| Intemediate Group | Advanced Group | ||
|---|---|---|---|
| Date | Speaker, Affiliation, Topic | Date | Speaker, Affiliation, Topic |
| Monday, September 22, 2014 |
Joshua Zucker Finding Fractions in an Infinite TreeSummary: We’ll learn a new way to arrange all the fractions, first described by Calkin and Wilf about 15 years ago, prove a few of the same results that they explained in their paper, and then attempt (and almost certainly fail) to solve at least one question about the arrangement that Calkin has been unable to solve himself. |
Monday, September 22, 2014 |
Cornelia Van Cott University of San Francisco Taxicab Geometry, or Sometimes Pi Equals 4 We explore creative ways to define distance between two points. Leaving behind the usual Euclidean definition, we will introduce the taxicab metric, post office metric, the elevator metric, and more. These new metrics cause us to change our usual notion of circles, triangles, and even pi, resulting in completely different geometries. We will, in particular, investigate taxicab geometry — the geometry that arises from using the taxicab metric. |
| Monday, September 29, 2014 |
Tom Davis http://www.geometer.org Projective Geometry |
Monday, September 29, 2014 |
Cornelia Van Cott University of San Francisco Taxicab Geometry, Part 2 We explore creative ways to define distance between two points. Leaving behind the usual Euclidean definition, we will introduce the taxicab metric, post office metric, the elevator metric, and more. These new metrics cause us to change our usual notion of circles, triangles, and even pi, resulting in completely different geometries. We will, in particular, investigate taxicab geometry — the geometry that arises from using the taxicab metric |
| Monday, October 6, 2014 |
Cornelia Van Cott University of San Francisco The Mathematics of Coloring We will investigate exactly when a doodle can be colored with only 2 different colors. Then we will try to understand what happens when “2” is replaced by another number — 3, 4, 5 … and we will see how coloring can help us solve seemingly impossible problems. |
Monday, October 6, 2014 |
Marc Roth Woodside Learning Center Polyhedra: Platonic and Otherwise We’ll take hands-on building of polyhedra and use the discovery method to find the formulas for finding the vertices, edges, faces, and numbers of each kind of face. Some students will know the Euler polyhedra formula, but Descartes angular defect theorem will probably be new to all. |
| Monday, October 13, 2014 |
Marc Roth Woodside Learning Center Polyhedra: Platonic and Otherwise |
Sunday, October 13, 2014 |
Joshua Zucker |
| Monday, October 20, 2014 |
Marc Roth Woodside Learning Center Polyhedra, Part 2 |
Monday, October 20, 2014 |
Stanislav Dubrovskiy San Francisco State University Vectors and coordinates in 2D, 3D and beyond We’ll talk about vectors, their properties, operations, and use them to solve problems in plane and solid geometry. |
| Monday, October 27, 2014 |
Kaushik Basu Academic Talent Development Program Walking the Plank: Pirates and the Delicate Art of Balancing Balancing identical planks on top of each other to get the maximum overhang is a wonderful interplay between the center of gravity in physics and the harmonic series in math. It also exemplifies how it is necessary to break the rules to take mathematics forward. We will discover and discuss how to balance Kapla blocks and quantify this using the idea of center of gravity. The challenge is to determine the center of gravity as the arrangement becomes non-symmetrical. Once we follow the rules and discern a pattern, we will break the rule of only allowing one block per layer of the stack and discuss some recent research work in this area. |
Monday, October 27, 2014 |
Ernesto Diaz Dominican University Mathematics of Digital Signals: Cryptography & Encryption This is the first in a periodic series of lectures regarding the mathematics associated with digital systems. In this particular talk we will take a look at the definition, goals and history of cryptography and cyphers and will cover a few hands-on examples of encrypting and decrypting cyphers using simple historical methods. We will introduce the idea of basic coding in modern computer systems and provide a couple of examples of areas of mathematics used in cryptography. |
| Monday, November 3, 2014 |
Zandra Vinegar Berkeley Math Circle |
Monday, November 3, 2014 |
Stan DubrovskiySan Francisco State University Vectors, Data, and Principal Component Analysis |
| Monday, November 10, 2014 |
