Analysis 1

The study of real analysis is indispensable for a prospective graduate student of pure or applied  mathematics. It also has great value for any undergraduate student who wishes to go beyond the routine manipulations of formulas to solve standard problems, because it develops the ability to think deductively, analyze mathematical situations, and extend ideas to a new context.

Our goal is to reinforce and extend the ideas and methodology of the elementary theory of the main conceptual chapters real numbers, sequences, continuity and differentiability . Each of these chapters begins by discussing a typical new Analysis student’s existing relevant knowledge; it then reframes this knowledge in a more sophisticated way by introducing key definitions, highlighting properties, consequences and application if there exist.