Welcome to the 150th Carnival of Mathematics. This is a monthly digest of selected mathematical blogs, hosted each month on a different site. The 1st Carnival has been published in February 2007, so this tradition already continues for more than 10 years. Thanks to everyone who submitted their blog posts to the 150th Carnival!
Following the tradition, we first ask what do we know about 150. It is the number of groups of order 900, the number of integer solutions to x2+y2+z2 = 152 (allowing zeros and distinguishing signs and order), and the number of squares on the 5x5x5 Rubik’s cube. It is a Niven number (aka Harshad number), i.e. it is divisible by the sum of its digits, and an abundant number, i.e. the sum of its divisors exceeds 2×150.
Now to the highlights of some recent mathematical blogs. Ben Orlin, the author of Math with Bad Drawings blog, published new post (with drawings!) called The State of Being Stuck. It is based on Andrew Wiles’ answer to the question by Ben asked at the Heidelberg Laureate Forum 2016. Being stuck is a part of the research process, and is not something to be afraid of – this is what Andrew Wiles would like to emphasize when talking about mathematics to a broader public. This year, Ben went to the Heidelberg Laureate Forum again, and you may find his account of the event here. Another blog post about the Heidelberg Laureate Forum 2017 has been published by Katie Steckles on the Aperiodical.
And if you’re stuck at something and need a break, then perhaps you may find inspiration through looking at nature’s beauty – for example, LThMath suggests to look at Symmetry and Butterflies, which may reflect concepts from various areas of mathematics, ranging from analysis to algebra and statistics.
Speaking of statistics, John D. Cook discusses an interesting application in Randomized response, privacy, and Bayes theorem. Suppose you have a database with sensitive information, and you would like deliberately corrupt it with random noise to anonymise records. How this can be done in a way to preserve privacy while still keeping the data statistically useful?
Rachel Traylor wrote several posts for The Math Citadel website: The Central Limit Theorem Isn’t A Statistical Silver Bullet, where she shows how The Central Limit Theorem, for all its power and popularity, is not a one-stop result to be used for all occasions, and Cauchy Sequences: The Importance Of Getting Close. The latter is a wonderfully accessible explanation of the Cauchy property of sequences, taking time to rigorously examine every piece of the definition.
Anthony Bonato has been interviewing prominent mathematicians in a series of blog posts, most recently Eugenia Cheng, researcher in category theory and the author of How to Bake Pi and Beyond Infinity, and Jennifer Chayes, one of the leading researchers in network science, working at the interface of mathematics, physics, computational science and biology.
Now to discrete mathematics. Reduce The Problem: Permutations And Modulo Arithmetic is another post by Rachel Traylor which in a very accessible manner explains permutation and introduces the concept of isomorphism.
In EKR, Steiner systems, association schemes, and all that, Peter Cameron discussed a class of graphs which give a context to two major results in combinatorial mathematics: the construction of Steiner systems, and the Erdős–Ko–Rado theorem (this story has a continuation in his later post here). Steiner systems also lead to a winning strategy in the card game described in the post MINIMOGs and Mathematical blackjack by David Joyner.
In the Quanta Magazine, Erica Klarreich writes about the recent result on O’Nan moonshine by Ken Ono, John Duncan and Michael Mertens (see their paper Pariah moonshine in Nature Communications) in her article Moonshine Link Discovered for Pariah Symmetries. Another new article in the Quanta Magazine is Mathematicians Measure Infinities and Find They’re Equal by Kevin Hartnett. It introduces recent results by Maryanthe Malliaris and Saharon Shelah, which lead to their Third Hausdorff Medal 2017 award.
Ian Gent published Why the world’s toughest maths problems are much harder than a chess puzzle, and well worth US$1m at The Conversation. There he explains the n-queens completion problem and gives some comments to the recent paper written by Chris Jefferson, Peter Nightingale and Ian Gent and published in the Journal of Artificial Intelligence Research, where they show that this problem is NP-complete.
Several posts in September reported news on mathematical software and its applications, in particular Parallel multivariate multiplication by Bill Hart, and Types of Gaussian Elimination and more technical High Performance Meataxe Interface redesign by Richard Parker. Katie Steckles reported about the new largest generalised Fermat prime, discovered by the PrimeGrid project.
The Carnival of Mathematics is a monthly digest of mathematical blogs, hosted by a different blog each month. The 150th Carnival of Mathematics will be published here at the CoDiMa website. Submissions are accepted until the end of September. To see further guidelines and submit at item to Carnival 150, please see this page. You may also find there links to all previous carnivals.
The CoDiMa project supported my participation in “All Kinds of Mathematics Remind me of You: Conference to celebrate the 70th Anniversary of Peter J. Cameron“, held at the University of Lisbon, 24-27 July 2017. This conference brought together many colleagues, students and collaborators of Peter Cameron, and a diverse range of interesting mathematical research (covering Peter’s diverse range of interests) was presented and discussed.
