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Although archived, it is open for learning without registration or enrollment. And it is very important to be familiar with a number of specific examples of functions and to understand the concepts of differentiation and integration before going on to learn the rules which enable one to actually differentiate and integrate functions. (In fact, calculus teachers are often annoyed when students, inventing the axiomatic approach on their own, as it were, discover that it is not really necessary to understand the concepts in order to do the calculations.) But a typical undergraduate course in Modern Algebra starts out saying something like, "A group consists of a set of elements which can be multiplied in such as a way that the following three axioms are satisfied." (Four axioms if one includes closure, which was in fact the key axiom and to some extent was the only one in the original development of group theory, associativity and the existence of an identity element and inverses being taken as pretty much self-evident.) It is understandable that a student might ask in bewilderment, "But what are these elements?
Pages: 202
Publisher: Birkhäuser; Softcover reprint of the original 1st ed. 1991 edition (December 21, 2012)
ISBN: 146126765X
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I agree with this to extent, but abstract algebra seems like it would be more applicable to graduate level math courses. I also am trying to find some areas where abstract algebra, or number theory are used in CS. It seems like a lot of people say taking high level math can be beneficial, and I am sure thinking abstractly can indeed help , cited: The Foundations of Analysis: A Straightforward Introduction: Book 1 Logic, Sets and Numbers: Logic, Sets and Numbers Bk. 1 1st (first) Edition by Binmore, K. G. published by Cambridge University Press (1981)
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Typically, in an undergraduate course in Modern Algebra (what is often referred to as a Herstein level course), we simply take the axiomatic approach for granted from Day One
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