A Few Math Resources

• Open Math Notes is a repository of freely downloadable mathematical works in progress hosted by the American Mathematical Society as a service to researchers, teachers and students.
• Mathematical Reviews (MathSciNet®), edited by the American Mathematical Society, is a useful reference tool for mathematicians (Every decent mathematician is indexed there). Its practical use is given in this tutorial, while the following page gives an account on the history of Mathematical Reviews.
• The January 2013 and May 2011 issues of the Notices of the American Mathematical Society contain two introductory papers on wavelets: Wavelets (2013), vol 60, 66-76, , and Discrete wavelet transformations and undergraduate education (2011), vol 58, 656-666, .
  See also the interview with Yves Meyer published in May 2018 in the Notices of the American Mathematical Society , and his 2017 Abel Prize lecture, entitled Detection of gravitational waves and time-frequency wavelets.
• Two lectures by Benoît Mandelbrot on Fractals:
  • L'anneau fractal de l'art à l'art à travers la géométrie, la finance et les sciences,
  • Fractals in Science, Engineering and Finance (Roughness and Beauty).
• Three books on the art of writing mathematics: the two standard texts by respectively Paul Halmos, How to write mathematics (1970) , and the trio Donald Knuth, Tracy L. Larrabee, and Paul M. Roberts Mathematical Writing, Mathematical Association of America, 1989, with the updates by Donald Knuth. Steven Krantz has recently issued the second edition of his book A Primer of Mathematical Writing, American Mathematical Society, 2017.
  Jean-Pierre Serre considers the other side of the issue with his funny lecture: How to Write Mathematics Badly. In the same spirit, the parody of scientific publication by Georges Perec: Experimental demonstration of the tomatotopic organization in the Soprano (Cantatrix sopranica L.). Georges Perec was a documentalist at the CNRS; I knew an economist well who had stopped working, said things that were just as delirious in conferences where he was at a loss to present the works written mainly by his youngest co-author, and therefore began his presentation with long digressions (among other things his grandmother petitioned to Queen Victoria...).
• MathJax is an open source Javascript library that uses \(\LaTeX\) and MathML for displaying mathematics on webpages, which works on all modern browsers and that I'm using for my web pages. Further details are provided by the paper published in the Notices of the American Mathematical Society MathJax: A Platform for Mathematics on the Web (2012), vol 59, 312-316, .
• The Scholarly Open Access website contains a critical analysis of scholarly open-access publishing, and in particular provides a list of predatory journals and publishers that must be avoided. Further details are given in J. Beall Predatory publishers are corrupting open access, Nature 489, 179, (13 September 2012) DOI.
• Plagiarism.org: This organization provides research institutes and academic places with a database for deterring and detecting plagiarism.

The list of recommended machine learning (ML) and computing science (CS) resources for the lectures and the dissertations are respectively here (ML) and here (CS).

• 2010-: Institut Mines-Télécom Atlantique, Brest, lectures (in French) on nonstationary processes (Mathematical and Computational Engineering Lectures).
  My 3^rd year lectures on nonstationary processes for the academic year 2020-2021 will take place in March 2021. They have been quite rewritten from scratch, after reviewing a long series of papers and books (over 70 and counting) on these issues for Mathematical Reviews®. The new section on deep learning and AI is obviously expanding. The writing of the book supporting these lectures is in progress.
  List of past lectures for the academic year 2020-2021:
  • Lecture 1 (Monday 8^th March 2021): Volatility models. GARCH model: definition, properties, dependence structure, QML estimation.
  • Lecture 2 (Tuesday 9^th March 2021): Exponential GARCH model. Bootstrap methods and their application to model-free prediction and inference of univariate models. Multivariate models. Change-point models.
  • Lecture 3 (Monday 22^th March 2021): Long-range dependent and multifractal volatility models. Wavelet analysis of volatility processes.
  • Lecture 4 (Tuesday 23^th March2021): Volatility estimation of high frequency time series. Deep Learning: convolutional, recurrent and hybrid architectures, with the PyTorch and fast.ai libraries.