Department of Mathematical Sciences, Unit Catalogue 2009/10 |
MA10209: Algebra 1A |
 Credits:
| 6 |
| Level:
| Certificate |
| Period: | Semester 1 |
| Assessment:
| EX 100% |
| Supplementary Assessment: | MA10209 Mandatory extra work (where allowed by programme regulations) |
| Requisites:
| While taking this unit you must take MA10207 |
| Description: | You must have A level Mathematics Grade A, or equivalent in order to take this unit. Aims: To provide a firm grounding in the basic and important objects of mathematics such as sets, functions, numbers, polynomials and matrices. Learning Outcomes: After taking this unit the students should be able to: * Demonstrate understanding of the elementary concepts of geometry and algebra. * Construct logical and correct proofs of theorems about these concepts, using techniques such as contradiction and induction. * Show command of abstract concepts of elementary linear algebra. * Solve systems of linear equations. Skills: Numeracy T/F A Problem Solving T/F A Written and Spoken Communication F (in tutorials). Content: Sets and functions. Direct and inverse image. Equivalence relations. Numbers (natural, integer, rational, real, complex). Arithmetic and prime factorisation. Euclid's algorithm. Polynomials: division with remainder. Groups, rings and fields (definitions and examples). Modular arithmetic. Linear algebra and geometry in R2 and R3; area/volume interpretation of determinants of linear transformations. Systems of linear equations: matrix representation, echelon form. Matrices as linear maps, matrix arithmetic over an arbitrary field. Vector spaces (definition and examples). Subspaces and linear maps, kernel and image. Linear independence and bases. Matrix of a linear map, change of basis, similar matrices. Affine and Euclidean transformations of R2 and R3. Geometry of the complex plane. |