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Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis

Abstract Details

2013, Master of Arts (MA), Ohio University, Philosophy (Arts and Sciences).
We attempt to clarify and evaluate what shall be called Mac Lane’s thesis—the thesis that nonstandard analysis (NSA) and smooth infinitesimal analysis (SIA) are alternatives to the standard approach to the calculus. In doing so, we outline the historical approaches to the calculus, the standard approach to the calculus, and two nonstandard approaches, namely NSA and SIA; we also attempt to clarify and evaluate a set of comparisons of NSA and SIA, namely John L. Bell’s 5 mathematico-philosophical contentions and Bell’s historical contention.
Philip Ehrlich, PhD (Advisor)
Stewart Shapiro, PhD (Committee Member)
Todd Eisworth, PhD (Committee Member)
84 p.

Recommended Citations

Citations

  • Houchens, J. P. (2013). Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis [Master's thesis, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1365705311

    APA Style (7th edition)

  • Houchens, Jesse. Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis. 2013. Ohio University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1365705311.

    MLA Style (8th edition)

  • Houchens, Jesse. "Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis." Master's thesis, Ohio University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1365705311

    Chicago Manual of Style (17th edition)