A Course of Pure Mathematics Third Edition

Originally published in 1908, this classic calculus text transformed university teaching and remains a must-read for all students of introductory mathematical analysis. Clear, rigorous explanations of the mathematics of analytical number theory and calculus cover single-variable calculus, sequences, number series, and properties of cos, sin, and log. Meticulous expositions detail the fundamental ideas underlying differential and integral calculus, the properties of infinite series, and the notion of limit.
An expert in the fields of analysis and number theory, author G. H. Hardy taught for decades at both Cambridge and Oxford. A Course of Pure Mathematics is suitable for college and high school students and teachers of calculus as well as fans of pure math. Each chapter includes demanding problem sets that allow students to apply the principles directly, and four helpful Appendixes supplement the text.

English mathematician G. H. Hardy (1877–1947) specialized in number theory and mathematical analysis and is responsible for biology's Hardy-Weinberg principle of population genetics. He mentored Indian mathematician Srinivasa Ramanujan, with whom he coined the Hardy-Ramanujan number, and he wrote the classic essay, "A Mathematician's Apology."

I. Real VariablesII. Functions of Real VariablesIII. Complex NumbersIV. Limits of Functions of a Positine Integral VariableV. Limits of Functions of a Continuois Variable. Continuous and Discontinuous FunctionsVI. Derivatives and IntegralsVII. Additionsal Theorems in the Differential and Integral CalculusVIII. The Convergence of Infinite Series and Infinite IntegralsIX. The Logarithmic and Exponential Functions of a Real VariableX. The General Theory of the Logarithmic, Exponential, and Circular FunctionsAppendix I. The Proof that Every Equation has a RootAppendix II. A Note on Double Limit ProblemsAppendix III. The Circular FunctionsAppendix IV. The Infinitive in Analysis and Geometry