Fall 2014 quarter  10/12/2014  We will jump right into tackling math problems from various national and international competition in our mathematical group relay! Before we cover a specific topic, we will be solving some fun problems from a previous year's Math Olympiad. In addition, we will be solving problems from various topics in mathematics in order to gauge our knowledge of these topics. Handouts: Initial Assessment  Math Olympiad Problems We'll learn various ways of sending and deciphering secret messages. Handouts: Week 1 handout Today we will begin our first topic of the quarter: proofs. We'll focus on different ways to logically organize a proof. Handouts: Handout 1 During this first meeting we will discuss some beautiful problems from the Russian Math Olympiad. We will solve problems from geometry, algebra, combinatorics, emphasising on how to organize our proofs. Handouts: Handouts In the Fall quarter, we will study Boolean algebra also known as the algebra of logic. A working knowledge of binary numbers is a prerequisite for the study. During this class, we will learn/refresh some basic properties of the binary numbers. As always, we will have some Math olympiadstyle problems for warm up. Handouts: handout  farmers and chicken solution  solutions In the Fall quarter, we will study Boolean algebra also known as the algebra of logic. A working knowledge of binary numbers is a prerequisite for the study. During this class, we will learn/refresh some basic properties of the binary numbers. As always, we will have some Math olympiadstyle problems for warm up. Handouts: handout  farmers and chicken solutuin  handout sols  10/19/2014  We will be investigating the different properities of modular arithmetic and how it will be useful to solve problems with large values. Handouts: Number Theory (part 1) This week, we will introduce sets and functions, and discuss some of the properties of functions. We will also solve a few fun problems at the end of the meeting. Handouts: Sets and Functions We'll discover some surprising properties of the Mobius strip. Handouts: Week 2 handout Today we will continue our study of proofs. We will continue doing examples of both direct proofs and proofs by contradiction, as well as introduce the idea of a proof using contrapositives. Handouts: Handout 2 Speaker: David Patrick (Art of Problem Solving) Handouts: Handouts During the first hour, we will finish the first handout by going through the binary completion, subtraction and division algorithms at the board, followed by discussing a solution to the farmers and chicken problem. The second hour will be a problem solving session. The central problem of the session has originated in the first century AD and is solved using binary numbers! Handouts: division algorithm  handout  alg solutions  handout solutions During the first hour, we will finish the first handout by going through the binary completion, subtraction and division algorithms at the board, followed by discussing a solution to the farmers and chicken problem. The second hour will be a problem solving session. The central problem of the session has originated in the first century AD and is solved using binary numbers! Handouts: division algorithm  handout  alg sols  handout sols  10/26/2014  Working in groups, we will solve a variety of geometry problems. In the second hour, each group will present a solution of one of the problems they worked out in the first hour. Handouts: Hints to selected problems  Geometry kaleidoscope (problem sets) This week, we will continue our explorations of functions on sets, focusing on countable infinite sets and their equivalence. We will finish with fun, miscellaneous problems. Handouts: Infinite Sets We'll work on some fun Halloweenthemed math problems. Handouts: Week 3 handout Today we will study the principle of Mathematical Induction, and solve problems on a variety of topics using it. Handouts: Proofs by Induction This Sunday we will focus on solving geometry problems in plane. We will focus mainly on studying the circle and cyclic quadrilaterals. Handouts: Handouts We will solve a few olympiadstyle problems for warmup and then proceed to study Boolean Algebra a.k.a. the algebra of logic. Handouts: handout  solutions We will complete our discussion of the Josephus Problem and then proceed to study Boolean Algebra a.k.a. the algebra of logic. Handouts: handout  solutions  11/2/2014  We will be using modular arithmetic to find divisibility rules and use them to tackle more number thoery questions! Handouts: Session Handout This week, we will be solving problems involving parity. We