

Mathematical prerequisites for ITPRNN course
The level of Mathematics assumed is 1A Maths for Natural Scientists.
All the following topics will be reviewed.
 Probability and statistics:
 definition of conditional probability,
joint probability, marginal probability;
 Bayes' theorem;
 definition
of independence;
 mean
and standard deviation of a sum of independent random
variables; law of large numbers.
 Linear algebra:
 inner products between vectors;
 Taylor
expansions and gradients of functions over vector spaces;
 eigenvectors and eigenvalues of symmetric matrices.
 Differentiation using Chain rule.
 Statistical physics:
 definition of partition function;
 obtaining
thermodynamic functions from the partition function;
 entropy
of a set of N binary spins as a function of the fraction x of
spins that are +1;
 relationship between canonical
ensemble and microcanonical ensemble, and equivalence of the
Boltzmann and Gibbs entropies S=k_B log and
S= p_i 1/p_i (for large systems).

Site last modified Sun Aug 31 18:51:05 BST 2014

