A Course of Pure Mathematics
G.H. Hardy's text is a good single volume refresher course for work in analysis and more advanced algebra, including number theory. Not quite as modern as Birkhoff and MacLane's text, or Manes' work, this volume forms the underpinnings of both works. If you have a good understanding of the preliminary work required in algebra and geometry, Hardy can be read directly and with pleasure. If you have a desire to understand the basis of what is presented in most first-year calculus texts, then Hardy's text is for you.
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Review: A Course of Pure MathematicsUser Review - Ian Carmichael - Goodreads
Beautiful writing, and typesetting. Read full review
Review: A Course of Pure MathematicsUser Review - Yasiru (reviews will soon be removed and linked to blog) - Goodreads
While more contemporary introductions to real analysis like Rudin's strive for elegance and perhaps seem tryingly terse while tying the subject neatly together, Hardy manages to convey an excitement ... Read full review