The Best Writing on Mathematics 2018最新文献_第2页

Computational Thinking in Science 科学中的计算思维

The Best Writing on Mathematics 2018 Pub Date : 2018-12-04 DOI: 10.1511/2017.124.13

P. Denning

{"title":"Computational Thinking in Science","authors":"P. Denning","doi":"10.1511/2017.124.13","DOIUrl":"https://doi.org/10.1511/2017.124.13","url":null,"abstract":"A quiet but profound revolution has been taking place throughout science. The computing revolution has transformed science by enabling all sorts of new discoveries through information technology. Throughout most of the history of science and technology, there have been two types of characters. One is the experimenter, who gathers data to reveal when a hypothesis works and when it does not. The other is the theoretician, who designs mathematical models to explain what is already known and uses the models to make predictions about what is not known. The two types interact with one another because hypotheses may come from models, and what is known comes from previous models and data. The experimenter and the theoretician were active in the sciences well before computers came on the scene. Computational thinking is generally defined as the mental skills that facilitate the design of automated processes. FULL TEXT Headnote The computer revolution has profoundly affected how we think about science, experimentation, and research. A quiet but profound revolution has been taking place throughout science. The computing revolution has transformed science by enabling all sorts of new discoveries through information technology. Throughout most of the history of science and technology, there have been two types of characters. One is the experimenter, who gathers data to reveal when a hypothesis works and when it does not. The other is the theoretician, who designs mathematical models to explain what is already known and uses the models to make predictions about what is not known. The two types interact with one another because hypotheses may come from models, and what is known comes from previous models and data. The experimenter and the theoretician were active in the sciences well before computers came on the scene. When governments began to commission projects to build electronic computers in the 1940s, scientists began discussing how they would use these machines. Nearly everybody had something to gain. Experimenters looked to computers for data analysis-sifting through large data sets for statistical patterns. Theoreticians looked to them for calculating the equations of mathematical models. Many such models were formulated as differential equations, which considered changes in functions over infinitesimal intervals. Consider for example the generic function / over time (abbreviated f(t)). Suppose that the differences in f(t) over time give another equation, abbreviated g(t). We write this relation as df(t)/dt=g(t). You could then calculate the approximate values of /(f) in a series of small changes in time steps, abbreviated At, with the difference equation f(t+At)=f(t)+Atg(t). This calculation could easily be extended to multiple space dimensions with difference equations that combine values on neighboring nodes of a grid. In his collected works, John von Neumann, the polymath who helped design the first stored program computers, described algorithms fo","PeriodicalId":411029,"journal":{"name":"The Best Writing on Mathematics 2018","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124330174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 40

The Bizarre World of Nontransitive Dice: 不可传递骰子的奇异世界

The Best Writing on Mathematics 2018 Pub Date : 2018-12-04 DOI: 10.2307/j.ctvc775mh.11

James Grime

引用次数: 0

Credits 学分

The Best Writing on Mathematics 2018 Pub Date : 2018-12-04 DOI: 10.2307/j.ctvc775mh.26

引用次数: 0

Tangled Tangles 纠结的缠结

The Best Writing on Mathematics 2018 Pub Date : 2018-12-04 DOI: 10.23943/princeton/9780691171920.003.0009

E. Demaine, M. Demaine, Adam Hesterberg, Quanquan C. Liu, Ron Taylor, Ryuhei Uehara

引用次数: 2

Six Essential Questions for Problem Solving 解决问题的六个基本问题

The Best Writing on Mathematics 2018 Pub Date : 2018-12-04 DOI: 10.2307/j.ctvc775mh.16

N. Kress

引用次数: 0

How To Play Mathematics 如何玩数学

The Best Writing on Mathematics 2018 Pub Date : 2018-12-04 DOI: 10.1515/9780691188720-003

M. Wertheim

引用次数: 1

The World War II Origins of Mathematics Awareness 数学意识的第二次世界大战起源

The Best Writing on Mathematics 2018 Pub Date : 2017-04-01 DOI: 10.1515/9780691188720-018

M. Barany

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引用次数: 1

What Does Active Learning Mean for Mathematicians? 主动学习对数学家意味着什么?

The Best Writing on Mathematics 2018 Pub Date : 2017-02-01 DOI: 10.1090/NOTI1472

B. Braun, Priscilla S. Bremser, Art M. Duval, E. Lockwood, D. White

{"title":"What Does Active Learning Mean for Mathematicians?","authors":"B. Braun, Priscilla S. Bremser, Art M. Duval, E. Lockwood, D. White","doi":"10.1090/NOTI1472","DOIUrl":"https://doi.org/10.1090/NOTI1472","url":null,"abstract":"This call is part of a broad movement to increase the use of active and student-centered teaching techniques across science, technology, engineering, and mathematics (STEM) disciplines. A landmark 2014 meta-analysis published in the Proceedings of the National Academy of Sciences [2] highlighted the efficacy of active learning techniques across STEM disciplines. In mathematics specifically, a comprehensive study of student outcomes for inquiry-based learning [3] has further established that active learning methods have a strong positive impact on women and members of other underrepresented groups in mathematics. This movement extends beyond the academic community—for example, at the federal level the White House STEM-for-All initiative [4] includes active learning as one of its three areas of emphasis for the 2017 budget. While robust support from education researchers, funding agencies, public policymakers, and institutions is a critical component of effective active learning implementation, at the end of the day these techniques and methods are put into practice by mathematics faculty leading classes of students. Thus, mathematics faculty need to be well informed about active learning and related topics. Our goal in this article is to provide a foundation for productive discussions about the use of active learning in postsecondary mathematics. We will focus on topics that frequently arise at the department level, namely: definitions of active learning, examples of active learning techniques and environments used by individual faculty or teams of faculty, things to expect when using active learning methods, and common concerns. An extended discussion of these issues and a substantial bibliography can be found in the six-part series on active learning [5] written by the authors for the AMS blog On Teaching and Learning Mathematics.","PeriodicalId":411029,"journal":{"name":"The Best Writing on Mathematics 2018","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125613097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 49