Conceptual Mathematics
by F. William Lawvere, Stephen Hoel Schanuel · first published 1997
82% recommend18% neutral
Why HN recommends it
Gentle, accessible introduction to category theory that needs only high-school math and builds from sets. Suits self-learners and programmers who find standard texts too dense, and it helps explain sum and product types.
Summarised by Claude from recommending comments
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…good foundation for mathematical thinking. Concrete Mathematics by Graham, Knuth, Patashnik Spivak’s Calculus How to Prove It by Velleman Polya’s How to Solve It E.T. Jaynes’ Probability Theory Conceptual Mathematics by Lawvere and Schanuel
on “Book: Mathematics for Machine Learning” ↗If you want an actual introduction to the topic, "Conceptual Mathematics: A First Introduction to Categories" by Lawvere and Schanuel is the right choice.
on “A concise introduction to category theory” ↗I can't comment on applications of category theory to computer programming or computer science, but I believe that the book Conceptual Mathematics by Lawvere and Schanuel is a nice introduction to the basic ideas of category theory. http://www.cambridge.org/catalogue/catalogue.asp?isbn=978052... I believe this book has been discussed "recently"…
on “Basic Category Theory” ↗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…
on “Ask HN: Math books like SICP?” ↗What kind of mathematics do you want to learn? If you are interested in discrete mathematics and algebra, Haskell has something to offer. I would also read http://www.amazon.com/Conceptual-Mathematics-First-Introduct... which is a great introduction (unspecific to code). If you are more interested in linear algebra or numerics, I would suggest to get to know numpy better.
on “Paul Hudak, co-creator of Haskell, has died” ↗For an even more basic introduction I'd recommend starting with Lawvere and Schanuel's Conceptual Mathematics: A First Introduction to Categories. Requires less abstract algebra. If you have some mathematical intuition then this is the book to start with. I'm surprised he cites Sets for Mathematics but doesn't…
on “Basic Category Theory” ↗> For an even more basic introduction I'd recommend starting with Lawvere and Schanuel's Conceptual Mathematics: A First Introduction to Categories. Requires less abstract algebra. If you have some mathematical intuition then this is the book to start with. It's a great book! Don't forget to do the exercises.…
on “Basic Category Theory” ↗I would highly recommend the book by Lawvere and Schanuel: "Conceptual Mathematics: A First Introduction to Categories". It is a very down-to-earth introduction to category theory, written by two masters of the field.
on “A monad is a monoid in the category of endofunctors, what’s the problem?” ↗…probability, logic. Wow! Yandell - The Honors Class: Hilbert's problems and their solvers. Lots of mini biographies with some information describing each of Hilbert's famous problems. Lawvere & Schanuel- Conceptual Mathematics. Some basic notions of category theory, geared towards teaching you Lawvere's clarification and generalization of the incompleteness theorems. Cormen - Algorithms Unlocked. Pop Science version of some…
on “Classic Mathematics Books for Lifelong Learners” ↗I was in the same boat a year ago and went to a mathematics professor teacher and he suggested this book: Conceptual Mathematics by Lawvere[1] The book teaches category theory to, smart, highschool students. It's a great start. After that I went with: Category Theory for Programmers by Bartosz Milewski [2] Next I would go…
on “Ask HN: How to Get into Category Theory?” ↗…Bryson, and John Terilla Check out this list: http://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf for others. Category theory: Categories and Toposes: Visualized and Explained - Southwell Conceptual Mathematics: A First Introduction to Categories - Lawvere Category Theory for Programmers - Milewski (if you like functional programming) Programming with Categories - Fong, Milewski, Spivak (if you like functional…
on “Physics Student Earns PhD at Age 89” ↗he would likely enjoy Lawvere's conceptual mathematics.
on “Bret Victor's favourite books” ↗…learn CT I recommend you learn abstract algebra first via Aluffi's "Algebra: Chapter 0". It's secretly a CT book, but is not trying to be so abstract. You can also learn a lot from Schanuel and Lawvere's "Conceptual Mathematics" which, I feel, is one of the better books for establishing the "category theoretic POV".
on “Applied Category Theory” ↗…kinds of topics. I think it's wonderfully enlightening for programming (although standard disclaimed applies that it's not necessary for programming). I recommend that paper, and I also recommend reading Conceptual Mathematics by Lawvere and Schanuel. It's easily my favorite book for getting into "how to think with CT".
on “The logic of Buddhist philosophy” ↗…here is better known as Category Theory. I highly, highly recommend learning more about it if you're interested. I cannot understate its beauty. As a starter guide, I highly recommend reading Lawvere's Conceptual Mathematics.
on “Algebraic Data Types” ↗