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Introduction to the Foundations of Mathematics
This classic undergraduate text acquaints students with the fundamental concepts and methods of mathematics. In addition to introducing many historical figures from the 18th through the mid-20th centuries, it examines the axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and other topics. 1965 second edition.
- GenresMathematicsPhilosophy
333 pages, Hardcover
First published September 1, 1965
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Displaying 1 - 3 of 3 reviews
July 21, 2019
Well written an thorough, comparable to Kunen's introduction
April 20, 2016
It is a classic of its sort and very rigorous. However if you want a gentle intro into the topic for a layman, it is probably too hard. Also if would benefit of more examples and visuals. But one has to appreciate it is written in the 60s of the last century.
But I think it would be excellent for an graduate student specialised in maths.
But I think it would be excellent for an graduate student specialised in maths.
March 29, 2017
Foundations of mathematics is defined by Wikipedia as follows, and sums up what this book is about quite nicely:
Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics.
The book is divided into two parts. The first part is dedicated to concepts in foundations, with some historic commentary along the way. It covers the axiomatic method, set theory, the real number system, and groups. The second part of the book provides a brief review of the history of foundations and its developments until the 1960's, along with a treatment of logic, and finishes with an investigation of mathematics and its cultural setting.
For a small book, it covers an impressive array of topics. For the most part the historical context is interesting, and Wilder goes out of his way to illustrate the usefulness of the topics he covers.
I would say the professed readable nature of the book is exaggerated. I found the writing style to be dated (which of course is not surprising), and some of the explanations to be opaque. But to be fair, most of these subjects aren't simple; your mileage may vary.
I'm not sure I'd recommend it to an undergraduate trying to get a handle on foundations, but if it's an area of interest I'd suggest taking a look.
Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics.
The book is divided into two parts. The first part is dedicated to concepts in foundations, with some historic commentary along the way. It covers the axiomatic method, set theory, the real number system, and groups. The second part of the book provides a brief review of the history of foundations and its developments until the 1960's, along with a treatment of logic, and finishes with an investigation of mathematics and its cultural setting.
For a small book, it covers an impressive array of topics. For the most part the historical context is interesting, and Wilder goes out of his way to illustrate the usefulness of the topics he covers.
I would say the professed readable nature of the book is exaggerated. I found the writing style to be dated (which of course is not surprising), and some of the explanations to be opaque. But to be fair, most of these subjects aren't simple; your mileage may vary.
I'm not sure I'd recommend it to an undergraduate trying to get a handle on foundations, but if it's an area of interest I'd suggest taking a look.
Displaying 1 - 3 of 3 reviews