This week, we'll continue with our exploration of ciphers by reviewing the reverse, Caesar, and Polybius Ciphers. We'll also learn about the Pigpen and Rail Fence Cipher.

This week, we'll continue with our exploration of ciphers by reviewing the reverse, Caesar, and Polybius Ciphers. We'll also learn about the Pigpen and Rail Fence Cipher.

This week, we'll finish lesson 2 by practicing with the Rail Fence Ciphers. Afterward, we'll begin Lesson 3 by doing a recap of everything we've learned so far.

This week, we'll finish lesson 2 by practicing with the Rail Fence Ciphers. Afterward, we'll begin Lesson 3 by doing a recap of everything we've learned so far.

This Sunday, we'll review the problems from the quiz, finish up Lesson 3, and, if we have extra time, jump over to Lesson 10 to explore the puzzling island of Knights and Liars.

This Sunday, we'll review the problems from the quiz, finish up Lesson 3, and, if we have extra time, jump over to Lesson 10 to explore the puzzling island of Knights and Liars.

We will introduce definitions in the hopes of constructing the shortest possible string of 0s and 1s that contains all possible codes of a certain length.

We start this week at 4pm. All enrolled families should already have received an email from Doug with the Zoom link and materials. Note that we are NOT posting materials publicly this year, because we do not have copyright permission to do so. If you did not receive Doug's email, please contact Oleg to confirm your registration.

We started the year with a fun competition/icebreaker! Students were assigned different groups for different parts of the competition, which were themed around algebra, arithmetic/number theory, geometry, and combinatorics/probability respectively.

Understanding planetary habitability is key to understanding how and why life developed on Earth as well as whether life is present on planets that orbit different stars (exoplanets). Whether a planet could be habitable is determined primarily by the planet's climate. This lecture will address insights we've gained from studying Earth's climate and how those have been used to make predictions about which exoplanets might be habitable, and how astronomical observations indicate the possibility of new climatic regimes not found on modern Earth. Finally, the lecture will cover some questions about the future of humanity and the Fermi paradox.

Dorian Abbot is an Associate Professor of Geophysical Sciences at the University of Chicago. In his research he uses mathematical and computational models to understand and explain fundamental problems in Earth and Planetary Sciences. Professor Abbot has also worked on problems related to climate, paleoclimate, the cryosphere, planetary habitability, and exoplanets. Recently he's been focusing on terrestrial exoplanets and habitability. He has an undergraduate degree in physics and a PhD in applied math, both from Harvard University.

Understanding planetary habitability is key to understanding how and why life developed on Earth as well as whether life is present on planets that orbit different stars (exoplanets). Whether a planet could be habitable is determined primarily by the planet's climate. This lecture will address insights we've gained from studying Earth's climate and how those have been used to make predictions about which exoplanets might be habitable, and how astronomical observations indicate the possibility of new climatic regimes not found on modern Earth. Finally, the lecture will cover some questions about the future of humanity and the Fermi paradox.

Dorian Abbot is an Associate Professor of Geophysical Sciences at the University of Chicago. In his research he uses mathematical and computational models to understand and explain fundamental problems in Earth and Planetary Sciences. Professor Abbot has also worked on problems related to climate, paleoclimate, the cryosphere, planetary habitability, and exoplanets. Recently he's been focusing on terrestrial exoplanets and habitability. He has an undergraduate degree in physics and a PhD in applied math, both from Harvard University.

Understanding planetary habitability is key to understanding how and why life developed on Earth as well as whether life is present on planets that orbit different stars (exoplanets). Whether a planet could be habitable is determined primarily by the planet's climate. This lecture will address insights we've gained from studying Earth's climate and how those have been used to make predictions about which exoplanets might be habitable, and how astronomical observations indicate the possibility of new climatic regimes not found on modern Earth. Finally, the lecture will cover some questions about the future of humanity and the Fermi paradox.

Dorian Abbotis an Associate Professor of Geophysical Sciences at the University of Chicago. In his research he uses mathematical and computational models to understand and explain fundamental problems in Earth and Planetary Sciences. Professor Abbot has also worked on problems related to climate, paleoclimate, the cryosphere, planetary habitability, and exoplanets. Recently he's been focusing on terrestrial exoplanets and habitability. He has an undergraduate degree in physics and a PhD in applied math, both from Harvard University.

Understanding planetary habitability is key to understanding how and why life developed on Earth as well as whether life is present on planets that orbit different stars (exoplanets). Whether a planet could be habitable is determined primarily by the planet's climate. This lecture will address insights we've gained from studying Earth's climate and how those have been used to make predictions about which exoplanets might be habitable, and how astronomical observations indicate the possibility of new climatic regimes not found on modern Earth. Finally, the lecture will cover some questions about the future of humanity and the Fermi paradox.

