DAYA SHANKAR PRATAP - Academia.edu (original) (raw)

Papers by DAYA SHANKAR PRATAP

International journal of advanced academic studies, 2019

I present a unified algebra that includes what are commonly called boolean algebra, number algebr... more I present a unified algebra that includes what are commonly called boolean algebra, number algebra, sets, lists, functions, quantification, type theory, and limits; this mathematics forms the foundation for much of computer science. I present the notations and the rules for the conduct of algebra, but it is not the purpose here to explore the possibilities for their use. I am laying foundations, not building upon them; I am designing the instrument, not playing the music. To appreciate the algebra, I rely on the reader's experience in using algebra.

International journal of applied research, 2018

This paper is about the symbols and notations of boolean algebra, and about the way the subject i... more This paper is about the symbols and notations of boolean algebra, and about the way the subject is explained. It is about education, and about putting boolean algebra into general use and practice. To make the scope clear, by "boolean algebra" I mean the algebra whose expressions are of type boolean. I mean to include the expressions of propositional calculus and predicate calculus. I shall say "boolean algebra" or "boolean calculus" interchangeably, and call the expressions of this algebra "boolean expressions". Analogously, I say "number algebra" or "number calculus" interchangeably, and call the expressions of that algebra "number expressions".

For contrast, a set represents a collection of objects in a package or container. The contents of... more For contrast, a set represents a collection of objects in a package or container. The contents of a set is a bunch. These vague descriptions are made precise as follows. A data structure is a collection, or aggregate, of data. The kinds of structuring we consider are packaging and indexing. These two kinds of structure give us four data structures.1.unpackaged, unindexed: bunch2.packaged, unindexed: set3.unpackaged, indexed: string4.packaged, indexed: listAny binary or number is an elementary bunch, or element.

International journal of advanced academic studies, 2019

I present a unified algebra that includes what are commonly called boolean algebra, number algebr... more I present a unified algebra that includes what are commonly called boolean algebra, number algebra, sets, lists, functions, quantification, type theory, and limits; this mathematics forms the foundation for much of computer science. I present the notations and the rules for the conduct of algebra, but it is not the purpose here to explore the possibilities for their use. I am laying foundations, not building upon them; I am designing the instrument, not playing the music. To appreciate the algebra, I rely on the reader's experience in using algebra.

International journal of applied research, 2018

This paper is about the symbols and notations of boolean algebra, and about the way the subject i... more This paper is about the symbols and notations of boolean algebra, and about the way the subject is explained. It is about education, and about putting boolean algebra into general use and practice. To make the scope clear, by "boolean algebra" I mean the algebra whose expressions are of type boolean. I mean to include the expressions of propositional calculus and predicate calculus. I shall say "boolean algebra" or "boolean calculus" interchangeably, and call the expressions of this algebra "boolean expressions". Analogously, I say "number algebra" or "number calculus" interchangeably, and call the expressions of that algebra "number expressions".

For contrast, a set represents a collection of objects in a package or container. The contents of... more For contrast, a set represents a collection of objects in a package or container. The contents of a set is a bunch. These vague descriptions are made precise as follows. A data structure is a collection, or aggregate, of data. The kinds of structuring we consider are packaging and indexing. These two kinds of structure give us four data structures.1.unpackaged, unindexed: bunch2.packaged, unindexed: set3.unpackaged, indexed: string4.packaged, indexed: listAny binary or number is an elementary bunch, or element.