MA2321 - Analysis in Several Real Variables
Dr. David R. Wilkins
Resources

MA2321 Michaelmas Term 2015: Resources

Basic Analysis: Introduction to Real Analysis (Jiří Lebl): This free online textbook is based on lecture notes for lecture courses taught by Jiří Lebl at the University of Illinois at Urbana Champaign and at the University of Wisconsin-Madison. It is also possible to buy paperback copies fo the book.
Advanced Analysis (Yan Min, Hong Kong University of Science and Technology).

Metric and Topological Spaces (P.M.H. Wilson, Cambridge University: These lecture notes relate more directly to MA2223 than to MA2321. Nevertheless there are close correspondences between the subject matter of modules MA2223 and MA2321, and accordingly the notes of the Metric and Topological Paces lecture course within the Cambridge Tripos, as taught by Prof. P.M.H. Wilson, have relevance for both modules MA2223 and MA2321.
Honors Analysis (MATH 55b) (Curtis McMullen, Harvard University).
Analysis II (MATH 114) (Curtis McMullen, Harvard University).

Real Analysis (YouTube videos): A lecture course on Real Analysis delived in Spring 2010 at Harvey Mudd College by Professor Francis Su

Essays on the Theory of Numbers, by Richard Dedekind, translated by Wooster Woodruff Beman: This book, available online from the Internet Archive, contains two essays. The first of these essays, entitled Continuity and Irrational Numbers develops a rigorous theory of real numbers, where such numbers are constructed via Dedekind Sections. A Dedekind section is a partition of the set of all rational numbers into two subsets A₁ and A₂, where every rational number belongs to exactly one of the sets A₁ and A₂, and where every rational number belonging to A₁ is less than every rational number belonging to A₂. Dedekind's original work, published in German, was translated into English by Wooster Woodruff Beman (1850—1922) (see the webapge at the Bentley Historical Library, University of Michigan).