Math & Computing Science Resources

A Few Math Resources

Open Math Notes is a repository of freely downloadable mathematical works in progress hosted by the American Mathematical Society (AMS) as a service to researchers, teachers and students.
Mathematical Reviews (MathSciNet®), edited by the AMS, is a useful reference tool for mathematician; this database contains entries for all notable and prominent mathematicians. This tutorial demonstrates its practical use, whilst the following page explores the rich history of Mathematical Reviews.
The interview with Yves Meyer published in May 2018 in the Notices of the American Mathematical Society, and his fascinating 2017 Abel Prize lecture, entitled Detection of gravitational waves and time-frequency wavelets.
A lecture by Benoît Mandelbrot on Fractals: 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, AMS, 2017.
Jean-Pierre Serre considers the other side of the issue with his funny lecture: How to Write Mathematics Badly. In the same spirit, Georges Perec wrote this parody of scientific publication by Experimental demonstration of the tomatotopic organization in the Soprano (Cantatrix sopranica L.). Georges Perec was a documentalist at the CNRS; I knew an economist who had stopped working. This economist would often say equally delirious things at conferences, where he was at a loss to present the work written mainly by his youngest co-author. Therefore, he would begin his presentations with long, irrelevant digressions (among other things his grandmother petitioned to Queen Victoria, etc.).
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 AMS: MathJax: A Platform for Mathematics on the Web (2012).
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.

Computer Science Resources

Donald Knuth's home page. Don Knuth is the author of the celebrated books: The Art of Computer Programming You can find there everything important on semi-numerical and numerical algorithms, \(\TeX\) etc.
The Digital Library of Mathematical Functions of the National Institute of Standards and Technology (NIST); R. Boisvert, C.W. Clark, D. Lozier, and F. Olver wrote a presentation published in the Notices of the AMS A special functions handbook for the digital age (2011). This new online library supersedes the celebrated book by M. Abramowitz and I. Stegun: the Handbook of Mathematical Functions.
The C++ programming language is still the most powerful language. Valgrind is a useful tool for memory leak debugging, profiling, etc.
NLopt is a free/open-source library for nonlinear optimization,
The NIST Statistical Reference Datasets (NIST StRD) for assessing the numerical accuracy of statistical software packages. This database is very useful for checking parts of statistical procedures.
Useful information on the issue of numerical accuracy of statistical software packages is available at B.D. McCullough's web page.

Online Lectures Material

The writing of the book supporting these lectures is in progress.

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