Scientific Programme and Courses

Academic Year 2022-2023

The International Mathematics Master is designed to prepare students for international-level PhD research programs in mathematics.

The IMM academic program for 2022-2023 consists of four courses in fundamental and central areas of mathematics and its applications. Each course will be taught by a small “team” of junior and senior professors, all of whom work in prestigious universities and are active in research at an international level. As long as the pandemic situation does not get worse, all courses will be taught in a hybrid mode, with some intensive weeks of in person teaching by visiting international professors and tutors, as well as online classes and tutorials for the remaining weeks. The final list of courses is the following:

Fall Semester 2022

Abstract Algebra

Mathematical Analysis

Spring Semester 2023

Functional Analysis

Dynamical Systems

The program is a fully accredited Master Degree awarded by COMSATS University Islamabad and the official degree certificate and transcripts are complemented by a certificate and letter confirming the details of the program and the philosophy and structure of the International Mathematics Master.

Curriculum

The IMM curriculum is greatly inspired by the well-established ICTP Diploma program in Mathematics, and is fully focused on consolidating the fundamental mathematics which students need in order to embark on a high-level research PhD program. It consists of 8 courses over 2 years in order to allow students to fully master the fundamental, albeit advanced, topics which constitute the core knowledge necessary before the specialization required in a PhD course of studies. The courses are offered on a two-year cycle. First- and second-year students take the same set of courses in any given year.

While this is essentially a standard curriculum for Master’s programs, it is not the case in most developing countries where Master’s programs are often based on a philosophy of premature specialization, leaving students with an unsatisfactory foundation on which to base their research, and the students who continue on to PhDs often end up working in narrow and abstract topics which do not have international interest or relevance. Within this landscape, the IMM is meant to become the elite program for students who are highly motivated to develop a research-based academic career in mathematics.

Teaching

The IMM teaching methodology is based on a combination of online teaching, using a variety of methods such as pre-recorded and live online lectures and tutorials, spread out over the entire semester, with several weekly sessions akin to regular courses, and intensive in-person visits by the international faculty which may last one or two weeks and during which the students focus completely on the one course given by the visiting professor(s) and have the opportunity to interact fully with them.

An international full-time academic program manager/senior tutor provides continuity and is a main academic reference point for the students and for the faculty, assisting with the actual teaching as well as coordinating the schedule for classes, tutorials and examinations.

Thesis

The purpose of the thesis is to foster the ability to investigate independently a non-trivial mathematical topic or result, to find relevant books and papers, to organize the relevant material, and to present clearly the results of the investigation in both oral and written forms. The thesis is written under regular supervision of an international or local supervisor (or both), during the third and fourth semesters. Students writing theses with local faculty have the option of taking one relevant course given by local faculty in place of a course given by international faculty.

Previous Years

Spring Semester 2022

LINEAR ALGEBRA

Daniele Angella (Firenze, Italy)
Diletta Martinelli (Amsterdam, Netherlands)
Maurizio Parton (Chieti-Pescara, Italy)
Francesco Pediconi (Firenze, Italy)

DIFFERENTIAL GEOMETRY

Marco Abate (Pisa, Italy)
Fabrizio Bianchi (Lille, France)
Eleonora Di Nezza (Ecole Polytechnique, Paris, France)
Francesca Tovena (Rome, Italy)

Matteo Fiacchi (Course Tutor, Pisa, Italy)

Fall Semester 2021

COMPLEX ANALYSIS

Alberto Abbondandolo (Bochum, Germany)
Gabriele Benedetti (Amsterdam, Netherlands)
Anna Miriam Benini (Parma, Italy)
Nuria Fagella (Barcelona, Spain)

PROBABILITY AND STATISTICS

Gianmarco Bet (Firenze, Italy)
Sophie Dabo-Niang (Lille, France)
Franco Flandoli (Scuola Normale Superiore, Pisa, Italy)
Carina Geldhauser (Lund, Sweden)


The faculty and students will also be supported throughout the academic year by tutors Douglas Coates and Dominic Veconi and by other tutors specific to each course.

Spring Semester 2020

COMPLEX ANALYSIS - Daniele Angella & Tutor Francesco Pediconi (10/02-21/02 2020), Alberto Abbondandolo & Gabriele Benedetti (23/03-17/04 2020, distance learning)

NUMERICAL LINEAR ALGEBRA - Krerley Oliveira & Thales Vieira (04/05-09/06/2020, distance learning), Jean Barbier (22/06-03/07/2020, distance learning)

Fall Semester 2019

ADVANCED DIFFERENTIAL GEOMETRY - Marco Abate & Tutor Fabrizio Bianchi (14/10 - 25/10 2019)

QUALITATIVE THEORY OF ODEs- Mark Roberts (11/11 - 22/11 2019), Sergey Tikhomirov & Tutor Yulia Petrova (25/11 - 29/11 2019)

ALGEBRAIC TOPOLOGY - Michel Jambu (4/12 - 13/12 2019)

Resident Semester Tutor: Douglas Coates


Fall Semester 2020

COMMUTATIVE ALGEBRA - Lothar Göttsche, Volkmar Welker, Sarfraz Ahmad & Tutor Angela Tabiri (September 2020-January 2021, distance learning)

MATHEMATICAL ANALYSIS - Emanuel Carneiro, Jose M Conde & Tutors Alexandra Otiman and Fabrizio Bianchi (September 2020-January 2021, distance learning)

Spring Semester 2021

FUNCTIONAL ANALYSIS - Sahibzada Waleed Noor, Alfonso Sorrentino (February-May 2021, distance learning)

DYNAMICAL SYSTEMS - Stefano Luzzatto, Jeroen Lamb, Liviana Palmisano (February-May 2021, distance learning)

  • • Advanced algebra

    • Advanced topology

    • Mathematical analysis I

    • Differential geometry

    • Complex analysis

    • Numerical algebra and analysis

    • Qualitative differential equation

    • Probability and statistical analysis

  • • Functional analysis

    • Mathematical analysis-II

    • Differential topology

    • Commutative algebra

    • Algebraic geometry

    • Enumerative combinatorics and discrete geometry

    • Homological algebra

    • Operator theory

    • Symmetry methods and conservation laws for differential equations

    • Mathematical biology

    • Advance partial differential equations.

    • Scientific computing

  • • To Be Announced