will look at how properties of even and odd numbers can help us solve problems involving chessboards, symmetry, dominoes, and other topics. Handouts: Parity We'll find patterns in sequences of numbers and explore ways to think about averages. Handouts: Week 4 handout Today we will continue working on proofs by induction and finish up the handout from last week. It would be helpful for the students to review Problems 1+2 on the second page of the handout from last week (available in last week's announcement) in preparation to today's session. Handouts: Proofs by Induction 2 We will talk about combinations and permutations, and we will count elements in a given set in two different ways. This will give unexpected formulas between combinations (also called binomial coefficients), that are very hard to prove algebraically. Handouts: Handouts We will solve a few warmup problems and then continue our study of Boolean algebra. Handouts: handout  sols We will solve a few warmup problems and then continue our study of Boolean algebra. Handouts: handout  sols  11/9/2014  This week we will be discovering our own divisibility rules for our favorite numbers and use them to problem solve! Handouts: Number Theory (Part 3) We will be discussing two alternatives to our "normal" method of multiplication: Egyptian multiplication and Russian Peasant multiplication. We will learn how these methods work, and determine which are more effective. Handouts: Egyptian and Russian Peasant Multiplication We'll hone our problem solving skills by working on some challenging and fun math problems. Handouts: Week 5 handout Today, we'll be studying ways to count without numbers. The key concepts will be bijections and codings. Handouts: Bijections Fullerton Mathematical Circle: The First Three Years. Selected Problems This time we will learn how to use Boolean Algebra to solve logical problems near effortlessly. Once finished, we will solve some problems that could help our AMC8 participants to perform better at the competition and should be interesting and entertaining for the rest of the class. Handouts: handout  sols
This time we will learn how to use Boolean Algebra to solve logical problems near effortlessly. Once finished, we will solve some problems that could help our AMC8 participants to perform better at the competition and should be interesting and entertaining for the rest of the class.
Handouts: handout  sols  11/16/2014  Handouts: AG F14 meeting 6 trigonometry 1 This week we will discuss a few facts about angles, and we will learn how to draw angles using protractors. Furthermore, we will learn how to draw a circle by using grid lines and by using a compass. Please bring the following items to the meeting: colored pencils, a ruler, a compass, and a protractor. Handouts: Challenge Problem We'll learn to use coordinates to describe where points in a plane are located. Handouts: Week 6 handout Today we will study some ways to talk about the "size" of an infinite set. Handouts: Bijections 2 This week, we have a guest speaker. Pooja Rao will tell us about the normal distribution, and at the end we will do an experiment, using the microwave and some popcorn. Handouts: Quiz 1  Quiz 2 We will learn to use geometry of cubes to simplify Boolean algebra formulas. Handouts: handout  sols
We will learn to use geometry of cubes to simplify Boolean algebra formulas.
Handouts: handout  sols  11/23/2014  Handouts: AG F14 meeting 7 complex 1 This week we will continue our discussion of symmetry using mirrors. Using ReflectIt Mirrors, we will explore 2mirror systems, 3mirror systems, and various triangular kaledeidoscope configurations. Handouts: Mirrors and Kaleidoscopes We'll figure out how to slay dragons with many heads and tails. Handouts: Handout 7 Today we will study some problems in graph theory, an area that has many applications to social media, including Facebook! Handouts: Ramsey Theory We will explore the combinatorics of placing nonattacking rooks in a chess board. In how many ways can we place n nonattacking rooks on a n x n board? how about if we do not allow rooks to be on the diagonal of the board? We will explore these and other questions and techniques for doing these counts. Handouts: Handouts 1  Handouts 2 We will take another look at the material we have studied, from the division algorithm to Boolean algebra to hypercubes. We will also solve a bunch of cool olympiadstyle problems. Handouts: handout  sols
We will take another look at the material we have studied, from the division algorithm to Boolean algebra to hypercubes. We will also solve a bunch of cool olympiadstyle problems.
