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Conceptual Mathematics: A First Introduction to Categories 2nd Edition

4.3 out of 5 stars 12 customer reviews
ISBN-13: 978-0521719162
ISBN-10: 1107654165
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Frequently Bought Together

  • Conceptual Mathematics: A First Introduction to Categories
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  • Category Theory for the Sciences (MIT Press)
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Product Details

  • Paperback: 403 pages
  • Publisher: Cambridge University Press; 2 edition (August 31, 2009)
  • Language: English
  • ISBN-10: 1107654165
  • ISBN-13: 978-0521719162
  • ASIN: 052171916X
  • Product Dimensions: 7 x 1 x 10 inches
  • Shipping Weight: 1.8 pounds (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (12 customer reviews)
  • Amazon Best Sellers Rank: #61,473 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

Format: Paperback
Over the last two years I have revisited different sections of this book and gain new profound insights with every read. With some dedication and time, this book will surely enrich your life! What this book offers is the truth. The concepts presented in this book are the underlying unifying ideas which make up mathematics itself in an even more general and profound sense than Set Theory (in fact, one of the authors has rigorously shown that set theory is a very special case of what is presented in this book). We can encounter categories not only at the microscopic level (where we define the fundamental ideas that allow us to construct mathematical concepts from the ground up), but at the macroscopic level as well (where complex constructions in distant fields become analogous to the microscopic building blocks). With these ideas we can show that multiplication and addition are actually more appropriately opposites of one another than addition and subtraction or multiplication and division. This book is the key to beginning a journey to discovering the true nature of mathematics. To continue (or supplement) your journey, also pick up a copy of Sets for Mathematics By F. William Lawvere and Robert Rosebrugh. With time and practice (attempt the exercises from both books!!!) you will be greatly rewarded. As a student of Mathematics, this has paid off in ways I never thought possible and continues to provide insight to nearly everything I learn in school and on my own.

A startling demonstration presented in this book is that Cantor's Diagonal Argument in generalized form not only proves that there are infinite different levels of infinity, but also Godel's Incompleteness Theorem!
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Format: Paperback
It has flaws, but is still one of the greatest maths book I've read. Aimed at high-school level and up, but towards the end it gets a bit complicated, so I doubt if a high school kid can fully understand it without consulting other books. But, most of the book is really easy to read, and the authors' effort to write such a book is admirable.

Lawvere is one of the developers of topos theory, where he found an axiomatization of the category of sets.

The last 2 sections are an introduction to topoi and logic. One key fact seems to be missing which caused me some perplexing: In the category of subobjects, 2 subobjects A and B has A > B if A includes B. Thus, the relation ">" creates a partial order amongst the subobjects. If A > B and B < A, then A = B, thus inducing an equivalence class, denoted by [A]. This is the reason why the subobject classifier has internal structure (different "shades" of truth values).

Also, the relation of topology to logic is analogous to the relation of classical propositional logic to the Boolean algebra of sets, with the sets replaced by open sets in topological space.

I've only read the 1st edition. The 2nd edition's first part is the same as the 1st edition, with additional advanced topics at the very end.
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Format: Paperback Verified Purchase
This is the best introductory book on Category Theory that I've read.

Not a simple read, but far gentler and more intuitive than the others. Uses illustration's and even at times an informal conversational style to highlight the concepts.

It does use proofs, and even asks you to do them using proper notation. But the notation is reasonable, and the proofs logical, and can be skipped altogether if desired.

I might like it to get to be shorter or get to the point quicker. You really do need to start at the beginning and work through the chapters. For the abstract groundwork laid by earlier chapters is essential to understanding the latter ones.

Sure, it could be better. It could be clearer and have even better illustrations. But a survey of the alternatives reveals this author's love for the topic and so clearly shines above similar works, that I give it a 5 star rating.
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Format: Kindle Edition Verified Purchase
I've been trying to expose myself to category theory through the literature. The literature of course demands a sophistication I have yet to attain. I have found this book to be a perfect primer on the subject. It is not easy, but accessible with some meditation on the examples. The connections the book makes from category theory to the more concrete concepts of the physical sciences are illuminating.
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Format: Kindle Edition Verified Purchase
Having read it myself when it first came out, I bought this copy for my niece, who is graduating the Danish gymnasium (high school equivalent) this summer, and as I had, she found it instructive and exciting.
It is exactly what it says on the label: a first introduction to category theory, by one of the founders of the field. Lawvere simply imho does an exemplary job of teaching a different way of thinking about math and logic: this is how it is supposed to be done.
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Format: Paperback Verified Purchase
This book is a simple introduction to category theory. It is strictly about categories, examples are easy to understand and relevant to beginners. You will not see references to vector spaces, matrices, algebras or topologies, but you will understand what category theory is about.
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