle!!! This week we will be solving the instant insanity puzzle. This puzzle is a mathematicians favorite as it is difficult to solve by “brute force,” but permits a very simple and elegant mathematical solution. We will begin by trying brute force tactics and when that fails us we will find a way to use graph theory to solve the puzzle very simply.here is the amazon link to the puzzle: Winning Moves Games Instant Insanity https://www.amazon.com/dp/B004KCN6EQ/ref=cm_sw_r_cp_api_i_QwSuEb6C13BXGIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Instant Insanity Puzzle!!! This week we will be solving the instant insanity puzzle. This puzzle is a mathematicians favorite as it is difficult to solve by “brute force,” but permits a very simple and elegant mathematical solution. We will begin by trying brute force tactics and when that fails us we will find a way to use graph theory to solve the puzzle very simply.here is the amazon link to the puzzle: Winning Moves Games Instant Insanity https://www.amazon.com/dp/B004KCN6EQ/ref=cm_sw_r_cp_api_i_QwSuEb6C13BXGIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Game Theory (I) We will begin a new unit on game theory.Handouts: Handout | Homework | Homework SolutionsIntermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: Game Theory (I) We will begin a new unit on game theory.Handouts: HandoutOlympiads 1: Practice Test 3 We solve five final practice problems for the Bay Area Mathematical Olympiad.Handouts: HandoutOlympiads 2: BAMO Practice Test BAMO 2016Handouts: Handout 3/1/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Point Mass Geometry Part 2 Handouts: Handout | SolutionsAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Point Mass Geometry II Handouts: HandoutAdvanced 2A [gr.11-12 (Adam, Matt)]: Measure and Probability II We will continue our study of probability by introducing random variables and distributions.Handouts: Measure and Probability IIAdvanced 2B [gr.11-12 (Aaron, Harris)]: Probability and Measures 2 Handouts: Probability 2Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Logic gates. (Oleg Gleizer) We will fist check some problems from the packet 12 homework. Then we will begin studying logic gates. Beginners 1B [gr.2-3 (Oleg, 5pm)]: Logic gates. (Oleg Gleizer) We will fist check some problems from the packet 12 homework. Then we will begin studying logic gates. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Polyhedra I Continued Warm-Up: If I give you two numbers, like 998 and 992, and I ask you to multiply them together using conventional math techniques, you end up writing a lot of numbers to generate the answer. But notice that 998 is just 2 shy of 1000, and 992 is just 8 shy of 1000. If you multiply 2 times 8, you get 16. And if you take 8 away from 998, or you take 2 away from 992, you get 990. And guess what? The correct answer is 990016. Similarly, if I ask you to multiply 990 times 991, you could work it out ... or you could recognize that 990 is 10 below 1000, 991 is 9 below, the product of 9 and 10 is 90, and 990 minus 9 is 981, and 991 minus 10 is also 981. The answer: 981090.The insight: if you rewrite 998 as (1000-2) and 992 as (1000-8), multiply the two we get 1000*1000 - 2*1000 - 8*1000 + 8*2. Hence we get (1000-2-8)*1000 + 16 = 990,016.We will be continuing our topic on Polyhedra from last week! Handouts: handout | solutionsBeginners 2B [gr.3-4 (TBA, 5pm)]: Polyhedra I Continued Warm-Up: If I give you two numbers, like 998 and 992, and I ask you to multiply them together using conventional math techniques, you end up writing a lot of numbers to generate the answer. But notice that 998 is just 2 shy of 1000, and 992 is just 8 shy of 1000. If you multiply 2 times 8, you get 16. And if you take 8 away from 998, or you take 2 away from 992, you get 990. And guess what? The correct answer is 990016. Similarly, if I ask you to multiply 990 times 991, you could work it out ... or you could recognize that 990 is 10 below 1000, 991 is 9 below, the