How We Got from There to Here: A Story of Real Analysis

The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis. This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context. This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.https://knightscholar.geneseo.edu/oer-ost/1019/thumbnail.jp

Differential Calculus: From Practice to Theory

Differential Calculus: From Practice to Theory covers all of the topics in a typical first course in differential calculus. Initially it focuses on using calculus as a problem solving tool (in conjunction with analytic geometry and trigonometry) by exploiting an informal understanding of differentials (infinitesimals). As much as possible large, interesting, and important historical problems (the motion of falling bodies and trajectories, the shape of hanging chains, the Witch of Agnesi) are used to develop key ideas. Only after skill with the computational tools of calculus has been developed is the question of rigor seriously broached. At that point, the foundational ideas (limits, continuity) are developed to replace infinitesimals, first intuitively then rigorously. This approach is more historically accurate than the usual development of calculus and, more importantly, it is pedagogically sound. The text also incorporates curated activities from the TRansforming Instruction in Undergraduate Mathematics Instruction via Primary Historical Sources (TRIUMPHS) project to provide students with ample opportunities to develop relevant competencies.https://knightscholar.geneseo.edu/oer-ost/1031/thumbnail.jp

Internet Addiction to Child Pornography

During the present age and time, it seems as though people in society have become addicted to nearly anything and everything, whether it be to a substance, an activity or an object. The Internet and pornography is no exception. While commonly thought of as a deviant behavior, many are displaying addictions towards the Internet and pornography. More alarming, however, are those who are viewing, downloading, or trading child pornography and displaying addictive Internet behaviors, for they are spending excessive amounts of time engaging in the proliferation of child pornographic materials. For this reason, addiction to the Internet and usage of child pornography are the main points of the current study. The self-reported survey, which was part of a larger project to fulfill requirements for a Master of Science degree, measured demographics, Internet usage and child pornography usage, to find valuable statistical data and to gain an understanding of those who are engaging in child exploitation on the Internet. The current study proved to measure child pornography usage on the Internet correlated with Internet addiction. While the study is not without limitations, it provides valuable information about those who are engaging in child pornography. The ultimate goal was to gain an understanding of those engaging in child pornography on the Internet, in order to prevent more children from falling victim of these predators. Keywords: child pornography, pornography, addiction, Internet, child exploitatio