Algebraic Topology|Lecture 1|Introduction,Path, Homotopy #topology #phdmaths #msc

?Welcome to Lecture 1 of the New Detailed Course on Algebraic Topology by Saurish Gupta, PhD Scholar at IISER Bhopal and CSIR NET December 2025 JRF – AIR 63. In this lecture, we begin our journey into Algebraic Topology by developing the fundamental concepts of paths and homotopy. The lecture focuses on building strong intuition and understanding the basic definitions that will be used throughout the course. 📌 Topics Covered in Lecture 1: Introduction to Algebraic Topology What is a Path? Definition and basic properties of paths Homotopy – Definition Understanding the intuition behind homotopy Examples of Homotopy Important examples and illustrations Connection between paths and homotopy Basic ideas leading towards fundamental groups 🎯 This course is useful for students preparing for: MSc Mathematics PhD Entrance & Interview Students interested in Higher Mathematics and Topology 👨‍🏫 Instructor: Saurish Gupta PhD Scholar, IISER Bhopal CSIR NET December 2025 – JRF, AIR 63 🏫 JSG MATHS EXCELLENCE ACADEMY If you find this lecture helpful: 👍 LIKE the video 🔄 SHARE it with your friends 🔔 SUBSCRIBE to the channel for the complete Algebraic Topology course. 📌 Stay connected and learn Mathematics with clarity, depth and intuition! #AlgebraicTopology #Topology #Homotopy #Path #Mathematics #CSIRNET #CSIRNETJRF #GATEMathematics #IITJAM #TIFR #ISI #CMI #MScMathematics #PhDMathematics #JSGMathsExcellenceAcademy #SaurishGupta