product of 9 and 10 is 90, and 990 minus 9 is 981, and 991 minus 10 is also 981. The answer: 981090.The insight: if you rewrite 998 as (1000-2) and 992 as (1000-8), multiply the two we get 1000*1000 - 2*1000 - 8*1000 + 8*2. Hence we get (1000-2-8)*1000 + 16 = 990,016.We will be continuing our topic on Polyhedra from last week!Handouts: handout | solutionsIntermediate 1A [gr.5-6 (Preston, 4-6pm)]: Probabiliy This week we will be working with probability! We will be learning how to calculate the expected value of a given game. This sort of "average" thinking is used all the time by everyone unconsciously and explicitly. Handouts: Probability sheetIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Probabiliy This week we will be working with probability! We will be learning how to calculate the expected value of a given game. This sort of "average" thinking is used all the time by everyone unconsciously and explicitly. Handouts: Probability sheetIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Game Theory (II) More game theory! We will introduce winning and losing positions.Handouts: Handout | Solutions | Homework Intermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: Game Theory (II) More game theory! We will introduce winning and losing positions.Handouts: Handout | SolutionsOlympiads 1: Complex Numbers We introduce and study the basic properties of complex numbers, with the goal of using them to solve geometry problems.Handouts: HandoutOlympiads 2: BAMO Problem Discussion Handouts: Handout 3/4/2020 AMC10/12 Training: AIME preparation We will go through some AIME problems from past exams 3/5/2020 Olympiads 1: Complex Numbers in Geometry We continue our discussion of complex numbers and start applying them to Euclidean geometry problems.Handouts: Handout 3/8/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Point Mass Geometry Part 2 Continued We continue working on the second handout on point mass geometry. This gets into negative masses and barycentric coordinates.Handouts: Handout | SolutionsAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Point Mass Geometry II (continued) Handouts: HandoutAdvanced 2A [gr.11-12 (Adam, Matt)]: Measure and Probability III We will continue our study of random variables by introducing the Bernoulli, geometric, and binomial distributions. As a final surprising example, we construct a famous example of a non-measurable set.Advanced 2B [gr.11-12 (Aaron, Harris)]: Probability and Measures 3 Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Double negation. (Joshua Enwright) We will finish studying logic gates and will study double negation.Beginners 1B [gr.2-3 (Oleg, 5pm)]: Double negation. (Joshua Enwright) We will finish studying logic gates and will study double negation.Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Euler's Formula This week we will be continuing our topic of Polyhedras, but this time developing a more rigorous relationship between edges, vertices, and faces!Handouts: handoutBeginners 2B [gr.3-4 (TBA, 5pm)]: Euler's Formula This week we will be continuing our topic of Polyhedras, but this time developing a more rigorous relationship between edges, vertices, and faces!Handouts: handoutIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Mathematical Dominoes (Game) This week we played the famous Math Dominoes Game with an added CHALLENGE ROUND. I hope everyone has a great time! Intermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Game Theory (III) Continuing our unit on game theory.Handouts: Handout | SolutionsIntermediate 2B [gr.7-8 (Christine, Cassandra, 4-6pm)]: Game Theory (III) Continuing our unit on game theory.Handouts: Handout | SolutionsOlympiads 2: Applications of Expected Value Handouts: 3/15/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Kahoot Competition over Zoom!! For our final (virtual) meeting of the quarter, we will be hosting a Kahoot competition over the Zoom application. Please make sure to download the app at https://zoom.us/download and join the meeting from 4-6 pm at the link sent via email. See you there!Advanced 2A [gr.11-12 (Adam, Matt)]: No Math Circle Meeting Advanced 2B [gr.11-12 (Aaron, Harris)]: CANCELLED Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Math Kangaroo preparation. (Oleg Gleizer) We will prepare for the upcoming Math Kangaroo competition. Beginners 1B [gr.2-3 (Oleg, 5pm)]: Math Kangaroo preparation. (Oleg Gleizer) We will prepare for the upcoming Math Kangaroo competition. