Alessio Corti,
Imperial College, London

The LMSMARMNCRST
lectures on
"From the
Integrals of elementary functions to the
monodromy of the PicardFuchs Equations"
or "a
friendly interdisciplinary introduction to
Algebraic Geometry"
Why is so easy to express
the integral of (x3x2)1 in terms of
elementary functions while is so hard to find
the same with (x3x)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
TWASTYAN

The LMSMARMRössing 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 nonempty 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 LMSMARMPupkewitz
Lectures on "Teaching and learning
Mathematics in the Digital Era"
The Covid19 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
minicourse 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 minicourse the
participants will be invited to reflect on
the challenges of the new hybrid postcovid
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 LMSMARMUNAMNUST Lectures
on "From the Gauss'
Egregium Theorem to the SemiRiemannian
Geometry"
The celebrated Egregium Theorem by Gauss says that
the extrinsic geometry of a regular surface in the
euclidean real 3dimenional 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 semiriemannian geometry. The latter had a
great impulse motivated by the universe models
inspired by the special and general relativity.
Summary
 Regular surfaces in R^{3},
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 semiriemannian geometry and
what has it to do with Mathematical Physics?




Luigi Preziosi, Politecnico
di Torino,
Italy

The LMSMARMAngloAmerican
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









