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;
and standard deviation of a sum of independent random
variables; law of large numbers.
- Linear algebra:
- inner products between vectors;
expansions and gradients of functions over vector spaces;
- eigenvectors and eigenvalues of symmetric matrices.
- Differentiation using Chain rule.
- Statistical physics:
- definition of partition function;
thermodynamic functions from the partition function;
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