Basic Algebraic Topology and its Applications (Relié)

This completely self-contained text is intended either for a course in honors calculus or for an introduction to analysis. Beginning with the real number axioms, and involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate math majors. This fourth edition includes an additional chapter on the fundamental theorems in their full Lebesgue generality, based on the Sunrise Lemma.
Key features of this text include : Applications from several parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more ; A heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero ; Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals ; A self-contained treatment of the fundamental theorems of calculus in the general case using the Sunrise Lemma ; The integral is defined as the area under the graph, while the area is defined for every subset of the plane ; 450 problems with all the solutions presented at the back of the text.