Yuktibhasa Seminar - Talk by Prof. Thamban Nair entitled "On Completeness and Denseness"

Abstract: In this talk on elementary notions on completeness and denseness, we discuss the following:

• A proof on the completeness of the set of real numbers.
• Identify a completion of a general metric space  X  as a subspace of the metric space  B(X) of the set of all bounded functions on  X.
• A characterization of completeness which would be useful to show certain metric spaces are not complete.
• Denseness of  P[a, b], the space of polynomials as functions on [a, b], in certain larger metric spaces than  C[a, b]  with sup-metric.
• Completion of a normed linear space  X as a subspace of the normed linear space B(S), where  S  is the unit sphere of the dual of  X.

 

Meeting link: https://zoom.us/j/91871554082
Meeting ID: 918 7155 4082
Time: 4-5 PM

About the Yuktibhasa seminar series:

The mathematics department at IIT Palakkad has been running monthly graduate-level expository webinars for over a year. We have had several young faculty as well as senior faculty speak on a wide variety of topics. We have now named this series of expository seminars/webinars as the Yuktibhasa seminar series.

The Yuktibhasa (literal meaning `rationale') is a major treatise on mathematics and astronomy, written by the Indian astronomer Jyesthadeva of the Kerala school of mathematics in the 16th Century.

Some of the important topics in the treatise include the infinite series expansions of functions; power series, including of π and π/4; trigonometric series of sine, cosine, and arctangent; Taylor series, including second and  third order approximations of sine and cosine; radii, diameters and circumferences; and tests of convergence. The unique aspects of this treatise are that it is written in the local language Malayalam and it is also one of the few Indian scholarly works that explains the proofs and derivations of the results.

We hope to follow in the tradition of Jyeshtadeva and have many more exemplary expository talks that are accessible to a wide audience in this series. We request your enthusiastic participation to make this series a grand success!