
LAMC Meetings Archive • Fall 2007–Summer 2020For 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 2013 quarter  9/29/2013  For the first week, we will be working on some problems that have appeared on Russian math olympiad contests! Handouts: Week 1 We will begin a minicourse on placevalue numerical systems. We will study the numerals base ten (decimals), base two (binaries), base three (trinaries), base eight (octal numbers), and base sixteen (hexadecimals or just hexs). Handouts: handout  solutions key We will solve several puzzles and problems about dividing and sharing. Handouts: Puzzles and Sharing Solutions  Puzzles and Sharing Today we will study what happens to different geometric concepts when we change the definition of distance. Handouts: Taxicab Geometry I For our first meeting of the fall quarter, we will discuss games from a mathematical point of view. Handouts: Game theory This week we will begin to explore properties of the decimal representations of fractions. The goal for this week is to prove that certain fractions have a terminating decimal equivalent. Handouts: Week 1 worksheet  Week 1 solutions Before we dive into a specific topic, we will have some fun doing a variety of problems for the first meeting similar to those of Math Olympiad. Handouts: Handout 1  10/6/2013  We will be spending one more week solving problems that have appeared on Russian math olympiads. This will help the kids strengthen their individual problem solving skills as well as prepare them for thinking outside the box, of which we will ask a lot this year!
NOTE: HOMEWORK DUE: Previous week's handout, Problem 9 and Problem 11. For problem 11, I asked students to come up with as many distinct solutions as they could. Attempting problem 12 is not necessary because it will appear again on this week's set. Handouts: Week 2 About 25% of the students have finished, or nearly finished, working through the first handout during the first session. These students will be given the second handout with various olympiadstyle problems at the beginning of the class. The rest of the students will resume studying the first handout at problem 14 on page 14. Once finished, they will be given the second handout with the olympiadstyle problems. Handouts: handout  solution key This week we will work on equations, through looking at balancing scales. Please remember to bring your kids on time so we can start class right away! Thanks! Handouts: Balance Scales  Balance Scales Solutions Today we will continue our discussion of Taxicab geometry we started last week. Handouts: Taxicab Geometry II In this talk, we will explore some special complex numbers called roots of unity and use them to solve various problems. Handouts: Problem set 1  Problem set 2 This week we work to show that every fraction has a repeating decimal equivalent. Handouts: Week 2 worksheet  Week 2 solutions This week we will be learning about the meaning of infinity by looking at Hilbert's paradox of the Grand Hotel. Handouts: Handout 2  10/13/2013  We will be delving into basic math induction this week!
Handout is here: http://www.math.ucla.edu/~radko/circles/lib/data/Handout561694.pdf We will continue the study of the placevalue numerical systems. Handouts: handout  hex addition table  solutions This week we will continue working with balancing scales. We are introducing how binary and trinary searches work by finding the minimum number of trials to find one fake coin among real (equal) coins by using a scale. Remember to have kids explain their solutions to you at home! Handouts: Balance Scales Part II  Balance Scales Part II Solutions Today we will explore the mathematical properties of Euclidean and taxicab distance. Along the way we will introduce the concept of a metric. Handouts: Taxicab Geometry III We will go over the games played two weeks ago and discuss winning strategies. For more details, you can check out the wonderful online notes on game theory by Prof. Ferguson
http://www.math.ucla.edu/~tom/Game_Theory/Contents.html Handouts: Game theory handout This week we'll work on proving the converse of what we did last week, i.e. proving every eventually period decimal comes from a fraction. Handouts: Week 3 Solutions  Week 3 Handout This week we continue the concept of infinity, but add infinite rockets to the mix. Handouts: Handout 3  10/20/2013  We will be continuing with Math Induction this week. PLEASE MAKE SURE LAST WEEK'S HANDOUT IS BROUGHT TO CLASS, WITH PROBLEMS 14 COMPLETED. Handout is here: http://www.math.ucla.edu/~radko/circles/lib/data/Handout561694.pdf Handouts: Induction II We will go over all the problems in the second and third handout that some students could not figure out themselves. It will be mostly students explaining their solutions to fellow students. The teachers will only help if there is on one else to solve a problem.
