# What is Mathematics Education, Really?

## Professor Alexandre Borovik

### 6:00-7:20 pm

#### Newton Lecture Theatre  INB0114 in the Isaac Newton building, University of Lincoln

As I argue in my paper, the current crisis in the school level mathematics education is a sign that it reaches a bifurcation point and is under increasing pressure to split in two streams:

* education for a selected minority of children / young people who, in their adult lives, will be filling increasingly small share of jobs which really require mathematical competence (I call them mathematical makers); and

** basic numeracy and mathematics awareness classes for the rest of population, end users of technology saturated by mathematics invisible to them.

In my talk, I will discuss challenges in mathematics education which will arise from this split. This is a theme which is rarely discussed in…

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## New paper accepted in Journal of Number Theory

The paper by Sandro Mattarei and Roberto Tauraso, From generating series to polynomial congruenceshas been accepted for publication in Journal of Number Theory.

(You may find the final version in preprint form at https://arxiv.org/pdf/1703.02322.pdf.)

Abstract: Consider an ordinary generating function $\sum_{k=0}^{\infty}c_kx^k$, of an integer sequence of some combinatorial relevance, and assume that it admits a closed form $C(x)$. Various instances are known where the corresponding truncated sum $\sum_{k=0}^{q-1}c_kx^k$, with $q$ a power of a prime $p$, also admits a closed form representation when viewed modulo $p$. Such a representation for the truncated sum modulo $p$ frequently bears a resemblance with the shape of $C(x),$ despite being typically proved through independent arguments. One of the simplest examples is the congruence $\sum_{k=0}^{q-1}\binom{2k}{k}x^k\equiv(1-4x)^{(q-1)/2}\pmod{p}$ being a finite match for the well-known generating function $\sum_{k=0}^\infty\binom{2k}{k}x^k= 1/\sqrt{1-4x}$. We develop a method which allows one to directly infer the closed-form representation of the truncated sum from the closed form of the series for a significant class of series involving central binomial coefficients. In particular, we collect various known such series whose closed-form representation involves polylogarithms ${\rm Li}_d(x)=\sum_{k=1}^{\infty}x^k/k^d$, and after supplementing them with some new ones we obtain closed-forms modulo $p$ for the corresponding truncated sums, in terms of finite polylogarithms $\pounds_d(x)=\sum_{k=1}^{p-1}x^k/k^d$.

Dr Evgeny Khukhro and The President of the University of Brasilia Professor Márcia Abrahão Moura

On 3 July a ceremony was held in University of Brasilia on occasion of bestowing on Evgeny Khukhro the title of Professor Honoris Causa.

The ceremony began with the British national anthem, followed by the national anthem of Brazil. Then Dr Emerson de Melo delivered a presentation on behalf of
the Department of Mathematics for the case of Evgeny Khukhro’s title. The President (Reitora) of the University Professor Márcia Abrahão Moura declared the Council’s decision of bestowing on Dr Evgeny Khukhro the title of Professor Honoris Causa, presented Evgeny Khukhro with the correspoding certificate, and adorned him with the academic stole in the colours of University of Brasilia. After that Dr Khukhro gave a short talk. He thanked the Reitora, other dignitaries present, colleagues and guests for the honour of the title, expressed his deep…

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## Industrial and Financial Mathematics module in Lincoln

Mathematics students in their second year gave great feedback on their Industrial and Financial Mathematics module. This module is intended to showcase some of the industrial applications of mathematics, with an emphasis in the second half on finance.

A series of guest lectures were given by people from industry who use mathematics in their line of work. Talks were given by people who have worked in:

• Banking (Goldman Sachs and Santander)
• Logistics (SYSTRA)
• Engineering (Siemens)
• Medicine (University Medical Center Groningen)

Students also had to produce a report for a simulated food-tech start-up in which they used big data analytical techniques to help launch a new product line.

## MEQ results: the best school in the University

As a result of the latest Module Evaluation by students (MEQ) the School of Mathematics and Physics came first amongst all the school in the University of Lincoln! The competition was tough, as the second school is just 1% behind us! Congratulations!

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## Conference “Groups, Rings and the Yang–Baxter equation”

Evgeny Khukhro gave an invited talk at the international conference “Groups, Rings and the Yang–Baxter equation”, which was held in Spa, Belgium, on June 18–24, 2017. He spoke on “Almost Engel finite, profinite, and compact groups”.

## Maths and physics outreach lectures in Isaac Newton Building

On Tuesday, 9th May 2017, the Lecture Theater of the Isaac Newton Building, was used for the first time for an outreach event, organised by Sandro Mattarei in collaboration with the university’s Marketing Team. Students from the Lincoln College attended a double lecture in Maths and Physics. Marco Pinna’s lecture on the mathematics of bird flocking was followed by a lecture on Platonic solids delivered by Sandro Mattarei.

## Maths & Physics at Lincoln: EDT Headstart residential course

On 11th July 2017 several members of the School of Mathematics and Physics will contribute lectures and workshops to a Headstart residential course at the University of Lincoln (see EDT Headstart). Thirty students in Year 12 from all over the country will stay from 10th to 13th July to experience several taster session of Mathematics, Physics, and Engineering.

The Maths and Physics activities will span six hours of 11th July and include sessions on the following topics:

• What is Chaos?
• Patterns in nature: mathematical views of the natural world
• Group Theory: algebra of transformations
• Pascal’s triangle and the Sierpinski gasket
• There’s more to light than meets the eye!

## Conference in Giessen

Anitha Thillaisundaram attended the Norddeutsches Gruppentheorie Kolloquium at Schloss Rauischholzhausen of the University of Giessen, Germany from June 9th-10th, 2017. She gave a talk in German on “Maximal subgroups of branch groups”.

## Call for new Kourovka problems in Group Theory

Evgeny Khukhro announced a start for preparation of the new 19th edition of the Kourovka Notebook” — the famous collection of unsolved problems in Group Theory and related areas. This publication originated in Novosibirsk in 1965, since then gained world-wide popularity and now includes more than 1000 problems by about 400 authors from all over the world. Nowadays it is published on the web but still retains discrete issues appearing every 3–4 years, with more frequent updates online.

For more than 50 years the “Kourovka Notebook” has served as a unique means of communication for researchers in Group Theory and nearby fields of mathematics. Maybe the most striking illustration of its success is the fact that more than 3/4 of the problems from the first issue have now been solved! (Of course, it is often easier to propose a new problem than to solved an old one…)

Everybody is welcome to propose new problems to be included in the new edition. Problems may “belong” to those who propose them, or otherwise. In the latter case, one can indicate the author(s) of the problem (if different from the person proposing), or simply that this is a “well-known problem”. In order that the progress would be “measured” and seen, the preference is usually given to concrete questions that admit “yes” or “no” answers.

The Editors also welcome any other comments on, or/and solutions of, existing problems; the current version on Arxiv incorporates all comments so far.

The problems and comments can be sent to any of the Editors (preferably by e-mail):

Evgeny Khukhro khukhro@yahoo.co.uk or Victor Mazurov mazurov@math.nsc.ru