cerkalo
» » Conceptual Mathematics: A First Introduction to Categories

Conceptual Mathematics: A First Introduction to Categories download ebook

by Stephen Hoel Schanuel,F. William Lawvere

Conceptual Mathematics: A First Introduction to Categories download ebook
ISBN:
0521478170
ISBN13:
978-0521478175
Author:
Stephen Hoel Schanuel,F. William Lawvere
Publisher:
Cambridge University Press; 1st edition (November 28, 1997)
Language:
Pages:
376 pages
ePUB:
1247 kb
Fb2:
1243 kb
Other formats:
docx azw rtf mbr
Category:
Mathematics
Subcategory:
Rating:
4.7

Conceptual Mathematics introduces the concept of category to beginning students, general readers, and practicing mathematical scientists based on a leisurely introduction to the important categories of directed graphs and discrete dynamical systems.

Conceptual Mathematics introduces the concept of category to beginning students, general readers, and practicing mathematical scientists based on a leisurely introduction to the important categories of directed graphs and discrete dynamical systems.

Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply categories to the most elementary mathematics

Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply categories to the most elementary mathematics. It thus serves two purposes: first, to provide a key to mathematics for the general reader or beginning student; and second, to furnish an easy introduction to categories for computer scientists, logicians, physicists, and linguists who want to gain some familiarity with the categorical method without initially committing themselves to extended study.

Lawvere, F. William; Schanuel, S. H. (Stephen Hoel), 1933 . Includes bibliographical references and index

Lawvere, F. (Stephen Hoel), 1933-. Includes bibliographical references and index.

William Lawvere is a Professor Emeritus of Mathematics at the State University of New York. At the 1970 International Congress of Mathematicians in Nice, Prof. Stephen H. Schanuel is a Professor of Mathematics at the State University of New York at Buffalo.

Conceptual Mathematics: A First Introduction to Categories (Paperback). F. William Lawvere (author), Stephen H. Schanuel (author). Paperback 404 Pages, Published: 30/07/2009. In the new appendices and annotated bibliography the reader will find concise introductions to adjoint functors and geometrical structures, as well as sketches of relevant historical developments.

Conceptual Mathematics book. William Lawvere, Stephen H. Schanuel. Written by two of the best known names in categorical logic, this is the first book to apply categories to the most elementary mathematics. The idea of a category-a sort of mathematical universe-has brought about a remarkable unification and simplification of mathematics.

A rst introduction to categories.

William Lawvere, Stephen H. Download PDF book format. Choose file format of this book to download: pdf chm txt rtf doc. Download this format book. Personal Name: Schanuel, S. Rubrics: Categories (Mathematics). Download now Conceptual mathematics : a first introduction to categories F. book below: (C) 2016-2018 All rights are reserved by their owners.

oceedings{lM, title {Conceptual mathematics - a first introduction to categories} .

oceedings{lM, title {Conceptual mathematics - a first introduction to categories}, author {F. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discret. ONTINUE READING. View PDF. Save to Library.

The idea of a "category"--a sort of mathematical universe--has brought about a remarkable unification and simplification of mathematics. Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply categories to the most elementary mathematics. It thus serves two purposes: first, to provide a key to mathematics for the general reader or beginning student; and second, to furnish an easy introduction to categories for computer scientists, logicians, physicists, and linguists who want to gain some familiarity with the categorical method without initially committing themselves to extended study.
Reviews:
  • Skiletus
Possibly a more apt subtitle for this book would be "A First Introduction to Ideas that Underlie Category Theory." Even after spending quite a bit of time with this book, I didn't really feel like I'd learned much category theory, per se. (Tom Leinster's Basic Category Theory seems like an excellent choice if you want to jump right into definitions of categories, functors and natural transformations, then start thinking in terms of adjoints, etc. He also makes that book available on arxiv.) But, early on, Lawvere/Schanuel's book introduced (quite clearly, I think) category-theoretic ideas like sections and retractions, which I hadn't even realized that I'd encountered before. (I'd spent some time with Tu's Intro to Manifolds before this book, and at first I wondered if his definition of a section in the discussion of vector bundles had typos in it or what; after some time with Lawvere/Schanuel, that section from Tu makes a lot more sense.)

As others have mentioned, the books seems like it might be quite simple, near the beginning. At first, given my lack of familiarity with category theory, this book made me wonder if category theory was the study of the consequences of associativity of composition laws, as that's a bit of a recurring theme in this book. And speaking of composition laws, if one wants to come up with a list of prerequisites for this book (or to start reading it, at least), I'd dare say that a familiarity with the composition of functions might be all you really need. That said, I should say this: I recently took a first pass at Rotman's Intro to Algebraic Topology and, after reading his discussion of Brouwer's fixed point theorem, I went back to Lawvere/Schanuel to revisit their section of the same topic, but still didn't feel clear about the Lawvere/Schanuel version after re-reading that section. (Rotman, on the other hand, I found quite easy to understand.) So while one could start this book with minimal prerequisites, I don't expect to feel like I'd understood it all, any time soon (and I'm well past the minimal prerequisites I just offered). And that's sort of a drawback -- the difficultly level of the book doesn't exactly scale smoothly, once you're into the latter half or so of the book. But that's probably my only criticism, as I find the discussion-driven parts of the book generally quite lucid and insightful.
  • Globus
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.
  • Manris
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.
  • Arashitilar
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.
  • Ance
Excellent introduction with well-designed, engaging examples and exercises.
There are some serious problems with typesetting in the Kindle edition. For example repeated concatenation of functions puts a new line between each of the function applications. Not impossible to read, but quite annoying.