620-142 Mathematics B

Students may only gain credit for one of [01]620-112, 620-122, 620-142, [05]620-192, [05]620-194 or 620-211.

Normally one of 620-140 or 620-141, or any one of [00]620-111, 620-120 (MUPHAS Mathematics) or 620-121.

This subject develops the concepts of vectors, matrices and the methods of linear algebra as tools for modern mathematics and introduces modular arithmetic. Students should develop the ability to use the methods of linear algebra and gain an understanding of methods of mathematical proof. Students will also gain experience in using a mathematical software system.

Linear algebra topics include real n-space Rⁿ, vector spaces in general, axioms, linear independence, bases, dimension, inner products; linear transformations, matrix representation of a linear transformation, change of basis, rank, inverse, solution of linear equations; eigenvectors and eigenvalues, rotation matrices, diagonal, real symmetric and orthogonal matrices. Modular arithmetic topics include computation modulo n, division with remainder and Euclid's Algorithm. Applications include error correcting codes, graphs and networks, and the classification of quadratic forms.

Up to 36 pages of written assignments or project work during semester (20%) and a 3-hour end-of-semester written examination (80%).