Handouts: handout  sols  11/30/2014  No Early Elementary meeting on Nov. 30, 2014.  12/7/2014  Handouts: AG F14 meeting 8 trigonometry 2 Handouts: Symmetry, Mirrors & Fun We'll figure out who's who on the Island of Knights and Liars. Handouts: Handout 8 Today we will continue our study of graph theory, specificially Ramsey Theory. Handouts: Ramsey Theory 2 Guest speaker: Brent Woodhouse Handouts: Handouts  Handouts
We will solve a bunch of cool problems preparing for the 12/14/2014 Math Wrangle between the Intermediate I and II classes.
Handouts: handout  sliding combs sol  sols We will solve a bunch of cool problems preparing for the 12/14/2014 Math Wrangle between the Intermediate I and II classes. Handouts: handout  sliding combs sol  sols  12/14/2014  We'll do problems that serve as a review for all topics covered this quarter. Handouts: Handout 9 We'll end our quarter with math relays!
The Intermediate I class will meet in the graduate students lounge, MS 6620, right away. Our regular room will be taken by another class. After an hour of problem solving, the Intermediate II class will join the Intermediate I class in MS 6620 and the fight will commence. In the meantime, volunteering parents will set up the tables in the rear part of MS 6620. At 6:00, the winners will be announced and rewarded, and the party will begin!
Handouts: handout
The intermediate II class will solve problems in their regular room, MS 6S 6201 for one hour. After an hour of problem solving, the Intermediate II class will join the Intermediate I class in MS 6620 and the fight will commence. In the meantime, volunteering parents will set up the tables in the rear part of MS 6620. At 6:00, the winners will be announced and rewarded, and the party will begin!
Handouts: handout  Winter 2015 quarter  1/11/2015  During the first meeting of the quarter, we will introduce percents and solve problems involving percentages. Handouts: Percents We'll do an experiment / game to illustrate some basic ideas of probability. Handouts: Week 1 handout Today we will study some basic combinatorics of words. We will build toward constructing de Bruin words. Handouts: Handout  Handout (with added graphs) Problem session, ranging from geometry, algebra, combinatorics. Handouts: Handouts We will learn a few theorems of classical geometry and use them as tools to estimate distances to and sizes of various remote objects. We will learn a few theorems of classical geometry and use them as tools to estimate distances to and sizes of various remote objects.  1/18/2015  This week we will work on word problems that involves two or more people or things working together to complete a task.
You can find this week's handout as well as solutions below.
For homework, please complete problems 12 from the Kangaroo Problems below. Show all your work and be prepared to explain what you did. Handouts: Working Together Handout  Practice Math Kangaroo Homework Problems  Working Together Solutions Building on our experiment from last week, we'll dive a bit further into probability, and compute the probabilities of various events when rolling a pair of dice. Handouts: Handout 2  Solutions Today we will continue studying combinatorics of words. We will focus on constructing words of varying "subword complexity". Handouts: Handout  Handout (with added graphs) Handouts: Handouts
We will complete the work on the first handout. If times remains, we will solve a bunch of cool olympiadstyle problems from the next handout.
We will complete the work on the first handout. If times remains, we will solve a bunch of cool olympiadstyle problems from the next handout.
 1/25/2015  This week we will continue doing word problems on percentages and working together.
For homework, complete the handout.
Please prepare your 2 problems (#10,11) on index cards to be able to exchange them with your fellow students.
Also, prepare complete solutions to #3,4 on the math kangaroo handout.
Handouts: Percentage & Work Overview  Mini Quiz  Percentage & Work Solutions We'll hone our problem solving skills by solving some challenging word problems. Handouts: Handout 3  Solutions Today we will go over some AMC 10 practice problems. We'll also allow students to finish last week's handout. Handouts: AMC Prep Followed by the a Crossnumber math game (like the one in Meeting 2 last quarter) Handouts: Handouts
We will solve a bunch of cool olympiadstyle problems and then get back to the study of similar figures.
