Mathematical Analysis: An Introduction (Undergraduate Texts in Mathematics)

About this book

This is a textbook suitable for a year-long course in analysis at the ad vanced undergraduate or possibly beginning-graduate level. It is intended for students with a strong background in calculus and linear algebra and a strong motivation to learn mathematics for its own sake. At this stage of their education such students are generally given a course in abstract algebra and a course in analysis which give the fundamentals of these two areas as mathematicians today conceive them. Mathematics is now a subject splintered into many specialties and sub specialties but most of it can be placed roughly into three categories: al gebra geometry and analysis. In fact almost all mathematics done today is a mixture of algebra geometry and analysis and some of the most in teresting results are obtained by the application of analysis to algebra say or geometry to analysis in a fresh and surprising way. What then do these categories signify? Algebra is the mathematics that arises from the ancient experiences of addition and multiplication of whole numbers; it deals with the finite and discrete. Geometry is the mathematics that grows out of spatial experience; it is concerned with shape and form and with measur ing where algebra deals with counting.