CCMAS Course Search

Formal languages; Chomsky hierarchy; formal computation and machine models; finite automata; pushdown automata; Turing machines; Church's Thesis; Recursively enumerable sets; Diagonal arguments; Reducibility; complexity classes

Topological vector spaces and generalized functions; Distribution calculus and topology; convolution; Tempered distributions and their Fourier transforms; Integral transforms of Mathematical Physics; Application

The theory on closed and bounded intervals: Gauges and integrals; Basic properties of the integral; The fundamental theorems of calculus; The Saks-Henstock Lemma; Measurable functions; Absolute integrability; Convergence theorems; Integrability and mean Convergence; Measure; measurability and multipliers; Mode of Convergences; substitution theorems; Applications; The theory on infinite intervals: General insight into integration on infinite intervals

Basic Postulates of thermodynamics of simple; homogeneous systems; Thermodynamic potentials and stability of thermodynamic systems; Gibb's theory of thermodynamics with interaction effects; Partition functions of difference ensembles; Fundamental equilibrium theory; Liouville's theorem and the Ergodic hypothesis; Distribution Functions; entropy and connections with thermodynamics; Microcanonical; canonical and grand canonical ensembles; Boltzmann and Maxwell Boltzmann distribution phases and transitions; phenomenology of phase equilibria; First and second order transitions; Applications to classical and quantum systems; Boltzmann equation; Einstein transition probability; Random variables; Brownian motion and their applications; Universality and scaling Critical indices

Signal Theory; Continuous and Discrete Fourier series; Convolution integral; Correlation integral; Power spectral analysis; Filtering techniques; Application to geophysical data processing; Practical Examples and Classwork

Theory of stochastic models and their forecasting; Model building: identification; estimation; Diagnostic checking; Analysis of stationary Data Co-integration and error correction techniques

Review of categories and functors; Homology; fundamental group; covering transformation; simplicial complexes; Singular homology; Universal co-efficient theorem for homology and cohomology; Spectral sequence

Helminth parasites of medical and veterinary importance; including life history of parasites; Food and vector-borne parasitic infections; Type of diseases caused by helminth parasites; The role of host behaviour in parasitic helminth transmission; Circadian rhythms in the transmission of helminth parasites (filarial periodicity); Control strategies

Parasitic Protozoa of medical and veterinary importance; Transmission patterns and types of diseases caused by protozoan parasites in the tropics; The role of vectors in the transmission of protozoan diseases; The role of host behaviour in the transmission of protozoan parasites