Handouts: handout
We will solve a bunch of cool olympiadstyle problems and then get back to the study of similar figures.
Handouts: handout  2/1/2015  This week, we will start our discussion of combinatorics going over the multiplication principle, the addition principle, multiple independent events and permutations.
For homework: please review the combinatorics handout and prepare complete solutions to Math Kangaroo problems 5 & 6. Handouts: Combinatorics Part 1 (handout)  Math Kangaroo Homework Problems  Combinatorics Part 1 (solutions) We'll continue to hone our problem solving skills and prepare for the Math Kangaroo by solving some challenging word problems. Handouts: Handout 4 Today we will study in more detail the idea of Eulerian paths introduced earlier in the quarter, and discuss various algorithms to find them. Handouts: Eulerian Paths
We will meet on the lawn next to the 5th floor entrance and spend the first half an hour of the class measuring various objects on campus, a building, a street light, and possibly a crane. We will then get back to the classroom and compare our findings. After that, we will get back to the second handout and resume working on it starting with Problem 13.
We will meet on the lawn next to the 5th floor entrance and spend the first half an hour of the class measuring various objects on campus, a building, a street light, and possibly a crane. We will then get back to the classroom and compare our findings. After that, we will get back to the second handout and resume working on it starting with Problem 13.
 2/8/2015  This week we will conitnue our discussion of combinatorics focusing on permutations and combinations. Handouts: Combinatorics Part II Handout  Combinatorics Part II Solution  Math Kangaroo  Mini Quiz 1 Solution We'll solve more Math Kangaroo problems in preparation for the Math Kangaroo contest. Handouts: Handout 5 Today we will begin discussing algorithms, focusing on the question "What makes up an algorithm?" and going over some basic examples of algorithms. Handouts: Algorithms 1
We will continue studying similar figures in the first half of the lesson. Then we will get acquainted with the most natural unit to measure angles, a radian.
Handouts: handout
We will continue studying similar figures in the first half of the lesson. Then we will get acquainted with the most natural unit to measure angles, a radian.
Handouts: handout  2/15/2015   2/22/2015  This week we are starting our exploration of modular arithmetic. For homework, prepare complete solutions to math kangaroo problems 9 &10.
**Math Kangaroo Problem 10 was originally posted with a typo. A corrected version is posted below.** Handouts: Modular Arithmetic Handout  Modular Arithmetic Solutions  Math Kangaroo Problem Set We'll do puzzles on the theme of identifying fake coins using a digital scale. Handouts: Handout 6 Today we will continue studying algorithms in more detail, culminating with a discussion of the "Halting Problem". Handouts: Algorithms 2 Typo in handouts: lnx is convex Handouts:
We will solve some fun problems collected from the previous Math Kangaroo competitions and occasionally modified to make them even more cool.
Handouts: handout
We will solve some fun problems collected from the previous Math Kangaroo competitions and occasionally modified to make them even more cool.
Handouts: handout  3/1/2015  We will continue to discuss modular arithmetic this week. More specifically, we will learn about congruency classes and how we can use modular arithmetic when discussing powers. Please redo the combinatorics quiz from last week and bring in your solutions. Handouts: Combinatorics Quiz  Modular Arithmetic Part II (Handout)  Modular Arithmetic Part II (Solutions)  Math Kangaroo Computers are made out of devices called "logic gates". We'll learn what they are and what they do. Handouts: Logic Gates Handout  Solutions (part 1)  Solutions (part 2) Today we will discuss two very useful strategies for solving mathematical problems: invariants and extremes. Handouts: Problem Solving 1 We will get back to geometry and prove a few more theorems discovered by the Ancient Greeks. Handouts: handout
We will get back to geometry and prove a few more theorems discovered by the Ancient Greeks.
