Teaching

The extended material for the courses on

  • Basic set theory
  • Metric and topological spaces
  • Measure and integration
  • Functional analysis
  • Fourier analysis
  • Analytic methods in partial differential equations
  • Representation theory of compact groups

with many examples and exercises, can be found in a single volume in this book.

Recent:

2017 M3P18/M4P18 Fourier Analysis and Theory of Distributions

Problems sheets, Solutions

(note that exercises in the above files go beyond what was covered in the course)

2014 TCC Course Pseudo-differential operators

Lecture notes

Coursebook: Chapters 1 and 2 here

Older 2004-2008:

2008: M2PM1 Analysis II.

Some short overview of the course is available here. Some (very incomplete) notes are available here. These are provided only for convenience, so notes taken during lectures should be the main reference for the course and exam, and those lecture notes are supposed to be used.
Last year exams should be available in the library.
In addition (but not necessary), any book on basic analysis could be also helpful, e.g. some possible books are:
William F. Trench, Introduction to Real Analysis, Pearson Education, 2003;
K.R.Davidson and A.P.Donsig, Prentice Hall, 2002;
Steven R. Lay, Analysis with an introduction to proof, 4th edition, Pearson Education, 2005.

 

2006: M2P1 Analysis II.

Summary of the course is here.

2006: M4P41/MSP11 Analytic methods in PDEs.
All the materials will be given during the course. Exercises for the course are here.

M3P1 Metric and Topological spaces. Summary of the course is here.
M2P1 Analysis II. Summary of the course is here for 2004 and here for 2005. Additional exercises from lectures are here.
M3P5 Geometry of curves and surfaces. Summary of the course is here.

Old:

Spring 2000 (Edinburgh): (Math 2Y:) Counting and Probability
Fall 1999 (Edinburgh): Mathematical Studies 1Ah, Lectures: TuF-12, AT Room 6; Tutorials Th-12
Fall 1999 (Edinburgh): Tutoring: Math 2X, Algebra + Analysis, Mo-10-11 and 11-12

Spring 1999 (JHU): Real Variables II, 606, MTW-2
Spring 1999 (JHU): Fourier Analysis and Generalized Functions, 443, TW-4
Fall 1998 (JHU): Real Variables I, 605, MTW-2