Hardy's "A course of Pure Mathematics" has been highly regarded since it was first published in 1908 because it was an innovative text: rigorous, modern, well-written. Its intended readership was always first year "honours" mathematics students. This book inspired innovation in subsequent generations of textbook writers.
However, in the 21st century, this book really can no longer be recommended for its original teaching purpose. As a textbook it is outdated (a term I hate, but it is true). It is now an historical curiosity - although one which I am pleased to own, and the exercises in the book are still worth a look.
Calculus teaching has progressed considerably since 1908. The construction of the real number system in Hardy's book, using the Dedekind Cut method is overly complicated - the use of the of Least Upper Bound is much simpler and clearer. Hardy defines the concept of integral solely as the anti-derivative; there is no discussion of Riemann sums, or Darboux sums, etc. I am sure I would not want to take Hardy's approach today.
I think we are better off recommending books are more modern.
I will start by recommending "Calculus" by Michael Spivak.
However, in the 21st century, this book really can no longer be recommended for its original teaching purpose. As a textbook it is outdated (a term I hate, but it is true). It is now an historical curiosity - although one which I am pleased to own, and the exercises in the book are still worth a look.
Calculus teaching has progressed considerably since 1908. The construction of the real number system in Hardy's book, using the Dedekind Cut method is overly complicated - the use of the of Least Upper Bound is much simpler and clearer. Hardy defines the concept of integral solely as the anti-derivative; there is no discussion of Riemann sums, or Darboux sums, etc. I am sure I would not want to take Hardy's approach today.
I think we are better off recommending books are more modern.
I will start by recommending "Calculus" by Michael Spivak.