Related papers: Dream of a Christmas lecture
The goal of this thesis is threefold: first, to provide a general semantic setting for reasoning about incremental computation. Second, to establish and clarify the connection between derivatives in the incremental sense and derivatives in…
High-dimensional computational challenges are frequently explained via the curse of dimensionality, i.e., increasing the number of dimensions leads to exponentially growing computational complexity. In this commentary, we argue that…
In this paper, we trace the development of the theory of the calculus of variations. From its roots in the work of Greek thinkers and continuing through to the Renaissance, we see that advances in physics serve as a catalyst for…
The 175th anniversary of the ASA provides an opportunity to look back into the past and peer into the future. What led our forebears to found the association? What commonalities do we still see? What insights might we glean from their…
This article was prepared in connection with the 2009 Barnett lecture at the University of Cincinnati, and deals with various classes of fractal sets and analysis on them.
Data science is the business of learning from data, which is traditionally the business of statistics. Data science, however, is often understood as a broader, task-driven and computationally-oriented version of statistics. Both the term…
The "Millennium Prize Problems" have a place in the history of mathematics. Here we tell some little-known anecdotes from the perspective of the planner of that project. These stories are far from their end; more likely they are just at…
This text arises from teaching advanced undergraduate courses in differential topology for the master curriculum in Mathematics at the University of Pisa. So it is mainly addressed to motivated and collaborative master undergraduate…
A few remarks on how mathematics quests for freedom.
We provide a syllabification algorithm for the Divine Comedy using techniques from probabilistic and constraint programming. We particularly focus on the synalephe, addressed in terms of the "propensity" of a word to take part in a…
Many pledges are made in the course of an election campaign, forming important corpora for political analysis of campaign strategy and governmental accountability. At present, there are no publicly available annotated datasets of pledges,…
This article has his origin in some lectures given at the University of Bologna, inside an interdisciplinary program of mathematics, history of science, physics and philosophy. Since they are at the junction of these fields, movement and…
Many people enjoy classical symphonic music. Its diverse instrumentation makes for a rich listening experience. This diversity adds to the conductor's expressive freedom to shape the sound according to their imagination. As a result, the…
We identified three most challenging points related to diverse, equitable, and inclusive (DEI) issues. First, the majority of our students entering the College lack the math skills essential to success in Calculus, as basic as College…
This lecture note is hopefully helpful to undergraduate and postgraduate students or beginning Ph.D students both in theoretical physics and in applied mathematics. Modern terminology in differential geometry has been discussed in the book…
In this paper, I explore what mathematical research can tell us about ourselves, and our role in the world, using examples from my own experience. The paper is a sequel to my piece "Mathematics is a Quest for Truth", published in the…
This is the transcript of a lecture given at UMass-Lowell in which I compare and contrast the work of Godel and of Turing and my own work on incompleteness. I also discuss randomness in physics vs randomness in pure mathematics.
Dialects introduce syntactic and lexical variations in language that occur in regional or social groups. Most NLP methods are not sensitive to such variations. This may lead to unfair behavior of the methods, conveying negative bias towards…
Several thoughts are presented on the long ongoing difficulties both students and academics face related to Calculus 101. Some of these thoughts may have a more general interest.
The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated…