620-142 Mathematics B

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

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

This subject develops the concepts of vectors, matrices and the methods of linear algebra as tools for modern mathematics and introduces the basic properties of sequences and series, including Taylor series for functions. Students should develop the ability to understand the methods of linear algebra and convergence of series and sequences.

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; eigenvectors and eigenvalues, rotation matrices, diagonal, real-symmetric and orthogonal matrices. 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.

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.