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The London Mathematical Society Program on

MENTORING AFRICAN RESEARCH in MATHEMATICS

with the collaboration and support of










The First Edition of the

Namibian International Spring School in Mathematics


Windhoek, Peter Katjavivi Lecture Hall, UNAM, October 23-27, 2022



TITLES AND ABSTRACT

program






Alessio Corti,
Imperial College, London
The LMS-MARM-NCRST lectures on  "From the Integrals of elementary functions to the monodromy of the Picard-Fuchs Equations"  or  "a friendly interdisciplinary introduction to Algebraic Geometry"

Why is so easy to express the integral of (x3-x2)-1 in terms of elementary functions while is so hard to find the same with (x3-x)-1? Following the Arianna thread to solve the enigma of this exciting yellow drama will surprisingly provide a friendly introduction to algebraic geometry, from a truly interdisciplinary point of view. The course is divided in four lectures of  fifty minutes each, as follows

Summary
  • Integrals and elementary functions
  • Plane algebraic curves: conics and cubics
  • Elliptic integrals and parametrizations of plane cubics
  • The complete elliptic integral and the Picard–Fuchs equation. The global monodromy of the Picard–Fuchs equation



Jaqueline Godoy Mesquita, Universidade de Brasilia
TWAS-TYAN



The LMS-MARM-Rössing Lectures on "Dynamic equations on time scales and applications"

The purpose of the short course is to give an elementary introduction to a new important emerging subject, that of Time Scale Calculus. A time scale is nothing but a non-empty closed subst of the real line. For instance the set N of the natural numbers is atime scale, while Q (the set of rational number) is not. The purpose of the calculus of time scales, initiated by Stefan Hilger is that of unifying discrete (e.g. difference equations) and continuous  (e.g. ordinary differential equations) analysis. Some applications will be discussed.

Summary
  • The "Delta" derivative and jump operators:
  • Classification of points in time scales;
  • From continuous to discrete, and conversely, with application to dynamical systems



Marina Marchisio,
Università di Torino,
Italy






The LMS-MARM-Pupkewitz Lectures on  "Teaching and learning Mathematics in the Digital Era"

The Covid-19 pandemic has accelerated a process of substantial renewal of teaching with technologies. In this new perspective teachers were required to make an educational investment that is increasingly capable of innovating and differentiating teaching strategies to make them more suitable for the current era and the needs of learnerss, taking advantage of the digital skills.
The mini-course is focused on the key role of the Digital Learning Environments in the teaching and learning processes of Mathematics and other STEM disciplines, the methodologies and theoretical approaches that they allow to introduce and to empower like adaptive teaching, problem posing and solving, automatic formative assessment, collaborative learning and team working. The use of Learning Analytics and Open Educational Resources will also be discussed and finally some examples of good practices will be presented. During the mini-course the participants will be invited to reflect on the challenges of the new hybrid post-covid scenario and will be guided in the design of teaching activities. The course is devoted to both students and scholars professionally interested in mathematical training as well as to math teachers in the High school who wants to explore new teaching ways to be implemented with their own learners, who are  alsowarmly encouraged to actively participate to the lectures.

Summary
  • Interated Digital Learning Environments: theoretical frameworks and applications
  • Innovative methodologies and design of didactic activities
  • Open Educational Resources, Leaning Analytics and Good Practices



Paolo Piccione,
Universidade de Sao Paulo,
Brasil



The LMS-MARM-UNAM-NUST Lectures on "From the Gauss' Egregium Theorem to the Semi-Riemannian Geometry"

The celebrated Egregium Theorem by Gauss says that the extrinsic geometry of a regular surface in the euclidean real 3-dimenional space is entirely determined by its intrinsic geometry (the coefficients of the first fundamental form). The importance of this theorem is that it paves the way to build on solid foundations the Riemannian and semi-riemannian geometry. The latter had a great impulse motivated by the universe models inspired by the special and general relativity.

Summary
  • Regular surfaces in R3, vector fields, the first fundamental form,
  • Second fundamentalk form, covariant derivative of a vector field along a curve, geodesics:
  • The Egregium Theorem by Gauss:
  • What is the semi-riemannian geometry and what has it to do with Mathematical Physics?



Luigi Preziosi, Politecnico di Torino,
Italy



The LMS-MARM-AngloAmerican Lectures on "Mathematical modelling for biomedical and environmental sciences"

The aim of the lectures is to teach how to conceive mathematical models for specific applications stating from the related phenomenological observation of the phenomena involved. The basic mathematical tools will then be explained. So, with the aim of pairing mathematical frameworks and application the following topics will be covered:
  • Ordinary differential equations, population dynamics and epidemics
  • reaction diffusion equations and drug delivery
  • Free boundary problems and tumour growth
  • Fluid mechanics of  sand movement and mitigation strategies