# THE BISECTION METHOD: A SINGLE TECHNIQUE YIELDING SIMPLE PROOFS OF THE FOUR "HARD" THEOREMS OF CALCULUS

## Presenter Information

9th - 12th Grade : Math

## Start Date

3-3-2023 10:50 AM

## End Date

3-3-2023 11:50 AM

## Description

The Intermediate Value Theorem, Boundedness Theorem, Extreme Value Theorem, and Integrability Theorem are all vital theorems of Calculus, yet are almost never proved in calculus textbooks. I will give simple proofs of these theorems using the Bisection Method, explain how I incorporated these into inquiry-style lessons at IMSA, and discuss the benefits to students. As a connection to Computer Science, the Bisection Method can be viewed as a Binary Search Algorithm.

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Mar 3rd, 10:50 AM Mar 3rd, 11:50 AM

THE BISECTION METHOD: A SINGLE TECHNIQUE YIELDING SIMPLE PROOFS OF THE FOUR "HARD" THEOREMS OF CALCULUS

The Intermediate Value Theorem, Boundedness Theorem, Extreme Value Theorem, and Integrability Theorem are all vital theorems of Calculus, yet are almost never proved in calculus textbooks. I will give simple proofs of these theorems using the Bisection Method, explain how I incorporated these into inquiry-style lessons at IMSA, and discuss the benefits to students. As a connection to Computer Science, the Bisection Method can be viewed as a Binary Search Algorithm.