Simon Brain

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At present I do not have any teaching duties.

As a research fellow at Radboud University Nijmegen, during the Spring Semester 2012-13 and the Winter Semester 2013-14 I taught:

Introduction to Partial Differential Equations (60 UE).

As a research fellow at the University of Luxembourg, during the Winter Semester 2011-12 I taught:

Algèbre I; jointly with Dr Chiara Pagani (in French, 60 UE in total).

During my graduate and post-graduate years at the University of Oxford (2000-07) I gained quite a lot of teaching experience. Upon finishing my PhD I took a stipendiary lectureship in pure mathematics at Pembroke College (2005-07), where I gave tutorials (usually 12 hours per week) to groups of two to three undergraduates, as well as intercollegiate classes (usually two hours per week) to groups of up to 12 undergraduate and master-level students.

In my final year as a graduate student (2003-04) I held a non-stipendiary lectureship in pure mathematics at St Anne's College, with similar teaching responsibilities (8-10 hours per week). For several years I taught a significant proportion of the applied mathematics syllabus at Mansfield College. Moreover, in my early graduate career, I acted as a Teaching Assistant in various sets of intercollegiate classes at the Mathematical Institute.

Here is a (reasonably comprehensive) list of the Oxford courses that I taught over the years, most of them more than once.

Moderations (First Year Undergraduate Syllabus)

  • analysis I: sequences and series;
  • analysis II: continuous and differentiable functions;
  • analysis III: integration of continuous functions on compact intervals;
  • linear algebra: vector spaces, bases, linear transformations, diagonalisation etc;
  • elementary group theory;
  • vector geometry; geometry of the complex plane;
  • partial differential equations;
  • Fourier series;
  • calculus in three dimensions.

Part a (Second Year Undergraduate Syllabus)

  • complex analysis;
  • linear algebra: ring theory, finite-dimensional inner product spaces.
  • differential and integral equations;
  • Lebesgue integration;
  • point-set topology;
  • group actions, introduction to splitting fields;
  • Lagrangian mechanics, calculus of variations;
  • incompressible fluid mechanics;
  • number theory;
  • electromagnetism;
  • quantum theory.

Part b (Third Year Undergraduate Syllabus)

  • quantum theory (as a TA and as class tutor);
  • special relativity (as a TA);
  • Hilbert spaces (as a TA).

Part c (Fourth Year Undergraduate Syllabus)