Handouts: handout  3/8/2015  This week, we will be using modular arithmetic to explain divisibility rules. We will be able to create divisibility rules for essentially any number. Please bring in your solutions to Math Kangaroo problems 11 and 12. Handouts: Modular Arithmetic Part III (Handout)  Modular Arithmetic Part III (Solutions)  Math Kangaroo Problem Set We'll continue our investigation of logic gates and logic circuits.
Handouts: Logic Gates Handout  Solutions (part 1)  Solutions (part 2) More on invariants. We will finish problems from the previous handout and also learn new tehniques. We will continue our journey into the realm of geometry and study a few cool theorems.
Handouts: handout
We will continue our journey into the realm of geometry and study a few cool theorems.
Handouts: handout  3/15/2015  We will be learning pi, and how it relates to the perimeters and areas of circles. Handouts: Celebrating Pi Day (Handout)  Digits of Pi Problems (Handout)  Celebrating Pi Day (Solutions)  Digits of Pi Problems (Solutions) Practice test for the upcoming Math Kangaroo exam, followed by a Pi Day activity and some pie. Handouts: Practice Math Kangaroo Exam
For an hour and a half we will learn a few interesting facts related to the number Pi. During the final half hour of the class, we will turn our attention form Pi to pies.
Handouts: Pi day handout
For an hour and a half we will learn a few interesting facts related to the number Pi. During the final half hour of the class, we will turn our attention form Pi to pies.
Handouts: handout  Spring 2015 quarter  4/12/2015  This week we will review the last handout from Pi Day and work on the toughest 2015 Math Kangaroo exam. Please make sure you completed all of the Pi Day handout prior to coming to class. Handouts: Math Kangaroo Workshop (Handout)  Math Kangaroo Workshop (Solutions) We'll go over some of the more challenging problems from the recent Math Kangaroo exam. Handouts: Handout  Handout with solutions Today we will study how to circumscribe varous polygons. That is, given a polygon we will try (if we can) to find a circle containing the vertices of the polygon. We will focus on exploring when we can circumscribe a quadrilateral. Handouts: Handout The goal of this lesson is to provide support for the upcoming Logarithms and Life talk by Samir Mallya. First, we will solve a couple of warmup problems. Then we will study some basic properties of exponential functions and logarithms. At the end of the class, if time permits, we will study carbon dating, a way to estimate the age of a fossil based on halflife of the Carbon 14 isotope. Handouts: handout  4/19/2015  This week, we are exploring 1D and 2D geometry.
Handout corrections:
Problem 2 (page 3 and 4), "AB=" should read "AP=" for all parts.
Problem 3d (page 6), "APBP" should read "BPAP". Handouts: Line Geometry (Handout)  Line Geometry (Solutions) Today we will introduce the mechanical notions of lever and center of mass and explore how to prove results in geometry using these ideas. Handouts: Handout This Sunday, Michael Puthwala will talk about countability and infinity. We will continue our study of logarithms for the first hour. Samir will present his MathMovesU project during the second. Handouts: handout  4/26/2015  This week, we are looking at 3D structures and their projections. Handouts: Geometry Part II (Handout)  Geometry Part II (Solution) We'll explore the geometric concept of area and compute areas of various shapes. Handouts: Handout  Handout with solutions Having learned to compute the area of a parallelogram, we'll next see how to compute the area of a triangle, and explore related ideas. Handouts: Handout  Solutions Today we will study some basic ways of coding messages. We'll also discuss the problems with these methods. Handouts: Handout In preparation for Tyler's MathMovesU project presentation, we will refresh our knowledge of Boolean algebra and study its new representation by means of logic gates, hardware devices that power our computers, smartphones, and more. Handouts: handout  5/3/2015  This week, we will start our exploration of number bases focusing on special relations between different bases.
For homework, complete the handout through page 5. Handouts: Number Base Part I (Handout)  Number Base Part I (Solutions) We'll learn about the famous Towers of Hanoi puzzle. Handouts: Handout  Handout with solutions Today we will continue our study of cryptography, focusing on publickey cryptography and the well known RSA algorithm.
