Category Archives: Teaching

Analysis of Boolean Functions – Week 7

Posted on October 13, 2013 by

Lecture 11 The Cap Set problem We presented Meshulam’s  bound for the maximum number of elements in a subset A of not containing a triple x,y,x of distinct elements whose sum is 0. The theorem is analogous to Roth’s theorem … Continue reading →

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Analysis of Boolean Functions week 5 and 6

Posted on October 7, 2013 by

Lecture 7 First passage percolation 1)  Models of percolation. We talked about percolation introduced by Broadbent and Hammersley in 1957. The basic model is a model of random subgraphs of a grid in n-dimensional space. (Other graphs were considered later as … Continue reading →

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Analysis of Boolean Functions – week 4

Posted on September 24, 2013 by

Lecture 6 Last week we discussed two applications of the Fourier-Walsh plus hypercontractivity method and in this lecture we will discuss one additional application: The lecture was based on a 5-pages paper by Ehud Friedgut and Jeff Kahn: On the number … Continue reading →

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Analysis of Boolean Functions – Week 3

Posted on September 18, 2013 by

Lecture 4 In the third week we moved directly to the course’s “punchline” – the use of Fourier-Walsh expansion of Boolean functions and the use of Hypercontractivity. Before that we  started with  a very nice discrete isoperimetric question on a … Continue reading →

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Analysis of Boolean functions – week 2

Posted on September 8, 2013 by

Post on week 1; home page of the course analysis of Boolean functions Lecture II: We discussed two important examples that were introduced by Ben-Or and Linial: Recursive majority and  tribes. Recursive majority (RM): is a Boolean function with variables … Continue reading →

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Analysis of Boolean Functions – week 1

Posted on September 3, 2013 by

Home page of the course. In the first lecture I defined the discrete n-dimensional cube and  Boolean functions. Then I moved to discuss five problems in extremal combinatorics dealing with intersecting families of sets. 1) The largest possible intersecting family … Continue reading →

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High Dimensional Expanders: Introduction I

Posted on November 12, 2011 by

Alex Lubotzky and I  are running together a year long course at HU on High Dimensional Expanders. High dimensional expanders are simplical (and more general) cell complexes which generalize expander graphs. The course is taking place in Room 110 of the mathematics building on … Continue reading →

Posted in Combinatorics, Teaching | 4 Comments

In how many ways you can chose a committee of three students from a class of ten students?

Posted on July 19, 2011 by

The renewed interest in this old post, reminded me of a more recent event: Question: In how many ways you can chose a committee of three students from a class of ten students? My expected answer: which is 120. Alternative … Continue reading →

Posted in Mathematics to the rescue, Riddles, Teaching | 1 Comment

Test Your Intuition (11): Is it Rational to Insure a Toaster

Posted on February 28, 2010 by

Here is a question from last year’s exam in the course “Basic Ideas of Mathematics”:   You buy a toaster for 200 NIS ($50) and you are offered one year of insurance for 24 NIS ($6).   a) Is it … Continue reading →

Posted in Probability, Rationality, Teaching, Test your intuition | Tagged , | 18 Comments

The Beauty of Mathematics

Posted on February 24, 2010 by

This semester I am teaching an introductory course in mathematics for students in other departments.  I taught a similar course last year entitled “Basic Ideas in Mathematics,” and this year, following a suggestion of my wife, I changed the name to “The Beauty of Mathematics”. Another … Continue reading →

Posted in Teaching | 26 Comments