### Dr Matthias Dörrzapf

Dr Matthias Dörrzapf is the Director of International Programmes. He is also the Director of Studies in Mathematics.

Dr Dörrzapf has a PhD in Mathematics from Queens' College, Cambridge. Before he joined St. John's College he had a postdoctoral research position at the Lyman Laboratory of Physics at Harvard University. He obtained his undergraduate qualifications in Mathematics and Physics at the University of Karlsruhe.

Dr Dörrzapf is interested in algebraic aspects of quantum field theories, in particular representations of symmetry algebras in conformal field theories and string theories. He has worked on the representation theory of superconformal algebras which plays a central role in string theory and has developed methods to classify superconformal representations. Dr Dörrzapf is also interested in probability theory and has worked on risk management models in financial mathematics in particular with respect to credit risk. He has done work for Deutsche Bank in Frankfurt and New York in collaboration with KMV corporation, San Francisco.

Dr Dörrzapf has lectured core courses such as* Vector Calculus* in Part IA and *Symmetries and Groups in Phyiscs* in Part II of the Cambridge Mathematical Tripos. For the College Dr Dörrzapf is teaching many of the core Part IA and Part IB applied mathematics courses.

### Part IA Vector Calculus

#### Tensors revision questions

Part IB exams 2005, paper 4, question 16

Part IB exams 2004, paper 1, question 6

Part IB exams 2004, paper 2, question 17

Part IB exams 2003, paper 2, question 2

Part IB exams 2003, paper 2, question 11

Part IB exams 2002, paper 2, question 2

Part IB exams 1999, paper 2, question 11

Part IB exams 1998, paper 4, question 2

Part IB exams 1997, paper 4, question 2

Lecture notes - Chapter I and II (Curves in R^3)

Lecture notes - Chapter III (Integration in R^2 and R^3)

Lecture notes - Chapter IV (Vector Operators)

Lecture notes - Chapter V (Integration Theorems, Laplace's Equation)

Lecture notes - Chapter VI (Laplace's Equation)

Lecture notes - Chapter VII (Cartesian Tensors)

Lecture notes - Complete Lecture Notes 2006

Lecture notes - Transparencies

Example sheets - Sheet 1

Example sheets - Sheet 2

Example sheets - Sheet 3

Example sheets - Sheet 4

Past Lecture Notes - 2005