Syllabus for `Managerial Mathematics`

Cheng-Hsi Hsieh (謝承熹)
E-Mail: chhsieh@mail.ntcb.edu.tw
Class Time: 2:20 p.m. - 5:20 p.m. on Monday, 2006

This is a one-semester course which represents an introduction to linear algebra. Moreover, some of its significant applications which relate to finance, econometric analysis, multivariate statistical analysis may be included. Students are required to have the background of calculus and to STUDY HARD. Also, discussion between students after classes are STRONGLY encouraged, sometimes are necessary, for better understanding the contents.

Textbook: Kolman and Hill, Introductory Linear Algebra: An Application-Oriented First Course, 8th Edition, Pearson Education, 2004.

Students will be evaluated by the following elements:
1. Mid-term examination: 35%
2. Final examination: 35%
3. Lab Session: 30%

Course Schedule:

(a) Linear Equation and Matrices.
Linear Systems. Matrices. Dot Product and Matrix Multiplication. Properties of Matrix Operations. Matrix Transformations. Solutions of Linear Systems of Equations.
(b) Determinants.
Definition and Properties. Cofactor Expansion and Applications. Determinants from a Computational Point of View.
(c) Vectors in Rn.
Vectors in the Plane. n-Vectors. Linear Transformations.
(d) Supplement Handout.
Calculus and Matrix Algebra, Optimization, Constrained Optimization, Partitioning the Mean Vector and Covariance Matrix
(e) Supplement Handout.
Mathematics of Portfolio Frontier

(f) Real Vector Spaces.
Real Vector Spaces. Subspaces. Linear Independence. Basis and Dimension. Homogeneous Systems. The Rank of a Matrix and Applications. Orthonormal Bases in Rn. Orthogonal Complements.
(g) Eigenvalues, Eigenvectors, and Diagonalization.
Eigenvalues and Eigenvectors. Diagonalization and Similar Matrices. Diagonalization and Symmetric Matrices.
(h) Supplement Handout.
Concept of Complete Market, Property of OLS, Guass-Markov Result