Date of Completion


Degree Type

Honors Thesis


Mathematics (MATH)

First Advisor

Michael Berg


The field of analysis is a newer subject in mathematics, as it only came into existence in the last 400 years. With a new field comes new notation, and in the era of universalism, analysis becomes key to understanding how centuries of mathematics were unified into a finite set of symbols, precise definitions, and rigorous proofs that would allow for the rapid development of modern mathematics. This paper traces the introduction of subjects and the development of new notations in mathematics from the seventeenth to the nineteenth century that allowed analysis to flourish. In following the development of analysis, we are introduced to Descartes’ higher powers, Fermat’s maxima and minima, Newton’s fluxions and fluents, Leibniz’s ò and d, Euler’s S and f(x), Cauchy’s lim., Weierstrass’ e-d proofs, Dedekind’s “cuts” and Â, and Bourbaki’s Ï, Æ, Þ, and Û, among other notations. Readers will grasp how notations allowed mathematics to advance by conveying clear, concise meanings that are universally understood, and how they knock down the language barriers that plague other fields.