This is the first of two courses on real analysis. This course is compulsory for students of mathematical sciences, and it is a prescribed elective course for students from other schools as well. The course aims to present a careful treatment of the principal topics of calculus I and Calculus II, such as real numbers, basic topology of the real line, sequences and series of numbers and of functions, and to illustrate the power of the subject through a variety of applications. After learning this course, you will be able to understand better many results from Calculus I and II which you studied without proofs.
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