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Scientific Programme Structure

The IMM programme leads to a fully accredited Master's Degree conferred by LUMS, complemented by a certificate granted by ICTP.

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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.

 

 

 

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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.

Program Structure

To meet the requirements, each student must enroll in a minimum of eight courses, including at least six from the core course list. Additionally, they must undertake a thesis project worth 6 credit hours for successful completion of the program.

Course Name

Course Type

Advance Algebra
Core
Advance Topology
Core
Mathematical Analysis I
Core
Differential Geometry
Core
Complex Analysis
Core
Numerical Algebra and Analysis
Core
Qualitative Differential Equations
Core
Probability and Statistical Analysis
Core
Functional analysis
Optional
Mathematical analysis-II
Optional
Differential topology
Optional
Commutative algebra
Optional
Algebraic geometry
Optional
Enumerative combinatorics and discrete geometry
Optional
Homological algebra
Optional
Operator theory
Optional
Symmetry methods and conservation laws for differential equations
Optional
Mathematical biology
Optional
Advance partial differential equations
Optional
Scientific computing
Optional

Admissions

Applicants are divided into two groups: "International Applicants" who have foreign citizenship and "Pakistani Applicants" who either hold Pakistani citizenship, have dual citizenship, or are Pakistanis residing outside the country.

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