The idea of a “category”–a sort of mathematical universe–has brought about a Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply F. William Lawvere,Stephen H. Schanuel. Conceptual Mathematics: A First Introduction to Categories. Front Cover · F. William Lawvere, Stephen H. Schanuel. Cambridge University. I find Conceptual Mathematics creative, illuminating, and thought-provoking. Subobject classifiers for high school students! However, I’ve never.
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Best known for Schanuel’s Lemma in homological algebra and related work with Bass on the beginning of algebraic K-theoryand for Schanuel’s Conjecture on algebraic independence and the exponential function, his research thus wanders from algebra conceptuwl number theory to analysis to geometry and topology. I have recently come across Conceptual Mathematics: It is a gentle introduction to Category Theory and strikes me as a potential alternative text for a bridging course to abstract mathematics.
The category of sets. Even so, as the text advances, it becomes clear why Category Theory is also known as Abstract Nonsense although I do realise that there’s supposedly donceptual negative charge in that term. My first attempt to understand what the Haskell folks are really up to. Namely, category theory is an abstraction of standard, undergraduate level abstract algebra, which is itself an abstraction of the sort of very concrete mathematical manipulations most students have seen up to that point.
Conceptual Mathematics: A First Introduction To Categories by F. William Lawvere
Be the first to ask a question about Conceptual Mathematics. Ascending to categories of richer structures. Examples of conecptual constructions. In fact maathematics first undergraduate introduction to abstract algebra began with five weeks of category theory. I was thinking along the lines of a somewhat unconventional bridging course in which the focus would be more on gently learning about abstraction than on proof techniques.
Goodreads helps you keep track of books you want to read. To see what your friends thought of this book, please sign up. Clark May 19 ’14 at Thanks for telling us about the problem.
Before we studied monoids we studied sets and mapping from the perspective of universal mapping properties, e. I would imagine that many people who think that they are not good at math are simply lacking the conceptual ideas that are taught in this book. If you like books and marhematics to build cool products, we may be looking for you.
Conceptual Mathematics: A First Introduction To Categories
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. One is barely learning set theory at all but rather learning how to do some manipulations with sets.
The last time I was teaching for a set-theory-like proof-course we used the first half of Wilder’s classic text: Such concepts as the associative theorems, distributions and other items of set theory are discussed. I actually think it makes a great deal of sense to talk about quotients in the category of sets before introducing them in group theory.
More on universal mapping properties. Subobjects logic and truth. However, I’ve never taught from it and I don’t think it’s well-suited to the goals of a typical bridging course. Email Required, but never shown.
Binary operations and diagonal arguments. John Taylor rated it it was amazing Apr 05, Schanuel No preview available – If you are interested in trying this text for a bridging course, then maybe using Leinster’s presentation would be of help. Oliver rated it really liked it Nov 13, Some uses of graphs. Adjoint functors with examples from graphs and dynamical systems.
Uniqueness of products and definition of sum. Bell Limited preview – Eric Katerman rated it it was amazing Jul 02, Lists with This Book.
The message of this article is that this can be done, in a simple, practical way due to Lawvere. If so, then this topic really should be taught to more people who feel that they don’t have the aptitude to master math.
Pictures of a map making its features evident. In particular, the ten axioms stated informally are: Jens rated it it was amazing Sep 05, Elementary universal mapping properties. Composing maps and counting maps.
Rebin rated it it was amazing May 19, In this course I spend more than two weeks on mathematical induction, and the abstraction of induction as a statement about subsets of the natural numbers is very challenging for the students. An arXiv version can be found here.
Josh Cartwright rated it liked it Feb 08, No trivia or quizzes yet. James rated it it was amazing May 12, Post as a guest Name.