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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There can be few textbooks of mathematics as well-known as Hardy's Pure Mathematics. Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned at the beginning of their undergraduate courses.

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