Dorian Abbot is an Associate Professor of Geophysical Sciences at the University of Chicago. In his research he uses mathematical and computational models to understand and explain fundamental problems in Earth and Planetary Sciences. Professor Abbot has also worked on problems related to climate, paleoclimate, the cryosphere, planetary habitability, and exoplanets. Recently he's been focusing on terrestrial exoplanets and habitability. He has an undergraduate degree in physics and a PhD in applied math, both from Harvard University.

Understanding planetary habitability is key to understanding how and why life developed on Earth as well as whether life is present on planets that orbit different stars (exoplanets). Whether a planet could be habitable is determined primarily by the planet's climate. This lecture will address insights we've gained from studying Earth's climate and how those have been used to make predictions about which exoplanets might be habitable, and how astronomical observations indicate the possibility of new climatic regimes not found on modern Earth. Finally, the lecture will cover some questions about the future of humanity and the Fermi paradox.

Dorian Abbot is an Associate Professor of Geophysical Sciences at the University of Chicago. In his research he uses mathematical and computational models to understand and explain fundamental problems in Earth and Planetary Sciences. Professor Abbot has also worked on problems related to climate, paleoclimate, the cryosphere, planetary habitability, and exoplanets. Recently he's been focusing on terrestrial exoplanets and habitability. He has an undergraduate degree in physics and a PhD in applied math, both from Harvard University.

In this class, we will finish comparing binary digits and decimal digits (Chapter 23), and start discussing parity (oddness and even-ness of numbers, Chapter 24). On the way we will find time for a brief review of Roman numerals.

Nim is a simple combinatorial game in which players take a certain number of elements from a pile. The last person to take an item is the winner. We will play games of Nim with multiple setups in order to determine winning strategies. Eventually, we will define a number system based on Nim.

Nim is a simple combinatorial game in which players take a certain number of elements from a pile. The last person to take an item is the winner. We will play games of Nim with multiple setups in order to determine winning strategies. Eventually, we will define a number system based on Nim.

Nim is a simple combinatorial game in which players take a certain number of elements from a pile. The last person to take an item is the winner. We will play games of Nim with multiple setups in order to determine winning strategies. Eventually, we will define a number system based on Nim.

We will review last week's homework and then continue to explore parity -- the idea of odd and even numbers -- following Lesson 25 within our workbooks.

We will study lesson 26, in which we learn to use binary decompositions to perform a magic trick. From there we will review how to use the Russian abacus to represent, add and subtract multi-digit numbers.

We continue our study of geometry. We will review the students' practice quizzes to see what areas we may need to review. If the students do not need review, we will move on to teaching the Pythagorean theorem.

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

Practice quiz below.

Homework Assigned:

Please re-read pages 1 through 12 of the "Introduction to Geometry: Lesson 1" packet to review euclidean geometry definitions. The students do not have to do the problems in this packet.

Please read and attempt the questions on pages 8 through 11 of the "Introduction to Geometry: Lesson 3" packet. Again, these proofs will be challenging so it is okay if the students do not complete the proofs. They should give the problems their time and effort of course, though.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu or Naji Sarsam at najisarsam@g.ucla.edu if you have any questions, comments, or concerns!

We will finish up discussion of adding and subtracting binary numbers, and then take a recap quiz on binary numbers, odd and evens and Roman numerals. We will then discuss Chapter 29; using binary numbers to represent letters and characters. Finally we will learn how to play two mathematical games.

We continue studying the Pythagorean theorem. This is the last class of the Fall session!

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

The student should read as far as they can starting on page 8 of the "Introduction to Geometry: Lesson 3" packet. On each page, the student should make a serious effort to solve the proofs on their own. Again, these proofs will be challenging so it is okay if the students do not complete the proofs.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu or Naji Sarsam at najisarsam@g.ucla.edu if you have any questions, comments, or concerns!

We will be looking at the volume of the partition that makes up the house and using building blocks to construct the house to correspond to the partition.

We will be looking at the volume of the partition that makes up the house and using building blocks to construct the house to correspond to the partition.

We begin the quarter continuing our study of geometry. We introduce the notion of parallel lines. Please download and print out the packet below.

Zoom Information:

This class and the January 16th class will be held online via zoom. We will announce soon if classes in the following weeks will be online as well. Here is the Zoom info for our recurring meeting room:

No homework will be collected. We have attached a pdf of review questions of last quarter's material for students who wish to review.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu or Naji Sarsam at najisarsam@g.ucla.edu if you have any questions, comments, or concerns!

We study Cauchy induction, a beautiful modification of the usual induction. If traditional induction goes forward one step at a time, Cauchy jumps from n to 2n and then goes backward if he misses the needed number.

We will introduce two methods for computing the number of spanning trees in a graph: deletion-contraction and the miraculous Matrix Tree Theorem. We will need to take a detour to the land of matrices for the second method.

We continue studying parallel lines in the Euclidean plane. Please download and print out the Introduction to Geometry - Lesson 4 packet below.

