IMSC Courses

Laplace Transform

Laplace transform is a fundamental tool in integral calculus. It is used to solve various types of differential equations, difference equations, integral equations etc., which arise naturally in engineering and basic sciences. Laplace transform technique…

• Swayam
• 4 weeks
• Finished
• Free Online Course

Algebra - I

Foundational PG level course in algebra, suitable for M.Sc and first year PhD students in Mathematics.PREREQUISITES :BSc-level linear algebra.INDUSTRIES SUPPORT :Not Applicable Week 1:Permutation Groups, symmetries of graphs.Week 2:Abstract Groups, homo…

• Swayam
• 12 weeks
• Finished
• Free Online Course

Algebra - II

Second part of Foundational PG level course in algebra. suitable for M.Sc and first year PhD students in Mathematics. Week 1:Fields, equations, extensions. Week 2:Ruler and compass constructions,Week 3:Finite Fields. Week 4:Galois Theory - 1Week 5:Galos…

• Swayam
• 12 weeks
• Finished
• Free Online Course

FUNCTIONAL ANALYSIS

Functional Analysis is a core course in any mathematics curriculum at the masters level. It has wide ranging applications in several areas of mathematics, especially in the modern approach to the study of partial differential equations. The proposed cour…

• Swayam
• 15 weeks
• Finished
• Free Online Course

An invitation to Topology

Topology is the study of abstract shapes and their properties which do not change under stretching or squeezing an object without tearing. Arguably, topology (along with the theory of numbers) lies at the heart of mathematics. I invite you to explore thi…

• Swayam
• 12 weeks
• Finished
• Free Online Course

Measure And Integration

A 12-week IMSC course delving into the theory of measure and integration, covering abstract measures, Lebesgue integral, differentiation, integration, product spaces, and L^p-spaces. Prerequisite: MSc in Mathematics.

• Swayam
• 12 weeks
• Finished
• Free Online Course

Sobolev Spaces And Partial Differential Equations

The modern theory of Partial Differential Equations relies heavily on functional analytic methods. This course will develop, in detail, the theory of distributions and study the important properties of Sobolev spaces. These will be applied to the study o…

• Swayam
• 12 weeks
• Finished
• Free Online Course

Measure Theory - IMSc

Measure theory is a tool for carrying out integration which behaves well with taking limits, and admitting a vast class of functions for which Riemann's integration theory is not applicable. Real-world applications of measure theory can be found in physi…

• Swayam
• 12 weeks
• Finished
• Free Online Course