Series and Matrices MQF LEVEL
6
STMARTINS.EDU/COMPUTING
TOTAL CREDITS: 4ECTS
This unit consolidates and builds upon mathematical material previously covered to provide students with more advanced subjects in mathematics particularly within the topics of Series and Matrices. Such subjects would help the students obtain a sound mathematical foundation for use within other subjects in the degree or diploma programmes. At the end of this unit the student will have acquired the responsibility and autonomy to: — distinguish between a sequence and a series; — define sequences by means of recurrence relations and initial terms and compute any terms within such a sequence; — recognise an arithmetic progression and find a recurrence relation for it; — recognise a geometric progression and find a recurrence relation for it; — define and compute the terms of the Fibonacci sequence; — define the principle of induction; — prove a result for all positive integers by induction; — prove by induction a formula for the nth term of a sequence, in particular when the sequence is given by initial terms and a recurrence relation; — express series in terms of the Sigma notation; — interpret and work out series represented by the Sigma notation; — find the sums of an AP and GP; — use standard results to find the sums of particular series; — write a system of linear equations as a matrix equation; — identify which arithmetic operations can be performed in matrices and evaluate examples involving such operations; — write down and interpret an augmented matrix from a system of linear equations; — use Gaussian elimination to reduce a matrix to row echelon form; — use Gaussian elimination and back substitution to find all solutions to a system of linear equations; — apply knowledge of matrices to interpret powers of the adjacency matrix of a graph/digraph. The assessment for this unit will be computed using the following weighting system: — 40% Assessed Coursework — 60% Examinations
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