This module is not currently running in 2024 to 2025.
Systems of linear equations appear in numerous applications of mathematics. Studying solution sets to such systems leads to the abstract notions of a vector space and a linear transformation. Matrices can be used to represent linear transformations and to do concrete calculations. This module is about the properties of vector spaces, linear transformations and matrices. The syllabus includes: vector spaces, linearly independent and spanning sets, bases, dimension, subspaces, linear transformations, the matrix of a linear transformation, similar matrices, the determinant, diagonalisation, bilinear forms, norms, and the Gram-Schmidt process.
Up to 48 hours of lectures and example classes
90% Examination, 10% Coursework
S Lipschutz Linear Algebra. (Schaum’s Outline Series, McGraw-Hill, N.Y., 1974) (R)
L Smith Linear Algebra. (Springer-Verlag, N.Y., 1984) (B)
G Strang Linear Algebra. (3rd ed., Harcourt, Brace, Jovanovich, San Diego, 1988) (B)
See the library reading list for this module (Canterbury)
The Intended Subject Specific Learning Outcomes. On successful completion of the module students:
(a) should have a reasonable understanding of the definitions and terms relating to Linear Algebra introduced in the module;
(b) should have a reasonable understanding of the statements, proofs and implications of the basic theorems given in the module (sufficiently well to be able to construct simple proofs of related results);
(c) should have confidence and reasonable skill in calculating with matrices and in specific vector spaces, etc. using the theorems derived during the module and with relatively little
guidence;
(d) should have developed a critical appreciation of the central role of linear algebra in Mathematics
and in its applications;
(e) should be able to present simple arguments and conclusions in Linear Algebra with reasonable
clarity;
(f) should be aware of the possibilities for using Maple to solve simple problems just beyond the range of "hand calculation".
The Intended Generic Learning Outcomes. On successful completion of the Module students will have:
-developed their problem-solving skills in relation to Linear Algebra.
-have acquired a reasonable facility in numerical and symbolic calculation with matrices and other related constructs in Linear Algebra.
-have furthered their time-management and organisational skills, as evidenced by the ability to plan and implement efficient and effective modes of working.
-have furthered their study skills in an area that lies at the heart of most advanced Mathematics,
Statistics and applications of these areas and is therefore valuable for continuing professional development.
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