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ABOUT THE COURSE: The objective of this course is to explore the foundations of mathematics at a level and at depth for someone ambitious to study higher mathematics. After completing the course, a student can realize what it means to do mathematics instead of only learning it or doing some computational exercises.INTENDED AUDIENCE: Under graduatePREREQUISITES: One course in real analysis available on NPTEL Portal is desirable.INDUSTRY SUPPORT: Any industry who practices Topological Data Analysis