Mathematical structures textbook recommendation

manpreet Best Answer 2 years ago

I am busy doing an undergraduate course called "Fundamentals of Mathematics". It is not well-defined as there is no syllabus nor recommended textbook (there are lectures and notes), but the course introduces one to quite complicated theoretical aspects of mathematics. I would like to find a textbook for this course which would help me to understand what is being taught.

What we have already covered or are covering:

Magmas and unitary magmas, preorders and orders, semilattices and lattices, semigroups, monoids, closure operators, equivalence relations (I am familiar with the definition of an equivalence relation, but I can revise the place a quotient set has in a canonical factorization of a map and so on), Russell Paradox, Boolean algebra, cardinality, categories, morphisms (including monomorphisms, endomorphisms and isomorphisms), sub-algebras, set-theoretic definition of natural numbers.

What I predict we will still cover, based on the notes:

Canonical factorization of homomorphisms, quotient algebras, classical algebraic structures, quotient groups, rings and modules, semirings and semimodules, pointed categories, products and coproducts, direct sums, free algebras and free semimodules.

I already have a textbook called "Introduction to Abstract Algebra", but this focuses on, and goes into depth about, algebraic structures, as opposed to briefly constructing the many structures mentioned above.

manpreet 2 years ago