Re:The Art of Mathematics
by chongli on Sunday November 18, 2018 @03:40PM
(#18482416)
One thing I cannot stand is the general lack of definitions. My mind is oriented to programming where anything outside of the language must be defined in scope. Or maps, which have a legend and define abstract symbols.
My first year linear algebra textbook is nothing like this. On page 1 (the very first page after the Roman numeral pages including the title page, table of contents, and forward) is a bright yellow box defining the set R^n.
The remainder of the book is chock full of these definition boxes. Additionally, there are blue boxes for remarks, green boxes for examples, mauve boxes for theorems, and red boxes for exercises.
It's really that straightforward. You could probably skip all of the prose text and just use these boxes to learn what you need to get through the exercises and pass the course. Other math texts I've read may not have this nice colour scheme, but they're still pretty easy to follow.
The exercises, on the other hand, will challenge you to think creatively and demand that you learn how to apply the definitions and theorems properly in your proofs.
My first year linear algebra textbook is nothing like this. On page 1 (the very first page after the Roman numeral pages including the title page, table of contents, and forward) is a bright yellow box defining the set R^n.
The remainder of the book is chock full of these definition boxes. Additionally, there are blue boxes for remarks, green boxes for examples, mauve boxes for theorems, and red boxes for exercises.
It's really that straightforward. You could probably skip all of the prose text and just use these boxes to learn what you need to get through the exercises and pass the course. Other math texts I've read may not have this nice colour scheme, but they're still pretty easy to follow.
The exercises, on the other hand, will challenge you to think creatively and demand that you learn how to apply the definitions and theorems properly in your proofs.