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Hypercomplex Numbers and Early Vector Systems: A History

Bushman, Nathan
http://rave.ohiolink.edu/etdc/view?acc_num=osu1585666516546138

Abstract Details

2020, Master of Mathematical Sciences, Ohio State University, Mathematical Sciences.
If one were to study mathematics without ever studying its history, they may be left with a rather skewed perception of how the discipline has developed. Vector algebra is a particularly good example of this. Students may be introduced to vectors as early as pre-calculus, and will certainly have become closely acquainted with them by integral and multivariable calculus. They are an essential means of representing and working with certain quantities -- velocity, force, etc. And so one may be led to believe that vectorial ideas must have been incorporated into mathematics long, long ago. However, the reality is quite different; it was actually not until the end of the nineteenth century that a vector system (or vector algebra or calculus) closely resembling our modern one was found, and not until the twentieth that it became widely used. The object of this thesis is to explore the interesting history behind this fact. We trace the widening of the idea of "quantity" from its conception in classical geometry and algebra to one that admits a vector. We explore early mathematical systems that dealt with vectorial ideas, especially W.R. Hamilton's quaternions. We explain how our modern vector system developed from this. The matters of how new ideas arise in mathematics and science, how such innovations are received, and how they evolve, are discussed both implicitly and explicitly.
James Cogdell (Advisor)
Herb (Charles) Clemens (Committee Member)
102 p.
Mathematics
math; mathematics; math history; mathematics history; history of mathematics; vectors; negative numbers; complex numbers; vector analysis; multiple algebra; quaternions; octonions; Hamilton; Grassmann; Maxwell; Tait; Gibbs; Heaviside; Mobius; Cayley

Recommended Citations

Citations

  • Bushman, N. (2020). Hypercomplex Numbers and Early Vector Systems: A History [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1585666516546138

    APA Style (7th edition)

  • Bushman, Nathan. Hypercomplex Numbers and Early Vector Systems: A History. 2020. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1585666516546138.

    MLA Style (8th edition)

  • Bushman, Nathan. "Hypercomplex Numbers and Early Vector Systems: A History." Master's thesis, Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1585666516546138

    Chicago Manual of Style (17th edition)

osu1585666516546138
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This open access ETD is published by The Ohio State University and OhioLINK.