Related papers: Notes for Miscellaneous Lectures
We summarize four different versions of our course notes on the limits of mathematics.
This paper is simply a collection of process diagrams for further use and reference. These are diagrams about different approaches to research.
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…
A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.
In this note I describe reliability standards for writing and reviewing mathematical papers; these standards are (in my opinion) vital for the progress of mathematics. I give examples of applying the described or other reliability…
These lecture notes accompanied the course Time-Frequency Analysis given at the Faculty of Mathematics of the University of Vienna in the summer term 2021. The material is suitable for an advanced undergraduate course in mathematics or a…
This paper shares a classroom story from Fall 2022 to Spring 2025 about a learner centered routine in undergraduate mathematics. I use four steps: an opening question, a short mini lecture about meaning, structured small group work, and a…
Today's lectures are often talks following a straight line of slides. In many lectures the process of content teaching is not as efficient as it could be. Technologies, such as smart-phones and wireless communication, enable a new level of…
These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…
The authors describe their approach to teaching a course on finite fields and combinatorial applications, including block designs and error-correcting codes, using a hybrid of lectures and active learning. Under the discussed classroom…
Informal lecture notes with examples on sheaf theory and the derived category of sheaves; sheaves and Morse theory; perverse sheaves, and some applications to representation theory. Added Oct 2021: cellular perverse sheaves. Proofs are…
This document contains the notes of a lecture I gave at the "Journ\'ees Nationales du Calcul Formel" (JNCF) on January 2017. The aim of the lecture was to discuss low-level algorithmics for p-adic numbers. It is divided into two main parts:…
The notes contain a streamlined account on stability of univariate polynomials and related problems
These are notes of a series of lectures on sieves, presented during the Special Activity in Analytic Number Theory, at the Max-Planck Institute for Mathematics in Bonn, during the period January--June 2002.
These are notes of a graduate course on representations of non-compact semisimple Lie groups given by the author at MIT.
The goal of these lecture notes is to introduce the developing research area of gravitational-wave phenomenology. In more concrete terms, they are meant to provide an overview of gravitational-wave sources and an introduction to the…
These are Notes prepared for nine lectures given at the Mathematical Sciences Research Institute, MSRI, Berkeley during the period January--March 1995. It is a pleasant duty to record here my gratitude to MSRI, and its staff, for making…
These are notes based on a course that I gave at the University of Chicago in Fall 2016 on "Loop measures and the loop-erased random walk." This is not intended to be a comprehensive view but rather a personal selection of some key ideas…
We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in Europe. While some of the core ideas stay and have stayed…
The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings,…