The plan for the class is as follows. First, Mark Ponomarenko presents his solutions to Problems 16 and 17 from the previous handout. Then we discuss some basic properties of the universal gates, the NAND and NOR operators. This takes the first hour. For the duration of the second hour, Tyler Weigand presents his MathMovesU project. Handouts: handout  5/10/2015  This week we will continue our exploration of number bases. Handouts: Number Bases Handout I  Number Bases Handout II  Number Bases I (Solutions)  Number Bases II (Solutions) Handouts: Handout  Solutions In preparation for Jessamine's presentation, we will take a look at the most fundamental law of nature, the energy conservation law. We will learn about the kinetic and potential enrgy of a body moving next to the Earht's surface, pay a short visit to Europa, an icy Jovian moon, and more. Handouts: handout  5/17/2015  This week, we learn to add and subtract vectors. Handouts: Vectors Handout  Vectors Solutions Handouts: Handout  Solutions We will continue studying the handout from the previuos class. If we finish it in one hour, Jessamine will make her presentation after it. If going through the handout takes the entire class, Jessamine's presentation will move to 5/31.
 5/24/2015  No meeting for holiday weekend
Part 1: Thaleia Zariphopoulou
Title: Outsmarting the risk of a bet! Learn what a derivative is, how to price it and how to hedge its risk.
Part 2: Renyuan Xu
Title: Magic, games, google, and ... math?? Do you want to be a mathematician? (Well, maybe not). How about a googler? (Well, maybe ...) What about know a few things about magic? (That is tempting...) Simple come and enjoy, maybe just the treats!
 5/31/2015  This week we explored the 27card trick that utilizes ternary bases (base 3). You can watch the video: https://www.youtube.com/watch?v=l7lP9y7Bb5g
For the second half of the class, we reviewed topics from the quarter. Handouts: Card Trick Handout  Card Trick Solutions  Review Handout  Review Solutions Handouts: Handout  Solutions For the first hour, we will continue studying the handout on kinetic and potential energy, and motion. Jessamine will present her MathMovesU project, Running through Math, after the break.  6/7/2015  This is the last meeting of math circle of the academic year. We will be playing "Dominoes." The class will be split into four teams competing in solving some very cool problems.
 Summer 2015 quarter  6/14/2015   6/24/2015  This week we worked on an initial assessment, as well as a series of Moscow Olympiad problems.
For homework, please complete the handouts. Handouts: Initial Assessment  Moscow Olympiad  Initial Assessment (Solutions)  Moscow Olympiad (Solutions)  7/1/2015  This week we will explore binary notations.
For homework, please complete the handout and make sure you are comfortable with binary notations. Handouts: Binary Notation (Handout)  Binary Notation (Solutions)  7/8/2015  We will be discussing two alternatives to our "normal" method of multiplication: Egyptian multiplication and Russian Peasant multiplication. We will learn how these methods work, and determine which are more effective. We will be discussing two alternatives to our "normal" method of multiplication: Egyptian multiplication and Russian Peasant multiplication. We will learn how these methods work, and determine which are more effective. Handouts: Handout  Solutions  7/15/2015  This week, we will solve tough problems related to percentages. For homework, complete the handout. Handouts: Percentages (Handout)  Percentages (Solutions)  7/22/2015  This week, we worked on 3D geometry. We started with a workshop on projections and continued with the handout found below. For homework, please complete the handout. Handouts: Geometry (Handout)  Geometry (Solutions)  7/29/2015  This week we will work on word problems that involves two or more persons or things working together to complete a task. You can find this week's handout as well as solutions below. For homework, please complete the handout and start reviewing past topics from the quarter. Handouts: Warm Up (Handout)  Warm Up (Solutions)  Working Together (Handout)  Working Together (Solutions) 