Cliff Stoll Acme Klein Bottle Bring your own scissors! |
Monday, November 10, 2014 |
Ernesto Diaz Dominican University of California Mathematics of Digital Signals: Cryptography & Encryption, Part 2 |
| Monday, November 17, 2014 |
Zandra Vinegar Berkeley Math Circle AMC-8 Preparation |
Monday, November 17, 2014 |
Kaushik Basu UC Berkeley’s Academic Talent Development Program (ATDP) Origami of Conic Sections |
| Tuesday November 18, 2014 |
AMC-8 Contest for 8th grade and under |
Tuesday November 18, 2014 |
AMC-8 Contest for 8th grade and under |
| Monday, November 24, 2014 |
Joshua Zucker Fast ExponentiationIn encryption, computers need to take truly huge powers. Straightforward repeated multiplication would take much too long — more than the lifetime of the universe. We’ll learn how computers do it in microseconds instead, and find ways for many numbers that are faster than the way that computers typically use. And the only tools we’ll need are simple addition and a lot of cleverness! |
Monday, November 24, 2014 |
Alon Amit Origami Logic |
| Monday, December 1, 2014 |
Zandra Vinegar Berkeley Math Circle Mad Hatter MathematicsThere is math. Like no math in school. And proofs full of wonder, mystery, and danger! Some say to survive them, you need to be as mad as a hatter! |
||
| Monday, December 8, 2014 |
Joint Session and Holiday Party Paul Zeitz University of San Francisco Density When you can’t answer precisely, try statistics. You can get AMAZINGLY SURPRISING insights. |
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| Monday, December 15, 2014 |
NO CLASS – Winter Break | Monday, December 15, 2014 |
NO CLASS – Winter Break |
| Monday, December 22, 2014 |
NO CLASS – Winter Break | Monday, December 22, 2014 |
NO CLASS – Winter Break |
| Monday, December 29, 2014 |
NO CLASS – Winter Break | Monday, December 29, 2014 |
NO CLASS – Winter Break |
| Monday, January 5, 2015 |
NO CLASS – Winter Break | Monday, January 5, 2015 |
NO CLASS – Winter Break |
| Monday, January 12, 2015 |
NO CLASS – Winter Break | Monday, January 12, 2015 |
NO CLASS – Winter Break |
| Monday, January 19, 2015 |
NO CLASS – Winter Break | Monday, January 19, 2015 |
NO CLASS – Winter Break |
| Monday, January 26, 2015 |
Zandra Vinegar Mathematics of Artificial Intelligence Part 1: Combinatorial Game Strategy How can you find the ultimate strategy to win games? And if you’re coaching a computer to win at a game, instead of a friend, how can you teach the computer to win and adapt to an opponent? |
Monday, January 26, 2015 |
Tom Davis geometer.org The Game of Hackenbush Red-Blue Hackenbush is a game with simple rules and not so simple mathematics, although every game position can be represented by a number. We’ll look at how to assign numbers to games and consider what makes a good strategy. |
| Monday, February 2, 2015 |
Zandra Vinegar Mathematics of Artificial Intelligence Part 2: Iterated Games and the Nash Equilibrium What happens if you play an AI against another AI over and over and over and over… again? |
Monday, February 2, 2015 |
Jan Reimann Penn State University Kolmogorov Complexity We will try to give a mathematical solution to the question of why we consider some binary sequences random and some not (like 00000000000 …000) even though the probability of production them with a fair coin is the same (if they have the same length). We will also touch on the basics of computability (Turing machines, etc.) |
| — | — | Tuesday February 3, 2015 |
AMC-10/12 Contest |
| Monday, February 9, 2015 |
Marc Roth Woodside Learning Center Modular Arithmetic and Elementary Finite Fields |
Monday, February 9, 2015 |
Zandra Vinegar Exploring Infinity Part 1: Monstrously Enormous Numbers and The Infinite ZooWhat is the largest, non-infinite that number you know how to describe? Before tackling infinity, we’ll take a quick tour past some of the infinite zoo’s outcast monsters: mother-board melting demons that can only even be written with great care. |
| Monday, February 16, 2015 |
NO CLASS – Ski Week | Monday, February 16, 2015 |
NO CLASS – Ski Week |
| Monday, February 23, 2015 |
Paul Zeitz University of San Francisco |
Monday, February 23, 2015 |
Zandra Vinegar Exploring Infinity Part 2: Infinity WranglingOnce infinity is your tamed, friend, there are many finite challenges that can actually be made EASIER by converting them into an infinite form. |
| Tuesday, February 24, 2015 |
Bay Area Mathematics Olympiad | ||
| Monday, March 2, 2015 |
Zandra Vinegar Turing Tour de Force Part 1: An introduction to many practical code building and hacking techniques, and a quick review of historically memorable codes. |
