These lecture notes treat some current aspects of two closely interrelated topics from the theory of convex polytopes: the shapes of f -vectors, and extremal constructions. The study of f -vectors has had huge successes in the last forty years. The most fundamental one is undoubtedly the “g-theorem,” conjectured by McMullen in 1971 and proved by Billera & Lee and Stanley in 1980, which characte...

The lecture will be an introduction to the model of economic equilibrium. The basic concepts: preferences, initial endowments and market clearing prices will discussed in general and by means of examples. I will indicate how fixed point theorems are used to demonstrate the existence of equilibrium prices and sketch an algorithm for Brouwers theorem. If time permits, there will be some remarks o...

hybrid learning 4th international conference ichl 2011 hong kong china august 10 12 2011 proceedings lecture notes in computer science. Book lovers, when you need a new book to read, find the book here. Never worry not to find what you need. Is the hybrid learning 4th international conference ichl 2011 hong kong china august 10 12 2011 proceedings lecture notes in computer science your needed b...

These lecture notes are dedicated to Dierk Rainer on the occassion of his 60th birthday in 2001. He pioneered the systematic treatment of the low-energy scale in the electronic theory of condensed matter.

Some course notes on Donsker’s theorem. These are for Math 7880-1 (“Topics in Probability”), taught at theDeparment ofMathematics at the University of Utah during the Spring semester of 2005. They are constantly being updated and corrected. Read them at your own risk. The authors thanks the National Science Foundation for their continued support. 1