MA2321 - Analysis in Several Real Variables
Dr. David R. Wilkins
MA2321 Michaelmas Term 2015: Resources
Lecture Courses available as Textbooks
- Basic Analysis: Introduction to Real Analysis (Jiří Lebl)
- This free online textbook is based on lecture notes for
lecture courses taught by
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).
Lecture Courses available as Online Notes
- 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).
Lecture Courses available as Videos
- Real Analysis (YouTube videos)
- A lecture course on Real Analysis delived
in Spring 2010 at Harvey Mudd College
by Professor Francis Su
Websites for computer algebra, 3D plotting etc.
- Wolfram Alpha
- 3D Function Grapher at http://www.math.uri.edu/~bkaskosz/flashmo/graph3d/
Resources related to Specific Topics
The Real Number System
- 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).
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Dr. David R. Wilkins,
School of Mathematics,
Trinity College Dublin.