The Nrich Maths Project Cambridge: Fractional Calculus I - http://www.nrich.maths.org/public/viewer.php?obj_id=1365&part=index&refpage=monthindex.php Using the gamma function, a definition of integration and differentiation performed a fractional number of times is presented.
Harmonic Analysis - http://www.math.ucla.edu/~tao/harmonic/ Maintained by Terence Tao, UCLA. Lists events, personal pages, preprints, research groups, other links.
An Introduction to the Gauge Integral - http://www.math.vanderbilt.edu/~schectex/ccc/gauge/ Discusses the properties of an alternative integration theory, and its relationship with the Riemann and Lebesgue integrals.
Advanced Calculus and Analysis - http://www.maths.abdn.ac.uk/~igc/tch/ma2001/notes/notes.html Lecture notes from the University of Aberdeen for a first course in Analysis.
On the Atiyah-Singer Index Theorem - http://www.abelprisen.no/nedlastning/2004/popular_english_2004.pdf An overview of the Atiyah-Singer Index Theorem that places the result in historical and mathematical context.
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