A Course of Pure Mathematics

Contents: 1. Real Variables. 2. Functions of real variables. 3. Complex numbers. 4. Limits of functions of a positive integral variable. 5. Limits of functions of a continuous variable. Continuous and discontinuous functions. 6. Derivatives and integrals. 7. Additional theorems in the differential and integral calculus. 8. The convergence of infinite series and infinite integrals. 9. The logarithmic, exponential and circular functions of a real variable. 10. The general theory of the logarithmic, exponential and circular functions.

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. The book contains a large number of descriptive and study materials together with a number of difficult problems with regards to number theory analysis.