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Euler's Formula This week we will be continuing our topic of Polyhedras, but this time developing a more rigorous relationship between edges, vertices, and faces!Handouts: handoutBeginners 2B [gr.3-4 (TBA, 5pm)]: Euler's Formula This week we will be continuing our topic of Polyhedras, but this time developing a more rigorous relationship between edges, vertices, and faces!Handouts: handoutOlympiads 2: Diophantine Chord Technique No in-person classHandouts: Spring 2020 quarter // Filter groups by: Advanced 1AAdvanced 1BAdvanced 2AAdvanced 2BBeginners 1ABeginners 1BBeginners 2ABeginners 2BBNPChess classIntermediate 1AIntermediate 1BIntermediate 2AIntermediate 2BOlympiads 1Olympiads 2 4/5/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Formal Proofs 1 Introduction to formal proof writing. Sets, functions, basic combinatorics and number theory proofsHandouts: Handout Advanced 1B [gr.9-10 (Anton, 4-6pm)]: Formal Proofs I We'll go over various proof techniques and practice writing rigorous proofs.Handouts: FormalProofsAdvanced 2A [gr.11-12 (Adam, Matt)]: Time Travel We review the material from last quarter.Handouts: Time TravelAdvanced 2B [gr.11-12 (Aaron, Harris)]: Math Circle Advanced 2B - Time Travel Travel back in time and revisit some of the old topics from Winter 2020Handouts: Time TravelBeginners 1A [gr.2-3 (Oleg, 3:45pm)]: Packet 14 and quiz 4. (Oleg Gleizer) We will discuss some problems from packet 14. Then students will take a quiz.Beginners 1B [gr.2-3 (Oleg, 5pm)]: Packet 14 and quiz 4. (Oleg Gleizer) We will discuss some problems from packet 14. Then students will take a quiz.Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Russian Math Olympiad Problems This helps students see what age-appropriate math problems look like in a different country!Handouts: handout | solutionsBeginners 2B [gr.3-4 (TBA, 5pm)]: Russian Math Olympiad Problems This helps students see what age-appropriate math problems look like in a different country!Handouts: handout | solutionsBNP [Breaking Numbers into Parts (Kindergarten)]: 1st spring meeting Intermediate 1A [gr.5-6 (Preston, 4-6pm)]: Casting out 9's This week we solved a mathematical trick using equivalence relations! Equivalence relations are extremely important in mathematics and allow mathematicians to formally categorize "objects" in a particular "Space."Handouts: Handout | SolutionsIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Casting out 9's This week we solved a mathematical trick using equivalence relations! Equivalence relations are extremely important in mathematics and allow mathematicians to formally categorize "objects" in a particular "Space." Handouts: Handout | SolutionsIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Induction (I) Welcome back to (virtual) Math Circle! We're kicking off the quarter with some proofs by induction. Handouts: Handout | Homework Olympiads 2: Rational Approximation Handouts: Lecture Notes | Handout 4/12/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Formal Proofs 2 Introduction to formal proof writing. Sets, functions, basic combinatorics and number theory proofsHandouts: HandoutAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Formal Proofs II We'll continue working on the handout on writing formal and rigorous proofs.Handouts: FormalProofs-2Advanced 2A [gr.11-12 (Adam, Matt)]: Fixed Points We use our knowledge of metrics to study and prove theorems about contraction maps.Handouts: Fixed PointsAdvanced 2B [gr.11-12 (Aaron, Harris)]: Math Circle Advanced 2B - Fixed Points We study fixed points, and a few theorems that let us find them.Handouts: Fixed PointsBeginners 1A [gr.2-3 (Oleg, 3:45pm)]: Lineland. (Oleg Gleizer) We will meet inhabitants of a 1-dimesional world, called Lineland. Beginners 1B [gr.2-3 (Oleg, 5pm)]: Lineland. (Oleg Gleizer) We will meet inhabitants of a 1-dimesional world, called Lineland. