Okay, some necessary information, I am majoring in Pure Mathematics, Physics and Computer Science, and I am hoping to study further in Pure Mathematics.
Currently I am going through a course in Discrete Mathematics as part of my Computer Science branch of modules.
One of the things I've noticed, is that generally Discrete Mathematics courses that fall under Computer Science departments treat a wide variety of different topics in small batches, from elementary Set Theory, Graph Theory, to Algebraic Structures.
So my question is: Is there any sort of discrepancy in the way that the topics covered in a typical Discrete Mathematics course, as compared to a Pure Mathematics course on those same topic (apart from the depth of content)? For example, are certain definitions altered for use in Discrete mathematics as composed to Pure Mathematics?
Furthermore are the usual 'go-to' books for Discrete Mathematics, such as Applied Discrete Stuctures by Al Doerr and Ken Levasseur and Concrete Mathematics by Donald Knuth, vastly different from a Pure Mathematical treatment of the topics covered in the books?
The reason I ask this, is I don't want to end up in a position where I develop the wrong intuitions about topics in Pure Mathematics as a result of going through a course in Discrete Mathematics.
EDIT: Developing the wrong intuition is something I want to avoid as having gone through Physics courses I had to get rid of all the wrong intuitions of vectors I had developed. Any student of both Pure Maths and Physics, would know of the story of how vectors are defined in Physics (as 'things' that have magnitude and direction', and their proper mathematical definition as elements of a vector space)
Is there anyone who has gone through a course in Discrete Mathematics, and has done courses in Pure Mathematics that can offer some opinions/advice on this matter?
Or is my view of a 'divide' between Discrete Mathematics and Pure Mathematics, or of the way they're treated in courses, wrong?