In this paper, I
have provided a brief introduction on M?bius transformation and explored some
basic properties of this kind of transformation. For instance, M?bius
transformation is classified according to the invariant points. Moreover, we
can see that M?bius transformation is hyperbolic isometries that form a group
action PSL (2, R) on the upper half
plane model.

Abstract:
Lecture notes in french of the lecture on surface tension given in 2015 and 2016 at the preparation to "Agr\'egation de physique" in the Ecole Normale Sup\'erieure de Lyon

Abstract:
These are the lecture notes for the introductory graduate course I taught at Yale during Spring 2007. I mostly followed [GS], [BGV], [AB], [Par2], and there are no original results in these notes.

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These are the lecture notes for the introductory course on Whitehead, Reidemeister and Ray-Singer torsions, given by the author at the University of Zurich in Spring semester 2014.

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This is a set of lecture notes that developed out of courses on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. Topics covered in these notes include the untyped lambda calculus, the Church-Rosser theorem, combinatory algebras, the simply-typed lambda calculus, the Curry-Howard isomorphism, weak and strong normalization, polymorphism, type inference, denotational semantics, complete partial orders, and the language PCF.

Abstract:
These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous foundation to modern dynamics, as well as field and gauge theories in physics, engineering and biomechanics. We give both physical and medical examples of Lie groups. The only necessary background for comprehensive reading of these notes are advanced calculus and linear algebra.

Abstract:
These lecture notes introduce the Galerkin method to approximate solutions to partial differential and integral equations. We begin with some analysis background to introduce this method in a Hilbert Space setting, and subsequently illustrate some computational examples with the help of a sample matlab code. Finally, we use the Galerkin method to prove the existence of solutions of a nonlinear boundary value problem.

Abstract:
These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as problems and bibliographic notes at the end of each chapter. The authors are currently preparing a set of slides based on the book that will be posted in the second half of 2012. More information about the book can be found at http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/.