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Distance Formula This week, we will be introducing the distance formula!Handouts: handout | solutionsBeginners 2B [gr.3-4 (TBA, 5pm)]: Distance Formula This week, we will be introducing the distance formula!Handouts: handout | solutionsBNP [Breaking Numbers into Parts (Kindergarten)]: 2nd Spring meeting Intermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Induction (II) We will continue working on proofs by induction. Handouts: Handout | HomeworkOlympiads 1: Complex Numbers in Geometry, Part 2 We solve a few more difficult geometry problems using complex numbers.Handouts: HandoutOlympiads 2: Bertrand's Postulate We prove that for all n there exists a prime number between n and 2*n.Handouts: Handout | Lecture Notes 4/13/2020 Intermediate 1B [gr.5-6 (TBA, 4-6pm)]: Levers and Weights This week we worked on some intuitive mathematics! By that I mean mathematics that can be reliably answered by the physical intuition we have all built up over our lives. This "weighty" way of thinking that we are all seemingly borne with was first formalized mathematically in Ancient Greece and this week we get to explore some of its implications.Handouts: Worksheet | Solutions 4/17/2020 BNP [Breaking Numbers into Parts (Kindergarten)]: 6th Spring meeting 4/19/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Golomb Ruler Handouts: HandoutAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Formal Proofs III We are finishing the handout on writing formal and rigorous proofs.Advanced 2A [gr.11-12 (Adam, Matt)]: Sperner's Lemma Sperner's Lemma is an interesting result about the coloring of special graphs. We connect the result with a famous result, the Brouwer fixed-point theorem.Handouts: Sperner's LemmaAdvanced 2B [gr.11-12 (Aaron, Harris)]: Math Circle Advanced 2B - Topologically-Flavored Graph Theory We discuss some interesting graph theory, including the Euler characteristic, and proving Brouwer's Fixed Point Theorem with Sperner's Lemma.Handouts: Graphs 1Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Lineland, continued. (Oleg Gleizer) We will continue to study packet 15 starting from the problem 15.10.Beginners 1B [gr.2-3 (Oleg, 5pm)]: Lineland, continued. (Oleg Gleizer) We will continue to study packet 15 starting from the problem 15.10.Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Rates using Trade We will be continuing the idea of rates from last week, but this time applying to trade! What is the best way to optimize the outcome of both parties in trade? When is trade not a win-win situation?Handouts: handoutBeginners 2B [gr.3-4 (TBA, 5pm)]: Rates with Trade We will be continuing the idea of rates from last week, but this time applying to trade! What is the best way to optimize the outcome of both parties in trade? When is trade not a win-win situation?Handouts: handoutBNP [Breaking Numbers into Parts (Kindergarten)]: 3rd Spring meeting Intermediate 1A [gr.5-6 (Preston, 4-6pm)]: Russian Olympiad This week we will be taking on some challenging problems from the Russian math Olympiad! These are questions designed to test some of the smartest young mathematicians. I hope everyone is challenged and excited!Handouts: HandoutIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Russian Olympiad This week we will be taking on some challenging problems from the Russian math Olympiad! These are questions designed to test some of the smartest young mathematicians. I hope everyone is challenged and excited! Intermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Induction (III) Proofs by induction in algebra, and some geometry.Handouts: Handout | Homework | SolutionsOlympiads 1: Notions of Probability We introduce basic notions of probability spaces, outcomes, events and independence, and solve a few related competition-style problems.Handouts: HandoutOlympiads 2: Quadratic Reciprocity Handouts: Handout 4/26/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Inequalities We take a look at the HM-GM-AM-QM inequalities and their applications.Handouts: HandoutAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Inequalities We take a look at the HM-GM-AM-QM inequalities and their applications.Handouts: InequalitiesAdvanced 2A [gr.11-12 (Adam, Matt)]: Sperner's Lemma and Further Topics We continue working on last week's worksheet, with a few extra problems on Brouwer's Fixed Point Theorem, Euler characteristic, and crossing numbers.Handouts: More GraphsAdvanced 2B [gr.11-12 (Aaron, Harris)]: Math Circle Advanced 2B - More Topologically-Flavored Graph Theory We continue working on last week's worksheet, with a few extra problems on Brouwer's Fixed Point Theorem, Euler characteristic, and crossing numbers.Handouts: More GraphsBeginners 1A [gr.2-3 (Oleg, 3:45pm)]: Math Kangaroo prep class. (Oleg Gelizer) We will prepare for the upcoming on-line MK competition. Beginners 1B [gr.2-3 (Oleg, 5pm)]: Math Kangaroo prep class. (Oleg Gelizer) We will prepare for the upcoming on-line MK competition. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Rates and Trade: Opportunity Cost This week, we will continue our discussion on trade, learning about opportunity costs as a way of determining when trade is a win-win situation and when it is not, as well as finding a rate that both traders will be happy withHandouts: handoutBeginners 2B [gr.3-4 (TBA, 5pm)]: Rates and Trade: Opportunity Cost This week, we will continue our discussion on trade, learning about opportunity costs as a way of determining when trade is a win-win situation and when it is not, as well as finding a rate that both traders will be happy withHandouts: handoutBNP [Breaking Numbers into Parts (Kindergarten)]: 4th Spring meeting Intermediate 1A [gr.5-6 (Preston, 4-6pm)]: Fractions and Decimals This week we will reviewing the solutions to the Olympiad as well as starting a section on decimals and fractions.Handouts: HandoutIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Decimals and Fractions Handouts: HandoutIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Induction (IV) We continue with induction!Handouts: Handout | Solutions | HomeworkOlympiads 1: Notions of Probability, Part 2 We introduce random variables, expectations, variance, independence and functions of random variables, then apply these notions to Olympiad-type problems.Handouts: HandoutOlympiads 2: Euler's Formula Handouts: Handout 5/3/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Inequalities 2 We continue with more applications of our HM-GM-AM-QM inequalities.Handouts: Handout | SolutionsAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Inequalities II We continue the handout on inequalities.Handouts: Inequalities-2Advanced 2A [gr.11-12 (Adam, Matt)]: Knot Theory I We introduce braids, knots, and links.Handouts: Braids and KnotsAdvanced 2B [gr.11-12 (Aaron, Harris)]: Math Circle Advanced 2B - Knots 1 We study braids and begin to study knots.Handouts: Knots Week 1Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Flatland and Math Kangaroo prep. (Oleg Gleizer) The class will be a mixture of the Flatland handout and MK preparation.Beginners 1B [gr.2-3 (Oleg, 5pm)]: Flatland and Math Kangaroo prep. (Oleg Gleizer) The class will be a mixture of the Flatland handout and MK preparation.Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Futoshiki A fun game played on a square grid... a twist on Latin squares!Handouts: handout | solutionsBeginners 2B [gr.3-4 (TBA, 5pm)]: Futoshiki A fun game played on a square grid... a twist on Latin squares!Handouts: handout | solutionsBNP [Breaking Numbers into Parts (Kindergarten)]: 5th Spring meeting Intermediate 1A [gr.5-6 (Preston, 4-6pm)]: Fractions and Decimals II Handouts: HandoutIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Fractions and Decimals Part II Handouts: WorksheetIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Bipartite Graphs and Geometry This week we will introduce our unit on bipartite graphs.Handouts: Handout | Solutions | HomeworkOlympiads 1: Sequences and Series We introduce the basic notions of convergence for sequences and series, and solve a few related problems.Handouts: HandoutOlympiads 2: Hall's Marriage Theorem Handouts: Handout 5/10/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: 6th Spring meeting Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Inversive Geometry 1 Handouts: HandoutAdvanced 1B [gr.9-10 (Anton, 4-6pm)]: Inversion 1 Advanced 2A [gr.11-12 (Adam, Matt)]: Knot Theory II We introduce Reidemeister moves and the idea of a knot invariant. We work up to an interesting knot invariant that has the structure of a quandle.Handouts: Knot Invariants and QuandlesAdvanced 2B [gr.11-12 (Aaron, Harris)]: Math Circle Advanced 2B - Knots 2 We study a knot invariant, with the structure of a quandle.Handouts: Knots Week 2Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Review of Lineland and Flatland and a quiz. (Oleg Gleizer) Students will review the Lineland and Flatland material and take a quiz. Beginners 1B [gr.2-3 (Oleg, 5pm)]: Review of Lineland and Flatland and a quiz. (Oleg Gleizer) Students will review the Lineland and Flatland material and take a quiz. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Game Theory! This week we will introduce the idea of Prisoner's Dilemma! Handouts: teaching notesBeginners 2B [gr.3-4 (TBA, 5pm)]: Game Theory! This week we will introduce the idea of Prisoner's Dilemma!Handouts: teaching notesIntermediate 1A [gr.5-6 (Preston, 4-6pm)]: Fractions and Decimals III Handouts: HandoutIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Fractions and Decimals Part III Handouts: WorksheetIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Bipartite Graphs (II) More work with bipartite graphs and geometry.Handouts: Handout | Solutions | Homework Olympiads 1: Sequences and Series, Part 2 We continue talking about sequences and series, and solve a few harder related problems.Handouts: HandoutOlympiads 2: Group Theory 1 Definitions, examples, subgroups and isomorphisms, and some philosophyHandouts: Handout 5/17/2020 Advanced 1B [gr.9-10 (Anton, 4-6pm)]: Inversion 2 Advanced 2A [gr.11-12 (Adam, Matt)]: Knot Theory III We introduce our most powerful knot invariants yet: the normalized Kauffman bracket and the Jones polynomial.Advanced 2B [gr.11-12 (Aaron, Harris)]: Math Circle Advanced 2B - Knots 3 We study a more difficult knot invariant - the Jones polynomial.Handouts: Knots Week 3Beginners 1A [gr.2-3 (Oleg, 3:45pm)]: Backward Reasoning. (Oleg Gleizer) Students will learn to solve problems working backward.Beginners 1B [gr.2-3 (Oleg, 5pm)]: Backward Reasoning. (Oleg Gleizer) Students will learn to solve problems working backward.Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Sticks and Stones This week, we will talk about a cool application of combinations and permutations!Handouts: homework | teaching notesBeginners 2B [gr.3-4 (TBA, 5pm)]: Sticks and Stones This week, we will talk about a cool application of combinations and permutations!Handouts: teaching notes | homeworkIntermediate 1A [gr.5-6 (Preston, 4-6pm)]: Tricky Percents Handouts: HandoutIntermediate 1B [gr.5-6 (TBA, 4-6pm)]: Tricky Percents Today we pivot from fractions and decimals and focus on percents, a related and equally important topic.Handouts: HandoutIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Inscribed Angle Theorem This week, we focus on geometry.Handouts: Homework | Handout | SolutionsOlympiads 1: Notions of Continuity and Differentiability We introduce continuous and differentiable