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PROMYS Guest Lecture

Title: Rounding sequences and counting by congruence classes
Speaker: Caleb Shor (Western New England University, Springfield, USA)
Date: 21 May 2024
Time: 11:45 am
Venue: LH-1, Mathematics Department

For $n$ a natural number, consider the sequence of $n$ rational numbers $n/1, n/2, n/3, \dots, n/n$. Round each to the nearest integer to obtain sequence of $n$ integers. How many are odd?

In this talk we will see how knowledge of sums of squares and a result of Gauss will help to lead us to a somewhat surprising result. Time permitting, we will discuss similar results.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 15 Jul 2024