If any time remains, we will do some olympiadstyle problems on the pigeonhole principle. This week we will be introducing Roman numerals to the class. We will learn what they are and how to add and subtract them. Please remember to bring your kids on time! Thanks :) Handouts: Roman Numerals  Roman Numerals Solution Expanding on the ideas we introduced last week, we define a metric space, and explore some examples. Handouts: Metric Spaces I To celebrate the 170 years (+4 days) anniversary of Sir William Rowan Hamilton's discovery, we will take a look at the quaternions, a cousin of the complex numbers. Handouts: Quaternions This week we'll be doing some practice AMC 8 problems and discussing solutions. Handouts: The test  The solutions We will be doing two lessons from the book, "Sideways Arithmetic from Wayside School" by Louis Sachar. The topics include cryptarithms and some logic T/F problems. Handouts: Handout 4  10/27/2013  We will be learning about propositional logic this week. How much about your life can you REALLY conclude? Handouts: Propositional Logic We will solve some fun problems using the pigeonhole principle as a tool. Handouts: handout  solution key This weekend we will be doing an assortment of Halloween riddles and puzzles. Handouts: HalloweenMeeting  HalloweenMeetingSolutions Today we will finish up our study of metric spaces, by looking at metrics on sets other than the real numbers. PLEASE look at homework problem 2 from last week's handout, and bring last week's handout this week! Handouts: Metric Spaces II No, not peanut butter, celery, and raisins. This week we will take a look at some classic and not so classic problems about crawling bugs, as well as problems to do with tiling a region in the plane. Handouts: Bugs and Tiling Problems We will learn to count, mainly about "n choose k". Using this we will count poker hands and Fibonacci numbers. Handouts: Worksheet  Solutions This week we will be doing a diverse set of problems that all fit the Halloween theme!
Handout corrections:
#4: The question should be, "At which house will both groups visit?" Handouts: Handout 5  11/3/2013  We will be spending one more week on propositional logic. Handouts: Propositional Logic II Students will take a test on placevalue numerals with two problems on the Pigeonhole Principle at the end. The best way to prepare is to study the first and third handouts for the placevalue numerals and the fourth handout for the principle. The test may take the stronger students about an hour to complete while weaker students may need two hours. The students finished working on the test will be asked to move to the neighboring room where some more problems on the Pigeonhole Principle will be discussed. This week we will start our first of a few sessions discussing binary numbers. This week, we will introduce the concept through balance scales. Handouts: Binary Numbers Through Scales  Binary Numbers Through Scales Solutions Today we will learn/review various properties of complex numbers, which will be useful in the coming weeks. Handouts: Complex Numbers I We will discuss how to divide a polygonal pizza between friends, pearl
necklaces between pirates, and other fair division problems.
Continuity plays a major role in all these problems. Handouts: Continuity Problems This week we will be telling stories to prove combinatorial identities! Handouts: Hand Out We will study Venn Diagrams this week. Handouts: Handout 6  11/10/2013  We will be working through a fulllength AMC practice exam to help with general problem solving skills as well as prep for those who will be participating in the AMC soon after. We will study some basic properties of parallelograms. Our studies will be based on the April 15, 2012 Junior Circle handout. Please see the following
URL.
http://www.math.ucla.edu/~radko/circles/lib/data/Handout345431.pdf Handouts: handout This week we will continue working on binary numbers. We will learn how to count in binary by using our fingers. We will also learn how to add and subtract in binary. Handouts: Adventures in Binary Land Continued  Adventures in Binary Land Continued SOLUTIONS Today we will explore how complex numbers can be applied to geometry. We will focus on how to view transformations of the plane as functions of complex numbers.