functions, and study a few of their basic properties.Handouts: HandoutOlympiads 2: Group Theory 2 Lagrange's theorem, quotients, maps between groups 5/24/2020 Advanced 1B [gr.9-10 (Anton, 4-6pm)]: No class! Memorial Day Holiday Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Memorial Day Weekend-- No Meeting! Beginners 2B [gr.3-4 (TBA, 5pm)]: Memorial Day Weekend-- No Meeting! Intermediate 2A [gr.7-8 (Hunter, 4-6pm)]: NO CLASS TODAY 5/31/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Backward reasoning, continued. (Oleg Gleizer) We will continue studying backward reasoning. Advanced 1B [gr.9-10 (Anton, 4-6pm)]: Inversion III We are finishing the Inversion handout.Advanced 2A [gr.11-12 (Adam, Matt)]: Game Theory Handouts: ProblemsAdvanced 2B [gr.11-12 (Aaron, Harris)]: Math Circle Advanced 2B - Game Theory Handouts: Game TheoryBeginners 1A [gr.2-3 (Oleg, 3:45pm)]: Backward reasoning, continued. (Oleg Gleizer) We will continue studying backward reasoning. Beginners 1B [gr.2-3 (Oleg, 5pm)]: Backward reasoning, continued. (Oleg Gleizer) We will continue studying backward reasoning. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Sticks and Stones Part II We will be going over the hw from last time, and working through a new application!Handouts: handout | solution sketchesBeginners 2B [gr.3-4 (TBA, 5pm)]: Sticks and Stones Part II We will be going over the hw from last time, and working through a new application!Handouts: handout | solution sketchesBNP [Breaking Numbers into Parts (Kindergarten)]: 8th Spring meeting Intermediate 1B [gr.5-6 (TBA, 4-6pm)]: Games and Strategy Handouts: HandoutIntermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Recap Time to put your Math Circle knowledge to the test! We will be revisiting some of the topics we've covered this past year. Handouts: Handout | SolutionsOlympiads 1: Notions of Continuity and Differentiability, Part 2 We finalize our discussion of differentiability with more rigor, and apply it to related Olympiad-type problems.Handouts: HandoutOlympiads 2: Group Theory 3 Group actions and Burnside's Lemma 6/7/2020 Advanced 1A [gr.9-10 (Eilon, 4-6pm)]: Kahoot! Competition We finish off the school year with a Kahoot individual competition emphasizing problems and techniques that we have done this year. Advanced 2A [gr.11-12 (Adam, Matt)]: Math Battle and Graduation Handouts: ProblemsAdvanced 2B [gr.11-12 (Aaron, Harris)]: Math Circle Advanced 2B - Math Battle, Graduation and Goodbyes Handouts: ProblemsBeginners 1A [gr.2-3 (Oleg, 3:45pm)]: Traveling on a cube. (Oleg Gleizer) We will help a mouse and two ants to travel through and around a cube. The journeys reveal a wealth of ideas and serve as an intro to studying nets of cubes. Beginners 1B [gr.2-3 (Oleg, 5pm)]: Traveling on a cube. (Oleg Gleizer) We will help a mouse and two ants to travel through and around a cube. The journeys reveal a wealth of ideas and serve as an intro to studying nets of cubes. Beginners 2A [gr.3-4 (Doug, 3:45pm)]: Final Meeting: Review! We will be reviewing the concepts we have learned for the quarterHandouts: questionsBeginners 2B [gr.3-4 (TBA, 5pm)]: Final Meeting: Review! We will be reviewing the concepts we have learned for the quarterHandouts: questionsBNP [Breaking Numbers into Parts (Kindergarten)]: Last Spring meeting Intermediate 2A [gr.7-8 (Hunter, 4-6pm)]: Math Game Finishing out the quarter with some friendly competition. Olympiads 1: Ordinary Generating Functions We introduce generating functions and apply them to combinatorial sequences such as binomial coefficients, the Fibonacci numbers and partitions.Handouts: HandoutOlympiads 2: Generating Functions Summer 2020 quarter // Filter groups by: Beginners 1aBeginners 1bBeginners 2aBeginners 2bIntermediate 1Intermediate 2aIntermediate 2bMiddle School Summer Club 6/27/2020 Intermediate 2a [grades 7-8]: Here are the two handouts for meeting 1 on 6/28.Handouts: | 6/28/2020 Beginners 1a [grade 2]: Roman numerals. (Nadya Kuzkina) We will begin to study