Faculty of Mathematic Handbook,1987 - University of Newcastle

Text
References
Hale. J.K.
Hirsch. M.W. &
Smale, S.
Marsden, J.E. &
McCracken, M.
Nayfeh, A.H. & Mook, D.T.
Stoker, I.I.
Nil
664192 Fluid Statistical Mechanics - C.A. Croxton
Prerequisite
Hours
Examination
Content
Ordinary Differential Equations (Wiley 1969)
Differential Equations, Dynamical Systems and
Linear Algebra (Academic 1974)
The Hopf Bifurcation and its Applications
(Springer-Verlag 1976)
Nonlinear Oscillations (Wiley 1979)
Nonlinear Vibrations (Wiley 1950)
Nil
About 27 lecture hours
One 2-hour paper
Cluster-diagrammatic expansions - low density solutions: integrodifferential equations
(BOY. HNe, PY) - high density solutions; quantum liquids - Wu-Feenburg fermion
extension; numerical solution of integral equations; phase transitions - diagrammatic
approach; critical phenomena; the liquid surface; liquid metals; liquid crystals; molecular
dynamics and Monte Carlo computer simulation; irreversibility; transport phenomena.
Polymeric systems.
Text
Croxton, C.A.
References
Croxton, C.A.
664120 Quantum Mechanics - C.A. Croxton
Prerequisite Nil
Hours About 27 lecture hours
Examination
Content
Introduction to Liquid State Physics (Wiley 1975)
Liquid State Physics - A Statistical Mechanical
Introduction (Cambridge 1974)
One 2-hour paper
Operators; Scbrodinger equation; one dimensional motion; parity; harmonic oscillator;
angular momentum; central potential; eigenfunction; spin and statistics; Rutherford
scattering; scattering theory phase shift analysis; nucleon-nucleon interaction; spindependent
interaction; operators and state vectors; Schrodinger equations of motion;
Heisenberg equation of motion. Quantum molecular orbitals; hybridization; LCAO
theory; MO theory.
Texts
Croxton, C.A.
Matthews, P.T.
664153 Algebraic Graph Theory - R.B. Eggleton
Prerequisite
Hours
Examination
Introductory Eigenphysics (Wiley 1974)
Introduction to Qantum Mechanics (McGraw Hill 196r
Topic D
About 27 lecture hours
One 2-hour paper
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Content
The adjacency matrix of a graph. Path lengths, shortest paths in a graph. Spectrum of a
graph. Regular graphs and line graphs. Homology of graphs. Spanning trees.
Complexity of a graph. The determinant of the adjacency matrix. Automorphisms of
graphs. Vertex transitive graphs. The course will then continue with a selection from the
following topics, as time permits. Symmetric graphs, with attention to the trivalent case.
Covering graph of a graph. Distance-transitive graph. Realisability of intersection arrays.
Primitivity and imprimitivity. Minimal regular graphs of given girth. Vertex colourings
and the chromatic polynomial.
Text
Biggs, N.
References
Bondy, J.A. &
Murty. U.S.R.
Harary, F.
Lancaster, P.
Wilson, R.J.
Algebraic Graph Theory (Cambridge 1974)
664173 Mathematical Problem Solving - R.B. Eggleton
Prerequisite
Hours
Examination
Content
Graph Theory with Applications corrected edn
(Macmillan 1977)
Graph Theory (Addison-Wesley 1969)
Theory of Matrices (Academic 1969)
Introduction to Graph Theory (Longman 1972)
Topic 0
About 27 class hours
One 2-hour paper
The class will be conducted by a team of several staff members with interests across a
wide spectrum of mathematics. The course will contain a series of mathematical
problems, presented for solution. Participants in the class will be expected to contribute
to initial discussion of the problems, then to attempt individual solutions, and
subsequently to present their full or partial solutions. In the case of problems solved only
partially by individuals, subsequent class discussion would be aimed at producing a full
solution on a team basis. Finally participants in the class will be expected to write up a
polished version of the statement and solution of each problem. The intention of the
class is to build up participants' experience in skills appropriate for mathematical
research. The final examination will be mainly concerned with problems actually solved
during the year.
References References will be suggested during the course.
664142 Topological Graph Theory - R.B. Eggleton
Prerequisite
Hours
Examination
Content
Topic CO
About 27 lecture hours
One 2-hour paper
This topic deals with drawings of graphs on various surfaces. It will begin with a brief
introduction to the theory of graphs, to be followed by a fairly detailed introduction to
the topology of surfaces, with particular attention to the classification of surfaces. The
main graph-theoretic areas to be treated are: Kuratowski's Theorem characterising graphs
which can be embedded in the plane; genus, thickness, coarseness and crossing numbers
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