PPT-History & Philosophy of Calculus, Session 10

The Return of the Infinitesimal So far on this course weve stayed close to mainstream mathematics In this final session we look at some more fancy material much of it very recent These arent just techniques for doing complicated calculations they represent new ways to think about geometry and continuity and so they promise to raise some old philosophical questions . for Academic Job Applications. Linda B. Nilson, Ph. D., Director. Office of Teaching Effectiveness and Innovation. 448 Brackett Hall, Clemson University. 656-4542 * . nilson@clemson.edu. * www.clemson.edu/OTEI. adding it all up. Integral Calculus. 1. Goal. Compute the . signed. area . under some portion of an arbitrary curve. Integral Calculus. 2. Divide and Conquer. Integral Calculus. 3. Animatedly. Integral Calculus. Chinese Philosophy. Philosophy has had a tremendous effect on Chinese civilization, and East Asia as a whole. . Many of the great philosophical schools were formulated during the Spring and Autumn Period and Warring States Period, and came to be known as the Hundred Schools of Thought. . By Masayuki Sato. Lecture Two. Intellectual . Foundation for . Chinese Philosophy. 【. 本著作除另有註明外，採取. 創用. CC. 「姓名標示－非商業性－相同方式分享」台灣. 8. Newton & Leibniz. History & Philosophy of Calculus, Session . 8. The invention of the calculus. Newton and Leibniz in 17. th. Century invented the algorithmic procedures underlying the calculus. Newton & Leibniz. Summary. Calculus seems to demand some concept of the infinitesimal. Magnitude. New number. Or both?. But infinitesimals lack . clarity . Concepts that are not mathematical being used to interpret mathematics?.  . What is . λ-calculus ?. . “Lambda . calculus.  . is . a formal . system.  in . mathematical logic.  and computer science for expressing computation based on function abstraction and application using variable . The Integral. In this session we meet . integration. , which in a sense is one half of the thing called calculus.. In the next session we meet the other half, so at that point we will (at last) have explained what calculus is.. What is philosophy?. Philosophy is what everyone does when they’re not busy dealing with their everyday business and get a change simply to wonder what life and the universe are all about.. Philosophy is not so much about coming up with the answers to fundamental questions as it is about the process of trying to find these answers, using reasoning rather than accepting without question conventional views or traditional authority.. The mathematics of continuous change. Instead of looking at average or overall results, calculus looks at how things change from second to second.. Calculus. The mathematics of continuous change. Instead of looking at average or overall results, calculus looks at how things change from second to second.. Session 5. The Derivative. Integrals . Review. Plot a graph of the function f(x), where f represents how something is changing (e.g. it might be speed or acceleration). We write something like f(x) = x. GCSE Taster Session. LOs. To know the difference between Core REP and GCSE REP.. To understand what we study at GCSE and how it is assessed.. To know why REP is valued by universities and employers.. Due 26 May 2011. HN. Intro to Philosophy Final . Project. Who was Hegel?. Georg Wilhelm Friedrich Hegel. was born in Stuttgart, Germany, in 1770.. Hegel worked as a professor in various German universities, where he became well acquainted with . AMS Committee on Education. Jessica. . Ellis. Colorado. . State. . University. http://. www.maa.org. /. cspcc. Acknowledgments. MAA. David . Bressoud. Michael Pearson. Linda . Braddy. Olga Dixon. San Diego State Univ..