Please review the handout from last week in preparation for this week! Handouts: Complex Numbers II We will discuss how to inscribe circles, triangles, rhombi and squares
into more complicated figures. Again, the continuity will play a
major role, but the arguments will turnout to be more sophisticated
while still elementary. Handouts: Inscribed figure and continuity We will talk about Mountain ranges and Random Walks. We will also continue the handouts from the last two weeks. Handouts: Random Walk Notes This week we will start working on Permutations! Here is a link to explain the method used for class: http://en.wikipedia.org/wiki/Braid_group Handouts: Handout 7  11/17/2013  We will be taking a quiz at the start of the class session, then working on problems that have appeared on acclaimed math contests in recent years. Most of the students didn't move past Problem 6 from the last week's handout. This time we will resume at Problem 7. We will continue proving properties of parallelograms using the Claim ? Reason charts. This week we will learn how to add and subtract in binary. Handouts: EE Fall 2013 Meeting 8 Adding in Binary  EE Fall 2013 Meeting 8 Solutions Today we will examine a certain class of algorithms, called greedy algorithms, as examine some situations where they lead to optimal solutions. Handouts: Greedy Algorithms I  Relevant Graphs Imagine in the future that we are able to build a spacecraft that is able to travel 186,250 miles per second. Suppose that a father goes on holiday to a nearby planet. His daughter takes him to the spaceship and bids him farewell. He tells her that he will be back in a year and to keep an eye on the house. When he comes back, he sees a strange old lady living in his house. He asks her, \Who are you and what are you doing in my house?" She says, "I'm your daughter, Dad." What is going here? By the end of this lecture, we will have an answer to this question. We will continue to talk about permutations today. We will learn about composition of permutations and the inverse permutation among other topics. Handouts: Handout 8  11/24/2013  A bit more geometry with proofs and claimreason charts. Handouts: handout This week we learned how to use binary notation to help find winning strategies in certain math games. Handouts: EE Fall 2013 Meeting 9 Binary Games  EE Fall 2013 Meeting 9 Binary Games Solutions Today we will continue our study of greedy algorithms, seeing a few examples where greedy algorithms are not always optimal. Handouts: Greedy Algorithms II  Relevant Graphs Imagine in the future that we are able to build a spacecraft that is able to travel 186,250 miles per second. Suppose that a father goes on holiday to a nearby planet. His daughter takes him to the spaceship and bids him farewell. He tells her that he will be back in a year and to keep an eye on the house. When he comes back, he sees a strange old lady living in his house. He asks her, \Who are you and what are you doing in my house?" She says, "I'm your daughter, Dad." What is going here? By the end of this lecture, we will have an answer to this question. This week we look at visual proofs of several theorems. Handouts: Worksheet Handouts: Handout 9  12/1/2013  Happy Thanksgiving!  12/8/2013  A fastpaced game in the vein of the classic Math Relays... with a twist! The class will be split into five teams. The teams will compete in solving math problems. The winners will get some cool prizes. Handouts: problems  Winter 2014 quarter  1/12/2014  Happy New Year! We will be beginning the quarter with an introduction to a powerful mathematical concept called an invariant. Handouts: Invariants  Questionnaire As usual, we will solve a few warmup problems at the beginning of the class. Then we will learn how to divide a straight line segment into any (positive integral) number of parts, using a compass and ruler as tools. We will further employ a ClaimReason chart to prove that our method works. In the next part of the class, we will introduce vectors as pointed segments, or arrows, and begin studying their properties. Handouts: handout This week we will be doing a variety of fun problems involving triangles and questions involving even and odd properties. Handouts: Flipping Triangles, Gears, and More Triangles  Flipping Triangles, Gears, and More Triangles Solutions Today we will begin studying vectors. Handouts: Vectors Welcome back everyone. This week