## Functional programming applied to computational algebra

##### Date

2018

##### Authors

Kessler, Ian Holm, author

Wilson, James B., advisor

Patel, Amit, committee member

Chitsaz, Hamidreza, committee member

##### Journal Title

##### Journal ISSN

##### Volume Title

##### Abstract

Underlying many, if not all, areas of mathematics is category theory, an alternative to set theory as a foundation that formalizes mathematical structures and relations between them. These relations abstract the idea of a function, an abstraction used throughout mathematics as well as throughout programming. However, there is a disparity between the definition of a function used in mathematics from that used in mainstream programming. For mathematicians to utilize the power of programming to advance their mathematics, there is a demand for a paradigm of programming that uses mathematical functions, as well as the mathematical categories that support them, as the basic building blocks, enabling programs to be built by clever mathematics. This paradigm is functional programming. We wish to use functional programming to represent our mathematical structures, especially those used in computational algebra.

##### Description

2018 Fall.

Includes bibliographical references.

Includes bibliographical references.

##### Rights Access

##### Subject

computer algebra

Scala

functional programming

category theory