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MA283 Linear Algebra
Amongst the topics to be covered are the following
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Vector spaces, bases, dimension, linear maps, matrix representation of
linear maps
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Matrix algebra, kernels and images, least squares fitting, inner product
spaces, the Gram-Schmidt process
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Fourier series, dual spaces, the rank of a matrix, determinants, eigenvalues
and eigenvectors, the characteristic polynomial, quadratic forms
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Diagonalisation of a symmetric or Hermitian linear map
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Triangularisation of a linear map
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The Hamilton-Cayley theorem, linear programming
Texts
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T.S. Blyth & E.F. Robertson, "Matrices and Vector Spaces and Linear
Algebra" (Chapman & Hall)
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S. Lipschutz, "Linear Algebra" (Schaum Outline)
References
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H. Anton, "Elementary Linear Algebra" (Wiley)
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J.W. Archbold, "Algebra" (Pitman)
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G. Birkhoff & S. MacLane, "A Survey of Modern Algebra" (Macmillan)
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I.N. Herstein, "Topics in Algebra" (Blaisdell)
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S. Lang, "Linear Algebra" (Springer)
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T.A. Whitelaw, "An Introduction to Linear Algebra" (Blackie)
MA284 Discrete Maths
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Enumeration: product rule, sum rule and sieve principle, selections and
distributions, the pigeonhole principle
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Graphs, the fundamentals (including various notions of 'path' and 'tree'),
plus a study of some of the following topics: colouring problems, bipartite
graphs, Hamiltonian graphs, planar graphs and tournaments. Algorithms and
applications are emphasised throughout.
Texts
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N.L. Biggs, "Discrete Mathematics", (Oxford)
Back to 2nd Year Syllabus
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