UCL School of Management

# MSIN107P: Mathematical Foundations of Management II

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#### Warning message

This is a past version of this module for MSIN107P 16/17.
Taught by
Level
First
Prerequisites
None
Eligibility
1st year undergraduates from Management Science BSc/MSci only
Terms
Term 2
Delivery method
2-hour lecture (x 8 weeks) and 2-hour seminar (x 8 weeks)
Assessment
20% coursework components (problem sets); 80% examination

#### Course overview

Mathematical Foundations of Management II develops students’ understanding of the concepts of linear algebra and provides experience with its methods and applications.

The module covers fundamental algebraic tools involving matrices and vectors to study systems of linear equations and Gaussian elimination, linear transformations, orthogonal projection, least squares, determinants, and eigenvalues and eigenvectors. The module includes examples that illustrate the concepts and their practical application in management.

The aim is to develop a rigorous understanding of key mathematical concepts that underpin the practice of management and develop strong quantitative thinking skills. The concepts and tools covered in the module will be applied in later modules to support the analysis of complex management problems and the development of associated mathematical models. Important concepts in other areas (e.g. economics, finance, data analytics) can be explored in more depth if students have a strong background in the underlying mathematics.

#### Learning outcomes

Upon successful completion of the module, students will be able to:

• Perform the operations of addition, multiplication and find the inverse and transposes of vectors and matrices.

• Solve systems of linear equations using Gaussian elimination.

• Define and identify linear dependence and independence of a collection of vectors.

• Calculate determinants using row operations, column operations, and expansion down any column or across any row.

• Calculate eigenvalues, eigenvectors and eigenspaces.

• Determine if a matrix is diagonalisable, and if it is, diagonalise it.

• Solve systems of dynamic linear equations using eigenvalues

#### Topics covered

• Systems of linear equations

• Linear transformations and inverses

• Matrices and operations

• Subspaces and their dimensions

• Orthogonality and least squares

• Determinants

• Eigenvalues and eigenvectors

• Discrete and continuous linear dynamic systems

• Singular value decomposition

• Applications of linear algebra

#### Assessment summary

20% is awarded for individual coursework, comprising four problem sets. 80% is awarded for a 3-hour written examination.