we will be looking to gain a deeper understanding of percentages. Handouts: Handout  Solutions 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 1  1/19/2014  We will be continuing our discussion of invariants. Handouts: Invariants II  Solutions We will use vector algebra to reprove some important theorems we have proven in the past; to slide a heavy box over the floor in an efficient manner; and to steer a spaceship. All that after a warmup that includes a cool card trick. Handouts: handout We will start by counting the number of squares of various sizes on a chessboard and continue with playing several games on a chessboard. Handouts: Handout Today we will generalize our study of vectors last week and introduce matrices. Handouts: Matrices AMC Preparation Handouts: 2006 AMC 12 This week we begin discussing sequences and series. We will focus on sequences this week. Handouts: Handout (1)  Handout (2) This week, we will be looking at the Fibonacci Sequence and where we see it in nature. Handouts: Handout 2  1/26/2014  We will be looking at some problems involving inequalities this week. Handouts: Inequalities I We will solve a Math Kangaroo test for one of the years past. Then we will take a break. We will have a fractions clinic after the break. Handouts: handout We will continue counting squares on the chessboard, as well as play some strategy games on the board. Handouts: Fun and Games on a Chessboard Continued  Fun and Games on a Chessboard Continued Solutions Today we will use the material we learned about vectors and matrices to learn the basics of linear algebra. Handouts: Linear Algebra AMC Preparation Handouts: 2004 AMC 12 We continue to work on topics related to sequences and series today! This week, we will be developing problem solving skills in preparation for the Math Kangaroo. Handouts: Handout 3  2/2/2014  We will be looking at more problems involving inequalities this week. Handouts: Inequalities II We will continue our study of the algebra of vectors. To better understand multiplication of vectors by some irrational numbers, we will also recall the Pythagoras theorem and use it compute some lengths. Finally, we will refresh our understanding of rational vs. irrational numbers. Handouts: handout In this lesson we introduced the class to function machines and how they work. The class worked through several different examples of functions. For homework, each student is making their own function machine. Handouts: EE Winter 14 Function Machine  EE Winter 14 Function Machine Solutions Today we continue our study of linear algebra and introduce the idea of a basis. Handouts: Basis This week we solved problems related to absolute values and distances (both on the real line and in the plane) Handouts: Worksheet This week, we will look at the distance formula. We will see how rate, time and distance are related. Handouts: Handout 4  2/9/2014  We will be learning about and beginning to work with the concept of infinity this week. Taught by Don Laackman. Handouts: Infinity We will solve a bunch of warmup problems and then switch back to studying vector algebra. We will work on Problems 7 through 17 from our 1/19/2014 session. We did not solve them back then. We will solve them this time.
Handouts: handout In this class we learned about functions being 11, as well as how to compose functions. Kids also introduced their own function machines and worked with them throughout the class. Handouts: EE Winter 14 Function Machine Contd  EE Winter 14 Function Machine Contd Solutions Today we finish our study of linear algebra by talking about linear transformations. Handouts: Linear Transformations As the title suggests, This week we introduce basic notions regarding set theory and infinity. Handouts: Worksheet  Solutions This week, we will continue our discussion on the distance formula. In particular, we will look at how we can solve problems using graphs of distance vs. time. We will also solve some problems involving people working together to complete tasks. Handouts: Handout 5  2/16/2014   2/23/2014  This week we will let the students work on problems from the 2013 Math Kangaroo contest.
Math Kangaroo 2013: https://kangaroo.math.ca/samples/2013/2013gr0102e.pdf
Handouts: Math Kangaroo 2007  Math Kangaroo 2008  Math Kangaroo 2006  Math Kangaroo 2009  Math Kangaroo 2010  Math Kangaroo 2011 We will be starting a twoweek study of taxicab geometry this week!
