Mathematics for Data Science 1 - W1_L7: Functions - domain codomain range & properties of mappings

Welcome to Week 1 Lecture 7 of the course Mathematics for Data Science I by Profs. Neelesh Upadhye, Madhavan Mukund. Full Course: https://study.iitm.ac.in/ds/course_pages/BSMA1001.html Video Overview This lecture introduces the concept of functions, explaining them as rules that convert inputs into outputs. We cover key definitions such as domain, codomain, and range, and explore the connection between functions and relations. The session also examines important properties like injectivity one-to-one, surjectivity onto, and bijectivity. We see how bijections are used to compare the cardinality of sets, including infinite sets, providing a deeper understanding of mappings in mathematics. About IIT Madras' online Bachelor of Science programme IIT Madras offers four-year BS programmes that aim to provide quality education to all, irrespective of age, educational background, or location. The BS programme has multiple levels, which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned, the learner can receive a Foundation Certificate from IITM CODE (Centre for Outreach and Digital Education), Diploma(s) from IIT Madras, or BSc/BS Degrees from IIT Madras. For more details, Visit: https://www.iitm.ac.in/academics/study-at-iitm/non-campus-bs-programmes #Mathematics #DataScience #MathForDataScience #functions #relations #domain #codomain #range #injective #surjective #bijective #onetoone #onto #cardinality #lecture #tutorial #mapping #input #output #functionproperties #settheory #lines #squarefunction #complexnumbers #IITMadrasBS #OnlineLearning #MathBasics