By James R. Munkres
From the preface:
"This booklet is meant as a textual content for a path in research, on the senior or first-year graduate level.
A year-long path in actual research is an important a part of the education of any power mathematician. For the 1st 1/2 the sort of direction, there's large contract as to what the syllabus may be. commonplace subject matters comprise: series and sequence, the topology of metric areas, and the by-product and the Riemannian necessary for services of a unmarried variable. there are many very good texts for this sort of path, together with books through Apostol, Rudin, Goldberg, and Royden, between others.
There is not any such common contract as to what the syllabus of the second one 1/2 this type of path can be. a part of the matter is that there are just too many subject matters that belong in this type of path for one for you to deal with all of them in the confines of a unmarried semester, at greater than a superficial level.
At M.I.T., we have now handled the matter by means of delivering self sustaining second-term classes in research. the sort of offers with the spinoff and the Riemannian quintessential for features of numerous variables, through a remedy of differential types and an evidence of Stokes' theorem for manifolds in euclidean house. the current ebook has resulted from my years of educating this path. the opposite bargains with the Lebesque fundamental in euclidean area and its functions to Fourier analysis."
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