Handout titled "bonus" is for those who finish the main taxicab handout. It will not be required knowledge for next week's handout, though it's an interesting problem. Handouts: Taxicab I  Bonus First, we will use vector algebra to prove the median theorem, the one we had skipped last time. Then we will see how vectors make clear the three laws of Newton. In the process, we will help Captain Solo defeat the Death Star and save the galaxy, again! Handouts: handout Today we will introduce the idea of a sequence, which will be our focus the next few weeks. Handouts: Sequence I If your child is interested in attending a selective college, you need to understand how today's college admissions has changed since you applied. This talk will cover topics including what you need to know about curriculum, testing, grades, extracurriculars, college essays, recommendations, interviews, and more. We looked at inequalities in polygons and at the shortest paths with some constraints. Handouts: Handout  Solutions This week, we will look at how the areas and volumes of objects are affected by scaling factors. Handouts: Handout 6  3/2/2014  We will continue studying the Laws of Newton using vector algebra. Handouts: handout We will be learning about projections of 3D solids, both on a 2X2 base and on a 3X3 base. Handouts: EE Winter 14 Projections  EE Winter 14 Projections Solutions Today we will continue our study of sequences from last week, and introduce the related concept of a series. Please review last week's handout in preparation for this week. In particular, students should be comfortable with at least questions 0:ah, 1:af, 2:ac, and 3. Handouts: Mathematical Biology and Graph Theory This week we will work on some interesting Math Kangaroo problems. Handouts: Problems (No solutions)  Problems (With solutions) This week, we will be looking at graphs to determine speeds of objects. In addition, we will introduce graphing lines and determining equations of lines. Handouts: Handout 7  3/9/2014  Many students will be taking the Math Kangaroo contest soon. We'll be working through a set of practice problems that have appeared on past contests. We will review most of what we have learned this quarter. Handouts: handout This week we continued working on projections of solids built on a 2X2 or 3X3 base. Handouts: Projections II  Projections II Solutions Today we will begin to study the idea of a limit of a sequence, and when it makes sense to say we can add up infinitely many numbers. We discuss many mathematical situations that come up on a chess board. Handouts: Handout We will be solving problems that will help us prepare for the upcoming Math Kangaroo exam. In addition, we will discuss some strategies for taking the exam. Handouts: Handout 8  3/16/2014  We'll be bringing back the classic, perhaps with a little bit of a twist this time! The students will be given a test covering the topics we have studied this quarter, vectors, velocity and acceleration, Newtonian laws, Pythagorean theorem, rational and irrational numbers, floor and ceiling of a number, and the inclusionexclusion principle. In addition, there will be a few olympiadstyle problems that require no special knowledge, but are nontrivial and fun to solve on the test. In this class we did a team competition where students worked together to solve many different problems. Handouts: Math Relays Winter 2014 Today we will continue our study of infinite series. This week we will be split into teams to solve problems. Winners will receive prizes! This week, we will do problems that will allow us to review the material that was covered this quarter. Handouts: Review  W14  3/23/2014   Spring 2014 quarter  3/30/2014  Math Circle will resume next week!  4/6/2014  We will be learning some important things about quadratics this week. Please bring this handout back next week, as we will be picking up with the Vieta's Theorem section! Handouts: Quadratics I For warmup, we will discuss the 27 card trick. Then we will begin our study of permutations. Our main goal will be to learn solving the 15 puzzle in the cases where a solution exists. Handouts: handout  Solution key, part 1  Solution key, part 2  Solution key, part 3  Solution key, part 4 This Sunday we will be learning about geometric figures and how to make patterns with them. In particular, we will study shapes that tessellate. Handouts: EE Spring 14 Tessellations Today we will introduce the concept of a model, and study models of different groups of axioms. We have tangentially met the pigeonhole principle several times. This week we will have an entire handout focused on this principle. We will start off the quarter by looking at the properties of graphs of insects' worlds. This will serve as a basic introduction to graph theory. Handouts: JC S14 Meeting 1  Insects  4/13/2014  We will be continuing last week's study of quadratic equations, with an emphasis on Vieta's Theorem. Please make sure to bring last week's handout as we will be finishing that up this week. Handouts: Quadratics II and Vieta There will be a short quiz at the beginning of the class. Then we will continue studying permutations and trying to solve the 15 puzzle. Handouts: handout This week we will continue to look at tessellations. In particular, we will look at tessellations made by combining regular hexagons, squares, and triangles. Handouts: Tessellations Week 1 & 2  Tessellations Solutions How hard can it be to count? The answer to that question may depend on how
much stamina you have. It might, for example, take an awfully long time to
count how many 125element subsets there are of {1, 2, ..., 250} by simply
listing all of them. There are faster ways to calculate this number, but
even then, at first glance it may appear to require a substantial amount of
computation in order to determine even the last digit of "250 choose 125".
