620-122 Mathematics B (Advanced)

Students may gain credit for only one of [01]620-112, 620-122, 620-142, [99]620-200, 620-211.

One of [00]620-111, 620-120 (MUPHAS Mathematics), 620-121 or a grade of H1 in either 620-140 or 620-141.

This subject gives a solid grounding in key areas of mathematics needed in modern science and technology, and is the gateway to all recent mathematical developments. Little of the material here has been seen at school, and the level of understanding required represents a distinct advance on the minimum necessary in previous subjects.

Sequences and series topics include convergence and divergence of sequences and series; tests for convergence; and Taylor's theorem and series representation of elementary functions. Linear algebra topics include vector spaces in general, axioms, linear independence, basis sets, dimensionality, R_n and C_n; inner products; linear transformations, matrix of a linear transformation, change of basis, rank, inverse, solution of linear equations; and eigenvectors and eigenvalues, quadrics and conics, rotation matrices, diagonal, real-symmetric and orthogonal matrices.

Up to 24 pages of written assignments, a 3-hour end-of-semester written examination and class tests totalling not more than 1.5 hours.