# Category Archives: Teaching

## Analysis of Boolean Functions – week 4

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

## Analysis of Boolean Functions – Week 3

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

## Analysis of Boolean functions – week 2

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

## Analysis of Boolean Functions – week 1

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

## High Dimensional Expanders: Introduction I

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 | Tagged | 4 Comments

## Course Announcement: High Dimensional Expanders

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 will take place in Room 110 of the mathematics building … Continue reading

Posted in Algebra, Combinatorics, Geometry, Teaching | Tagged | 2 Comments

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

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

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

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## The Beauty of Mathematics

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

## A Proof by Induction with a Difficulty

The time has come to prove that the number of edges in every finite tree is one less than the number of vertices (a tree is a connected graph with no cycle). The proof is by induction, but first you need … Continue reading

Posted in Teaching, What is Mathematics | Tagged , | 17 Comments