Monday, March 2, 2015 |
Marc Roth Woodside Learning Center Triangle, Finite Differences, and Quadratic Functions |
| Monday, March 9, 2015 |
Zandra Vinegar Turing Tour de Force Part 2: Try your own hand at making new codes out of combinations of existing codes. And see if you can break the codes designed by other Math Circle students. |
Monday, March 9, 2015 |
Pratima Karpe Catalan Numbers We’ll look at the Catalan numbers and various applications to which the Catalan numbers apply. We’ll prove a direct formula as well as a recurrence relation for calculating Catalan numbers. |
| Monday, March 16, 2015 |
Kaushik Basu Pinball Museum and UC Berkeley’s Academic Talent Development Program Origami with a Single Fold We normally associate origami with complex and beautiful birds, polyhedrons, or dinosaurs. However, a single fold on a square origami paper opens up rich mathematical questions, and will provoke us to address the questions that arise most naturally from a single fold which is about polygons. After discovering what they are, we will prove the conditions in which they arise. |
Monday, March 16, 2015 |
Zandra Vinegar Combinatorial Game Strategy How can you find the ultimate strategy to win games? And if you’re coaching a computer to win at a game, instead of a friend, how can you teach the computer to win and adapt to an opponent? We’ll be using some combinatorics games, such as dots and boxes and gomoku, to understand various strategies. |
| Monday, March 23, 2015 |
Kaushik Basu Rock, Paper…Kale Drawing our way into understanding flat, spherical, and hyperbolic objects. An introduction to mathematical drawing. |
Monday, March 23, 2015 |
Zandra Vinegar Iterated Games and the Nash Equilibrium What happens if you play an AI against another AI over and over and over and over… again? |
| Monday, March 30, 2015 |
Marc Roth Perfect Numbers |
Monday, March 30, 2015 |
Kaushik Basu Cavalieri’s Principle A pre-Newtonian concept of Calculus. |
| Monday, April 6, 2015 |
Zandra Vinegar The Mathematical Logic of Codes |
Monday, April 6, 2015 |
Kaushik Basu Biking Adventures and Mamikon’s Theorem We follow Sherlock Holmes and Watson trying to figure out which way a bicycle went by looking at its tracks and stumble upon clues leading us to the celebrated Mamikon’s Theorem. |
| Monday, April 13, 2015 |
NO CLASS — Spring Break | Monday, April 13, 2015 |
NO CLASS — Spring Break |
| Monday, April 20, 2015 |
Zandra Vinegar Part 1: Learn how to hack a website.Part 2: How to hide secrets in plain sight (steganography) |
Monday, April 20, 2015 |
Joint with Intermediate Group |
| Monday, April 27, 2015 |
Kaushik Basu To compute is human, but to approximate is divine We will investigate some problems where approximation tools shine over analytical methods. Revisiting some problems using the lens of dimensional analysis, extreme case reasoning, and thinking in pictures will enable us to gain more insight while keeping the problems tractable. We will wind up the talk with a surprisingly simple approximation tool for powers, roots, and division. |
Monday, April 27, 2015 |
Zandra Vinegar The lion, the witch and the chess board: Measuring entropy and creating optimal codes |
| Monday, May 4, 2015 |
Kaushik Basu Computing volume by guessing, checking, arguing, and lopping off heads! We will take a journey into an ancient problem — with a modern twist. The volume of a pyramid or cone can be computed using very interesting arguments which will show us where that strange factor of 1/3 comes from. Once we figure out a powerful method due to a student of Galileo’s, we will extend our methods into a more interesting object using symmetry, a touch of physics, and your imagination. |
Monday, May 4, 2015 |
Zandra Vinegar Noise, error correction and a perfectly horrible hat puzzle |
| Monday, May 11, 2015 |
Zandra Vinegar Mathemagical Card Tricks Even wished you were telepathic or telekenetic? Well, I can’t teach you that, but I can show you how to seem like you have aces up your sleeve! |
Monday, May 11, 2015 |
Jan Reimann Penn State The Problem of Measure We will explore a question that has arguably shaped modern mathematics like few others: How do we define the length/area/volume of a set? This is not hard for very simple sets like rectangles or triangles, but can we actually do it in a consistent way for ALL sets? |
| Monday, May 18, 2015 |
Half Math, Half Party | Monday, May 18, 2015 |
Half Math, Half Party |
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