Archives 2014 – 2015

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.
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 Zoo
What 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 Wrangling
Once 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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