# Mathematics 2B: Linear Algebra MATHS2004

**Academic Session:**2019-20**School:**School of Mathematics and Statistics**Credits:**10**Level:**Level 2 (SCQF level 8)**Typically Offered:**Semester 1**Available to Visiting Students:**Yes**Available to Erasmus Students:**Yes

#### Short Description

This course covers the fundamentals of linear algebra that are applicable throughout science and engineering, and in particular in the physical, chemical and biological sciences, statistics and other parts of mathematics.

#### Timetable

Lectures on Wednesdays and Fridays at 10am or Wednesdays and Fridays at 11 am. There may be extra lectures on Monday of teaching week 1. Weekly tutorials on Mondays which will cover Maths 2A and Maths 2B course material.

#### Requirements of Entry

Mathematics 1R or 1X at grade D and 1S or 1T or 1Y at grade D and a pass in the level 1 Skills test.

#### Excluded Courses

Mathematics 2R: Algebra 1 and Mathematics 2W: Linear Algebra, 2AB: Linear Algebra.

#### Assessment

One degree examination (80%) (1 hour 30 mins); coursework (20%).

**Main Assessment In:** December

#### Course Aims

This course covers the fundamentals of linear algebra that are applicable throughout science and engineering, and in particular in the physical, chemical and biological sciences, statistics and other parts of mathematics. The aim of the first part of the course is to introduce the idea of a finite dimensional vector space, including the concepts of linear independence, basis, dimension and linear map. The relation between linear maps and matrices will be explained, and this will motivate further study of matrices in the second part of the course, in which the determinant, eigenvalues and eigenvectors of a matrix will be studied. Throughout, all new ideas will be illustrated by examples drawn from applications in low dimensions.

#### Intended Learning Outcomes of Course

Students should be familiar with all definitions and results covered in lectures, should understand the proofs of results, and should be able to apply the results to problems involving the course contents. Students should, moreover, learn to be rigorously logical in their presentation of solutions to problems. By the end of the course, students should be able to (1) handle fluently problems involving matrices and their entries; (2) recognise vector spaces and subspaces over R and C: (3) test sets of vectors for linear independence and spanning properties, and understand methods for obtaining bases for a specified subspace of a vector space; (4) decide whether or not a map between spaces is linear, describe a linear map in matrix form, and calculate various objects (eg image, kernel) associated with a linear map; (5) evaluate determinants recursively and using elementary row and column operations, factorize algebraic determinants, and apply results about determinants in theoretical problems; (6) find the characteristic polynomial of a square matrix, and use it to determine the eigenvalues and eigenvectors of the matrix, and deal with theoretical problems involving eigenvalues.

#### Minimum Requirement for Award of Credits

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.