In this talk, we will find this last digit, and explore some related
topics. (Hint: the last digit is not zero  that would be too easy!) In 2012, UCLA Professor Emeritus Lloyd Shapley won the Nobel Prize in Economics. The award was in recognition of the GaleShapley Algorithm. You will learn that algorithm and also another of Shapley's important concepts called the Shapley Value. Today we will begin a study of a levers and barycentric coordinates (this week we focus on levers) We will continue our discussion of "insect worlds", and work with graphs. We will discuss properties of paths, circuits, Euler Circuits, and Euler paths. Handouts: JC S14 Meeting 2  Circuits  4/20/2014  We will be continuing last weeks studies as well as exploring factorizations of polynomials. Handouts: Factorizations The students who have finished working through the second handout on permutations will be given some olympiadstyle problems to solve. Other student will join as soon as they finish the permutations handout. Handouts: handout In this session we will be working with the geometry of a cube. Handouts: Spring 2014 Meeting 3 Nets and Cubes  Spring 2014 Meeting 3 Nets and Cubes Solutions Today we will study different attempts at models of arithmetic as well as other common structures. We continue our discussion from last week, this time focusing on Barycentric coordinates. Handouts: Barycentric Coordinates Handout We will continue our discussion of Euler paths and Euler Circuits. In addition, we will introduce dual graphs and how to draw them. Handouts: JC S14 Meeting 3  Graph Proofs  4/27/2014  Please see attached handout. Problems 5, 10, and 11 were assigned as homework. Handouts: Operations and Relations We will make one more step towards understanding the 15 puzzle  learn what a parity of a permutation is and how to compute it. If time permits, we will also solve some more olympiadstyle problems. Handouts: handout  solutions This week we will introduce logical statements and their negations, through a fun activity with "Mr. No" and "Mr. Yes". Handouts: Meeting Mr. No  Meeting Mr. No Today we will start studying group theory by examining the permutation group Sn. In these lectures we will explore an area of mathematics called knot theory. A knot is a closed loop in three dimensional space, and two knots are called equivalent if they can be deformed into each other. We can distinguish knots by assigning to them certain quantities, called invariant.
This week we discuss vectors and attempt to apply our knowledge to prove some facts about geometry.
Handouts: Handout This week, we will begin our discussion on modular arithmetic. Handouts: JC S14 Meeting 4  Modular Arithmetic  5/4/2014  Not every proof needs to have two columns for "statements" and "reasons," or an assumption that is contradicted. We'll learn about a different way this week; if you don't want to tell me how, show me how  with a picture! Handouts: Proofs Without Words
A USC physics professor and the father of one of our students, Vitaly Kresin, is going to show the class some cool experiments related to the Newtonian Laws of motion we studied at the end of the 2014 Winter quarter. Once he is finished, we will get back to the 15 puzzle and learn the last tool we need to unravel it, taxicab geometry.
Handouts: handout  sols to the first part Today we will begin studying the basics of group theory. We continue our incursion into knot theory. We will discuss more knot and link invariant, including the linking number.
USC physics professor Vitaly Kresin gives a special demonstration of elementary physics principles.
