Name: Sets for mathematics
ISBN: 9780511077944

Sets for mathematics

Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. This book, first published in 2003, uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure of the axiom of choice. An appendix provides an explicit introduction to necessary concepts from logic, and an extensive glossary provides a window to the mathematical landscape.

What Hacker News says

auggieroseDec 2019

I very much like: "Sets for Mathematics", which I currently read and which finally clicks with me. I always found expositions of category theory tiring in that it bombarded me with trivialities and examples that were kind of obvious. Instead, "Sets for Mathematics" describes one particular and probably the most familiar and important category, the category of sets, and I very much like this fresh look at sets.

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tobbe2064May 2018

You should check out "Conceptual mathematics" and then "sets for mathematics", both written by lawvere. They are the amazing

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nextosNov 2017

Conceptual Mathematics and Sets for Mathematics from Lawvere are really good for this purpose too. Challenging but doable with the mathematical maturity that most programmers have after extensively working with functions and types.

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decasteveApr 2014

If you've already covered Vector Spaces, Groups, and Rings in your studies, I would suggest checking out Bill Lawvere's "Conceptual Mathematics: A First Introduction to Categories". i.e. An introduction to category theory through the category of sets. His "Sets for Mathematics" is also good but it's a more concise presentation of the topic but a less than gentle introduction than the former book.

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nextosApr 2014

What about Lawvere's Conceptual Mathematics or Sets for Mathematics?

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decasteveApr 2014

A lot of the same ground but Sets for Mathematics is more concise and probably goes into more depth by the end. If you've previously done rings, groups, vector spaces, topological spaces, the concepts tie nicely together in Sets for Mathematics.

Conceptual Mathematics puts a lot more time up front motivating the material with examples and tries to build your intuition before getting into the details. If all you've done previously was linear algebra and some discrete math, this book is probably better.

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