Mathematics Asked by Beginner on December 15, 2020

There are many books on this subject.

Since, for teaching the course, I am searching, whether there is a single book which can be completely followed during the semester, and which contains the following topics. The following topics mostly either do not come in book, or very short highlight of these topics is given in such books.

(1) Construction of natural numbers, well-ordering principle, with rigorous definitions and proofs.

(2) Construction of integers, rationals, reals, with basic theorems (with proof) (Although students may be familiar with {it use of theorems}, they may not have come before the thorough understanding of them, up to some extent. I mean, I do not want to see just statements of basic theorems on natural numbers, rationals, reals, etc. I want to see their systematic construction, with rigorous proofs!)

(3) Multivariable calculus (including Gauss divergence theorem, Stokes theorem, Greens theorem, with proofs).

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