We will continue our discussion of modular arithmetic this week. We will look at addition and multiplication tables, as well as determining divisibility rules for some numbers. Handouts: Modular Arithmetic Part II  5/11/2014  This set contains fewer problems than many other handouts; students should attempt to solve all four. Handouts: Week 7 Problems
We will learn the last tool we need to figure out why Sam Loyd's configuration of the 15 puzzle is not solvable. Called the taxicab (a.k.a. L_{1}) geometry, it is important in various areas of math and physics and quite entertaining in its own right. In particular, we will see that a taxicab geometry circle is ... a square! Once finished, we will solve some cool olympiadstyle problems.
Handouts: handout
We introduce the Mayan Number system, and learn how to convert between Base 10 numbers and Mayan Numbers.
Handouts: Mayan Numbers Part I  Mayan Numbers Part I Solutions
Today we will continue studying group theory, focusing on the concept of an elements "order" inside the group.
Handouts: Handout  Solutions This lecture is about tilings of plane polygons by other plane polygons. We shall see many examples of impossible tilings but the proofs will get more and more involved. Colouring argument is a simple yet strong argument. However, there are problems that colouring argument alone cannot solve. One way of tackling tiling problems is using Conway's tiling group. This method transforms tiling problems into creating specific group structures.
This week we explore some logic puzzles.
Handouts: Handout
We will apply modular arithmetic to derive test of divisibility by 3. In the second half of the class we will study different types of polyhedra.
Handouts: Polyhedra I  Solutions  5/18/2014  We'll be starting our culmination projects this week. Presentations will be on June 1. Handouts: Culmination Project
We will review permutations, taxicab distance, and the 15 puzzle. If time remains, we will solve a few cool olympiadstyle problems.
Handouts: handout We will continue to work with Mayan numbers, this time focusing on how to manipulate them.
Handouts: Mayan Notation II WarmUp  Mayan Notation II  Mayan Notation II Solutions Today we'll study how symmetries of geometric objects form a group. Specificially, we will study the so called "dihedral group".
This lecture is about tilings of plane polygons by other plane polygons. We shall see many examples of impossible tilings but the proofs will get more and more involved. Colouring argument is a simple yet strong argument. However, there are problems that colouring argument alone cannot solve. One way of tackling tiling problems is using Conway's tiling group. This method transforms tiling problems into creating specific group structures. This week we will introduce the basics of propositional logic.
Handouts: Handout We will introduce the topic of planes, and learn how to construct crosssections of polyhedra by planes.
Handouts: Tetrahedra and crosssections  Solutions  5/25/2014   6/1/2014  Make sure to email me your group's handout. I look forward to hearing your presentations! Handouts: MC_Advanced_Project Students will take a 2hour test on permutations, taxicab distance, and the 15 puzzle. At the end of the test, there will be four olympiadstyle problems, the last of them extra credit.
This weekend we will be learning about pairity and the coordinate plane through a game called Leap Frog. Handouts: Leapfrog Today we will briefly study the idea of a field, and see some applications to basic number theory.
This week we will continue our study of symbolic logic. Handouts: Handout We will review some of the topics we covered during this academic year. Emphasis will be placed on material covered this quarter. Handouts: End of Year Review  6/8/2014  Fun, math games, and goodbyes. We will meet at 3:30 PM at the lawn near the 5th floor Math Building entrance and take pictures of the class. We will get down to the classrrom, split the students into four teams, and start the competition afterwards. The winning teams will get prizes. Some special prizes will be given to the most useful team member on every team.
This week we will be playing a team competition where students will have to work together to solve various types of problems. For the last meeting of the quarter, we will be having math relays. Handouts: Relay problems with answers  Relay problems without answers We will be playing the Dominoes game this week!  Summer 2014 quarter  6/11/2014  We will solve some warmup problems and then proceed to study permutations and the 3 puzzle, a (greatly) simplified version of the famoius 15 puzzle.
Handouts: handout  6/18/2014  We will learn to multiply permutations. Finishing the first handout, we will figure out what configurations of the 3 puzzle are solvable and what are not. If time permits, we will finish the lesson solving some olympiadstyle problems.



