Presentation Title

The Arithmetic Derivative: How to Differentiate a Number

Presenter Information

Heather M. PaightFollow

Presentation Type

Oral Presentation

School

School of Sciences and Social Sciences

Discipline

Mathematics

Mentor

Vincent Ferlini

Date & Time

April 9th at 11:30 AM - 12:30 PM

Location

David F. Putnam Science Center, Room 102

Abstract

The arithmetic derivative of a natural number n , denoted n’ , is defined as follows: If n is prime then n’=1 and for natural numbers a and b, then (ab)’=ab’+ba’. This rule for (ab)’ has the same form as the Leibniz Rule in Calculus. This talk will explore some basic properties of the arithmetic derivative with an emphasis on those that have analogs in Calculus. The definition will then be extended to apply to integers and rational numbers. Connections between the arithmetic derivative and two famous unsolved problems in number theory, Goldbach's Conjecture and the Twin Primes Conjecture, will be included.

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Apr 9th, 11:30 AM

The Arithmetic Derivative: How to Differentiate a Number

David F. Putnam Science Center, Room 102

The arithmetic derivative of a natural number n , denoted n’ , is defined as follows: If n is prime then n’=1 and for natural numbers a and b, then (ab)’=ab’+ba’. This rule for (ab)’ has the same form as the Leibniz Rule in Calculus. This talk will explore some basic properties of the arithmetic derivative with an emphasis on those that have analogs in Calculus. The definition will then be extended to apply to integers and rational numbers. Connections between the arithmetic derivative and two famous unsolved problems in number theory, Goldbach's Conjecture and the Twin Primes Conjecture, will be included.