620-122 Mathematics B (Advanced)

Students may gain credit for only one of [01]620-112, 620-122, 620-142, [05]620-192, [05]620-194 or 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 many 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.

Linear algebra topics include vector spaces in general, axioms, linear independence, basis sets, dimensionality, Rⁿ and Cⁿ; inner products; linear transformations, matrix of a linear transformation, change of basis, rank, inverse, and solution of linear equations; and eigenvectors and eigenvalues, rotation matrices, diagonal, real-symmetric and orthogonal matrices.

Applications include error correcting codes, graphs and networks, and the classification of quadratic forms, conics and quadrics.

Modular arithmetic topics include computation modulo n, division with remainder and Euclid's Algorithm.

Up to 24 pages of written assignments during semester (15%) and a 3-hour end-of-semester written examination (85%).