Unit of study_

# MATH2022: Linear and Abstract Algebra

Linear and abstract algebra is one of the cornerstones of mathematics and it is at the heart of many applications of mathematics and statistics in the sciences and engineering. This unit investigates and explores properties of linear functions, developing general principles relating to the solution sets of homogeneous and inhomogeneous linear equations, including differential equations. Linear independence is introduced as a way of understanding and solving linear systems of arbitrary dimension. Linear operators on real spaces are investigated, paying particular attention to the geometrical significance of eigenvalues and eigenvectors, extending ideas from first year linear algebra. To better understand symmetry, matrix and permutation groups are introduced and used to motivate the study of abstract group theory.

Code MATH2022 Mathematics and Statistics Academic Operations 6
 Prerequisites: ? MATH1XX2 or (a mark of 65 or above in MATH1014) None MATH2922 or MATH2968 or (MATH2061 and MATH2021) or (MATH2061 and MATH2921) or (MATH2961 and MATH2021) or (MATH2961 and MATH2921)

At the completion of this unit, you should be able to:

• LO1. be fluent in analysing and constructing arguments involving matrix arithmetic, permutation and abstract groups, fields and vector spaces
• LO2. understand the definitions, main theorems and corollaries for linearly independent sets, spanning sets, basis and dimension of vector spaces
• LO3. be fluent with linear transformations and operators, and in interpreting, analysing and applying associated abstract phenomena using matrix representations and matrix arithmetic
• LO4. develop appreciation and strong working knowledge of the theory and applications of elementary permutation groups, their decompositions and relationship to invertible phenomena in linear algebra
• LO5. be fluent with important examples, theorems, algorithms and applications of the theory of inner product spaces, including processes and algorithms involving orthogonality, projections and optimisation.

## Unit outlines

Unit outlines will be available 2 weeks before the first day of teaching for the relevant session.