Roman numerals.Beginners 1b [grade 2]: Roman numerals. (Nadya Kuzkina) We will begin to study Roman numerals.Beginners 2a [grades 3-4]: Ciphers 1. (Oleg Gleizer) We will study the Polybius and Caesar ciphers.Beginners 2b [grades 3-4]: Ciphers 1. (Vivian Dinson) We will study the Polybius and Caesar ciphers.Intermediate 1 [grades 5-6 (in Fall 2020)]: Modular Arithmetic Handouts: HandoutIntermediate 2b [grades 7-8]: LAMC Class - AMC 8 Math Problems! LAMC class for intermediate 2b. We work on Math kangaroo problems!Handouts: 1998 AMC 8 math problems!Middle School Summer Club: Week 1 - Diagnostic Test We'll start off this summer with a lecture on basic test-taking techniques. Students will take the 2018 AMC 8 as a diagnostic test. You can access the problems and solutions from that exam on the AoPS website. 7/12/2020 Beginners 1a [grade 2]: Move a stick. (Nadya Kuzkina) We will use craft sticks to solve more challenging Roman numerals problems. Beginners 1b [grade 2]: Move a stick. (Nadya Kuzkina) We will use craft sticks to solve more challenging Roman numerals problems. Beginners 2a [grades 3-4]: Ciphers, lesson 2. (Oleg Gleizer) We will check the first homework and move on to study the second packet. Beginners 2b [grades 3-4]: Ciphers, lesson 2. (Vivian Dinson) We will check the first homework and move on to study the second packet. Intermediate 1 [grades 5-6 (in Fall 2020)]: Graph Theory Handouts: HandoutIntermediate 2a [grades 7-8]: Induction 1 We'll look at the principle of mathematical induction and how we can use it to prove various algebraic and geometric statements.Handouts: Induction 1Intermediate 2b [grades 7-8]: LAMC Class - Mathematical Induction! We introduce mathematical induction in this class. Handouts are scheduled to be sent out the morning of.Handouts: Induction 1Middle School Summer Club: Week 2 - Combinatorics After week one's diagnostic test, we start the official AMC 8 prep portion of the course with an introductory lesson on combinatorics. See the attached documents below for resources used in class that can be helpful for future study. 7/19/2020 Beginners 1a [grade 2]: More Roman numerals. (Nadya Kuzkina) We will study more complex Roman numerals.Beginners 1b [grade 2]: More Roman numerals. (Nadya Kuzkina) We will study more complex Roman numerals.Beginners 2a [grades 3-4]: Ciphers, part 3. (Oleg Gleizer) We will review anagrams and then study the pigpen and rail fence cipher.Beginners 2b [grades 3-4]: Ciphers, part 3. (Vivian Dinson) We will review anagrams and then study the pigpen and rail fence cipher.Intermediate 1 [grades 5-6 (in Fall 2020)]: Knights and Knaves Handouts: HandoutIntermediate 2a [grades 7-8]: Induction 2 We'll continue looking at induction and solve problems involving more complicated sequences and the Fibonacci numbers. Handouts: Induction 2Intermediate 2b [grades 7-8]: Mathematical Induction 2! Middle School Summer Club: Week 3 - Statistics and Probability This week, we'll be using the combinatorial skills from week two to solve more advanced problems in statistics and probability. All handouts and resources should be posted below. 7/26/2020 Beginners 2a [grades 3-4]: More ciphers. (Oleg Gleizer) We will review the rail fence cipher and the ciphers we have studies earlier. Beginners 2b [grades 3-4]: More ciphers. (Oleg Gleizer) We will review the rail fence cipher and the ciphers we have studies earlier. Intermediate 1 [grades 5-6 (in Fall 2020)]: Probability Handouts: HandoutIntermediate 2a [grades 7-8]: Modular Arithmetic 1 We'll look at the properties of looking at integers mod m. Handouts: Modular Arithmetic 1Intermediate 2b [grades 7-8]: Introduction to Graph Theory, Part One! We introduce graph theory.Handouts: Part 1 Introduction to Graph TheoryMiddle School Summer Club: Week 4 - Number Theory This week, we'll once again be building on our previous knowledge by learning about number theory, the mathematical study of integers. All associated resources used in class should be posted below.