Numbers, Sets and Axioms : The Apparatus of Mathematics (PB)

By: Hamilton, A. GLanguage: English Publication details: Cambridge Cambridge University Press 1982Description: ix, 255pISBN: 9780521287616 (PB)Subject(s): Set theory | Numbers | Axioms | Number theory | Mathematics
Contents:
1. Numbers 2. The size of a set 3. Ordered sets 4. Set theory 5. The axiom of choice 6. Ordinal and cardinal numbers
Summary: Following the success of Logic for Mathematicians, Dr Hamilton has written a text for mathematicians and students of mathematics that contains a description and discussion of the fundamental conceptual and formal apparatus upon which modern pure mathematics relies. The author's intention is to remove some of the mystery that surrounds the foundations of mathematics. He emphasises the intuitive basis of mathematics; the basic notions are numbers and sets and they are considered both informally and formally. The role of axiom systems is part of the discussion but their limitations are pointed out. Formal set theory has its place in the book but Dr Hamilton recognises that this is a part of mathematics and not the basis on which it rests. Throughout, the abstract ideas are liberally illustrated by examples so this account should be well-suited, both specifically as a course text and, more broadly, as background reading. The reader is presumed to have some mathematical experience but no knowledge of mathematical logic is required.
Item type: BOOKS
Tags from this library: No tags from this library for this title. Log in to add tags.
    Average rating: 0.0 (0 votes)
Current library Home library Call number Materials specified Status Date due Barcode
IMSc Library
IMSc Library
510 HAM (Browse shelf (Opens below)) Checked out to Pralay Chatterjee (PRALAY) 01/11/2024 77673

Includes References (247-248) and Index

1. Numbers
2. The size of a set
3. Ordered sets
4. Set theory
5. The axiom of choice
6. Ordinal and cardinal numbers

Following the success of Logic for Mathematicians, Dr Hamilton has written a text for mathematicians and students of mathematics that contains a description and discussion of the fundamental conceptual and formal apparatus upon which modern pure mathematics relies. The author's intention is to remove some of the mystery that surrounds the foundations of mathematics. He emphasises the intuitive basis of mathematics; the basic notions are numbers and sets and they are considered both informally and formally. The role of axiom systems is part of the discussion but their limitations are pointed out. Formal set theory has its place in the book but Dr Hamilton recognises that this is a part of mathematics and not the basis on which it rests. Throughout, the abstract ideas are liberally illustrated by examples so this account should be well-suited, both specifically as a course text and, more broadly, as background reading. The reader is presumed to have some mathematical experience but no knowledge of mathematical logic is required.

There are no comments on this title.

to post a comment.
The Institute of Mathematical Sciences, Chennai, India

Powered by Koha