The Department of Mathematics at Indraprastha Institute of Information Technology Delhi (IIIT-Delhi) announces its fUndergraduate Mathematics Summer Program at IIIT-Delhi. This programme is designed for undergraduate mathematics students who are in second or third year of their undergraduate studies. This program will be completely funded by IIIT-Delhi. The participants will attend the lectures on various topics in higher mathematics. They will get the chance to talk with IIIT-Delhi faculty members about mathematics to deepen their understanding and expertise of the subject. We believe that sincere candidates will benefit from this program by having a broader perspective on higher mathematics and its applications in other scientific domains. Therefore, we strongly encourage the students - who are interested in Mathematics and hope to pursue a career in this field - to apply.
Program
1. Crash courses on selected topics in Algebra, Analysis, Geometry & Topology, and Applied Mathematics.
2. Problem-solving sessions and group discussion.
3. Talks by experts.
Who can apply
Undergraduate students of 2nd and 3rd year
Selection process
The selection will solely be on the basis of merit, taking into account both academic records and a recommendation letter from a mathematics Professor who knows the individual well.
Local hospitality
During the training at IIIT-Delhi campus, meals and accommodation will be provided to all candidates. Travel support will be provided to all outstation candidates.
Registration
Schedule
Coming Soon..
Mentors & Teachers
Analysis
Satish Kumar Pandey (Mentor), Antika (Teacher), Aarushi Kansal (Teacher), Esha Jain (Teacher), Deep Chandra Pathak (Teacher)
Algebra
Nabanita Ray (Mentor), Bittu (Teacher), Kritika Aggarwal (Teacher), Nisha Kumari (Teacher)
Geometry & Topology
Prahllad Deb (Mentor), Ujjal Timshina (Teacher), Sourav Das (Teacher), Mahesh Dutt (Teacher)
Applied Mathematics
Ashish Kumar Pandey (Mentor), Anupam Singh (Teacher), Nitesh Sharma (Teacher), Sudhir Singh (Teacher)
Dr. Ashish Kumar Pandey
Affiliation: Assistant Professor, IIIT-Delhi
Area : Differential Equations
Syllabus: Distribution theory and its applications in Poses: (1) Distribution in 1d: test functions, definition and examples of a distribution, order, derivative, product by a smooth function, support, sequences; (2) Distribution in higher dimensions; (3) Convolution of distributions: differentiation and integration inside the bracket, tensor products, convolution, application to constant coefficient PDEs; (4) Fourier transform: Schwartz space, Fourier transform in Schwartz space, space of tempered distribution and their Fourier transform; (5) Sobolev spaces; (6) Applications in Laplace and heat equations.
×Dr. Kaushik Kalyanaraman
Affiliation: Assistant Professor, IIIT-Delhi
Area : Geometry and Topology
Syllabus: Elementary Applied Topology: Homology and Cohomology: Basics of Topology: Topological spaces – set theory; equivalence relations; definition of a topology; discrete, product, and quotient topology; vector bundles; sheaf theory – presheaves, sheaves, posets, direct limit, stalks, morphisms of sheaves and exactness, abstracted example: heat diffusion on a graph to understand evolution of opinions on social media. Basics of Homology: Simplicial complexes; nerve of a cover; simplicial and singular homology; snake lemma and long exact sequence; Mayer-Vietoris, Rips, and Čech complexes; computational example (via Python): holes in a sensor network. Basics of Cohomology: Simplicial, Čech, and de Rham cohomology; Hodge decomposition; abstracted example: ranking pairwise alternatives; computational example: designing vector fields. If time permits (!): CW complexes, cellular homology, Poincaré and Alexander duality.
×Dr. Nabanita Ray
Affiliation: Assistant Professor, IIIT-Delhi
Area : Algebra
Syllabus: Field Theory: Example of fields, Field extensions, Algebraic and Transcendental elements of a field, Degree of a field extension, Splitting fields and Algebraic closures, Finite Fields, The fundamental theorem of Galois Theory.
×Dr. Prahllad Deb
Affiliation: Assistant Professor, IIIT-Delhi
Area : Algebra, Geometry and Topology
Syllabus:
Algebra
Towards Lie Groups through a path of Linear Groups: Concrete matrix groups - Topology of matrix groups, Groups and geometry, Quaternionic matrix groups; The matrix exponential function - Definition and elementary properties, Applications (No small subgroup theorem and One parameter subgroup theorem), The Baker-Campbell-Dykin-Hausdorff formula; Linear Lie Groups: The Lie Algebra of a Linear Lie Group, Computation of Lie Algebras of Linear Lie Groups.
Geometry and Topology
Basics of Differential topology: Smooth manifolds, smooth maps, submanifolds, transversality, smooth homotopy and stability theorems, Sard's theorem and application (Morse Lemma and Whitney's embedding theorem for smooth manifolds)
Dr. Satish Kumar Pandey
Affiliation: Assistant Professor, IIIT-Delhi
Area : Real Analysis
Syllabus:
×Dr. Subhajit Ghosechowdhury
Affiliation: Assistant Professor, IIIT-Delhi
Area : Real Analysis
Syllabus: Dual space of a Banach space, Dual of C(X), The Hahn-Banach Theorem, Weak Topology, Alaoglu's Theorem, The Krein-Milman Theorem, De branges proof of Stone - Weierstrass Theorem. (If time permits, Victor Lomonosov's Theorem will be mentioned as an application of the technique)
×Dr. Subhashree Mohapatra
Affiliation: Assistant Professor, IIIT-Delhi
Area : Differential Equations
Syllabus: Introduction to one dimensional finite element method and its implementation.
×Organizing Team
Dr. Ashish Kumar Pandey
Dr. Kaushik Kalyanaraman
Shruti Sharma
Venue
Indraprastha Institute of Information Technology, Delhi
Okhla Industrial Estate,Phase III
(Near Govind Puri Metro Station)
New Delhi, India - 110020
Contact Us
Email Id - msp@iiitd.ac.in
Contact No. - 011-26907548