Weekly_Blog (1)

The last subject we covered in class was The Fundamental Theorem of Calculus which brings this course full circle with a proof that proves all the basic things we used in every Calculus class we have been in. I have stated the definition: Fundamental Theorem of Calculus:  (i) If is integrable and then (ii) If […]

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By: Abraham Schroeder and Tongzhou Wang Early Calculus In the past few weeks of class we have been rigorously defining and proving all of the rules of calculus. The proofs that we have been learning in class are rooted in the definitions for functional limits and continuity. Strangely enough these proofs and definitions for calculus were […]

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Authors: Brittney D’Oleo, Elise Favia Date: October 27, 2017   Introduction: This week’s topic, (global) modulus of continuity is an extension of last week’s topic, the (local) modulus of continuity. In the blog, we will explore the new definition and compare it to last weeks definitions. We will also prove an interesting result creating an […]

By: Rhiannon Begley and Shuyi Chen Introduction In class we have begun to and will continue to discuss functions, their continuity, and their limits at a particular point. Although we can determine the continuity and limits of functions with the tools we have learned in class, we cannot determine how quickly the function is converging […]

By Nick Wan and Elaine Wissuchek Introduction to the Cantor Set Cantor set is a special subset of the closed interval [0, 1] invented by a German mathematician Georg Cantor in 1883. In order to construct this set, we need to construct infinitely many subset of inductively and take the intersection of all of them. […]

By: Jonathan Rodriguez and Shivani Patel Introduction: In this class, we often work with different parts of the real numbers, such as natural numbers, integers, and rational numbers. We can easily take real numbers for granted since they seem to encompass everything that we work with in the class. In order to fully appreciate the […]

By Zehao Dong and Zihan Hu 1 Introduction In Chapter 2, we studied the definition of sequence and the convergence of a sequence. Topological spaces provide a general framework for the study of convergence. However, instead of a distance function, we can think of the basic structure on a topological space as a collection of […]