Zoom Information:

This class will be held online via zoom. We will announce soon if classes in the following weeks will be online as well. Here is the Zoom info for our recurring meeting room:

We ask that all students read through pages 6 through 8 of the Introduction to Geometry - Lesson 4 packet (attached below). We also ask that the students attempt Problems 8 and 9.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu or Naji Sarsam at najisarsam@g.ucla.edu if you have any questions, comments, or concerns!

Josephus and his forty soldiers were trapped in a cave. This means that there was a total of 41 fighters in the circle. Let us number 1 the first fighter to raise his sword, let us number 2 the fighter to his right, etc. The goal of this lesson is to solve the following two problems.

Problem 1 What was the position of Josephus in the circle?

Problem 2 Suppose that there are n soldiers, including Josephus, in the cave. What should the position of Josephus be in order for him to stay alive?

Peano axioms provide a rigorous foundation for the natural numbers and arithmetic. We will list the axioms and develop competing systems for the counting numbers.

We will review the rules of Roman numerals, and do some problems associated with them. Then we will form small groups to learn a mathematical game and its winning strategy.

We ask that all students read through pages 6 through 8 of the Introduction to Geometry - Lesson 4 packet. We also ask that the students attempt Problems 8 and 9.

Homework Assigned:

We ask that students read pages 5 and 6, and attempt problem 3 in the Vector Geometry - Lesson 1 packet. We will be reviewing pages 3 and 4 of the packet next lesson, as some students expressed confusion. However, these pages are not strictly necessary for the students to complete the homework. As always, we will review the homework with the students next lesson to ensure their understanding.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu or Naji Sarsam at najisarsam@g.ucla.edu if you have any questions, comments, or concerns!

Peano axioms provide a rigorous foundation for the natural numbers and arithmetic. We will list the axioms and develop competing systems for the counting numbers. Can we make it all the way to the rational numbers with only a handful of axioms?

We ask that students read pages 5 and 6, and attempt problem 3 in the Vector Geometry - Lesson 1 packet. We will be reviewing pages 3 and 4 of the packet next lesson, as some students expressed confusion. However, these pages are not strictly necessary for the students to complete the homework. As always, we will review the homework with the students next lesson to ensure their understanding.

Homework Assigned:

We ask that students read and attempt all problems on pages 7 through 9 in the Vector Geometry - Lesson 1 packet.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

To celebrate our return to in-person, we'll have a competition day with some problems relevant to the last 4 weeks, as well as a potpourri of miscellaneous problems.

We continue studying vector geometry. Please download and print out the Vector Geometry - Lesson 1 packet below.

Location and Time:

This class will be held in person from 4 - 6 pm at Mathematical Sciences 6221.

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

We ask that students read and attempt all problems on pages 7 through 9 in the Vector Geometry - Lesson 1 packet. As always, we will review the homework with the students next lesson to ensure their understanding.

Homework Assigned:

We ask that students complete the Vector Geometry - Lesson 1 packet. Most students should have already completed the packet in lecture or potentially have one or two more pages left.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

The first hour will be a lecture by our instructor Natalie and me about hat puzzles. We invited other groups to listen. In the second hour, we will do the attached worksheet on hat puzzles.

Math Circle's own Natalie Deering and Nikita Gladkov have solved a fun problem about the combinatorics of ordinal numbers, and will present their findings!

We continue studying vector geometry. We will complete Vector Geometry - Lesson 1 and begin Vector Geometry - Lesson 2.

Location and Time:

This class will be held in person from 12 - 2 pm at Mathematical Sciences 5117 as it is Superbowl Sunday.

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

We ask that students complete the Vector Geometry - Lesson 1 packet. Most students should have already completed the packet in lecture or potentially have one or two more pages left.

Homework Assigned:

There will be homework due by the February 27th class. We ask that students complete problems 1, 2, 3, 11, and 12 in the Vector Geometry - Lesson 2 packet. The material in-between problems 3 and 11 (page 4 through the top of page 9) will be covered in class as it is quite difficult. The students do not need any of that material to answer the problems assigned for homework.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!

We will try to crack each other's codes from last class. We will then study the fencepost cipher, which rearranges letters in a much more complicated way than the reversal cipher that we met in the last class.

We continue working through the Vector Geometry - Lesson 2 packet.

Location and Time:

This class will be held in person from 4 - 6 pm at Mathematical Sciences 6221.

Required Resources:

A pencil, eraser, compass, and straightedge.

Homework Due:

We ask that the students complete problems 1, 2, 3, 11, and 12 in the Vector Geometry - Lesson 2 packet.

Homework Assigned:

None.

Contact Information:

Please reach out to the instructors Andy Shen at andyshen55@g.ucla.edu, Naji Sarsam at najisarsam@g.ucla.edu, or Rachel Zhang at rzhang319@g.ucla.edu if you have any questions, comments, or concerns!