This conference gave me the opportunity to present and discuss my recent algorithms and programs (in GAP/GRAPE) to exploit graph symmetry in graph colouring, in particular in the difficult problem of computing the chromatic number of a graph. I was also able to discuss the application of these programs to the determination of the “non-synchronizing” primitive permutation groups (of interest to researchers in semigroup and automata theory) of degree at most 255.
In June 2017 Alexander Konovalov took part in the conference “Groups, Rings and the Yang-Baxter equation” (Spa, Belgium). He gave a talk “GAP Group Rings Toolkit” with an overview of the functionality to work with group rings available in GAP and four of its packages, demonstrated the Jupyter kernel for GAP, and organised a coding sprint to work on the Wedderga package. As a result, Wedderga development version has been migrated from Bitbucket to GitHub (https://github.com/gap-packages/wedderga), and a new collaborator, Dr Sugandha Maheshwary (ISER Mohali), had submitted her first pull request to Wedderga.
We will run two additional GAP tutorials in the UK this summer:
- GAP tutorial as a part of the Summer School on Finite Geometry in Brighton on 26th-30th June 2017.
- GAP tutorial on August 13th-14th as a satellite event to the Groups St Andrews 2017 in Birmingham. It has independent registration from Groups St Andrews. The deadline for booking discounted accommodation on campus is July 25th, after that it will be only available at standard price subject to availability. See this page for further details and the link to the registration page.
Jointly with the Horizon 2020 OpenDreamKit project, we have organised the workshop “Computational Mathematics with Jupyter”, which took place at the International Centre for Mathematical Sciences in Edinburgh on 16-20 January 2017. You can find some reports from the workshop here:
On October 17-21, 2016 we organised the Second CoDiMa training school in Discrete Computational Mathematics in Edinburgh (our first school took place in Manchester in November 2015). This time it was hosted at the International Centre for Mathematical Sciences, and had been attended by 26 learners representing 11 institutions around the UK. The majority of them were PhD students in mathematics and computer science. Their participation was supported by the CoDiMa project, which covered their travel, accommodation and subsistence needed to attend the school.
The school started with the hands-on Software Carpentry workshop covering the UNIX command line and version control (instructed by Alexey Tarutin and Leighton Pritchard), and the Software Carpentry lesson on GAP given by Alexander Konovalov (for published versions of these lessons, see here, here and there on Zenodo). The 2-days Software Carpentry workshop created the basis for more in-depth explanation of the following topics on GAP and computational algebra during the remaining part of the week:
- debugging and profiling
- advanced GAP programming
- GAP type system
- distributed parallel calculations
- demonstration of the new GAP Jupyter interface
- examples of some algorithms and their implementations
delivered by Christopher Jefferson, Alexander Konovalov, Steve Linton, Markus Pfeiffer and Wilf Wilson. Furthermore, John Cremona gave a presentation of LMFDB (The L-functions and modular forms database project) which offered interesting insight into the internals of designing and maintaining mathematical database such as LMFDB. Also on Thursday Viviane Pons (Université Paris-Sud) gave an introduction to SageMath, and on the final day we had “Is your research software correct?” talk by the EPSRC Research Software Engineering Fellow Mike Croucher (Sheffield), and a panel discussion joined by Neil Chue Hong, who is the director of the Software Sustainability Institute.
For further details, please see the school webpage which contains links to the presentations and supplementary materials for all school’s programme. You can also find all #codima2016 tweets on Storify (they provide very good day by day coverage of the whole week), and school photos courtesy of ICMS here on Flickr. It was a really exciting event, and it is a great pleasure to thank everyone involved: all participants, speakers, instructors, helpers; Software Sustainability Institute and personally Giacomo Peru who coordinates Software Carpentry activities in the UK; all contributors to Software Carpentry lessons that we taught; ICMS staff for welcoming us and being attentive to all our requests; Blue Sky Catering for nice lunches; and Vittoria on the Bridge for the school dinner!
We plan at least three more such schools in 2017-2019. Besides training events, we also organise annual workshops. The first one was in the form of GAP-SageMath days at St Andrews in January 2016, and the next one is “Computational Mathematics with Jupyter” which we organise jointly with the Horizon 2020 project OpenDreamKit at the International Centre for Mathematical Sciences in Edinburgh on January 17-20, 2017.
Alexander Konovalov wrote two blog posts about the Software Carpentry lesson on GAP. The first one is “Programming with GAP”, written for the Software Carpentry website and telling how the lesson has been established. The second one is “Publishing Software Carpentry lesson on GAP” which contains more details about the research-like problem on which the lesson is based.
Jointly with the Horizon 2020 OpenDreamKit project, we are currently organising the workshop “Computational Mathematics with Jupyter”. It will take place at the International Centre for Mathematical Sciences in Edinburgh on 16-20 January 2017. Please see the workshop website here for further details.