Geometry & Convergence (CPD) (U03830)

? Credit Points : 10 ? SCQF Level : 8 ? Acronym : MAT-1-GCo

Core first year course for Honours Degrees in Mathematics and/or Statistics. Syllabus summary: (Coordinate and vector geometry) Vector geometry, dot and cross product, lines and planes. Matrices as linear transformations, orthogonal matrices. Coordinate geometry, conics, etc. (Sequences and iteration) Induction. Arithmetic and Geometric Progressions and their sums. (Convergence) Definition of convergence of sequences and some elementary results. Introduction to sums of series. Convergence of sums by comparison with integrals, convergence of standard Taylor series using the integral form of the remainder.

Entry Requirements

? This course is not available to visting students.

? Pre-requisites : H-Grade Mathematics or equivalent; prior attendance at MAT-1-PCa and MAT-1-SEq or their equivalent

? Prohibited combinations : NB : Not available to full-time Undergraduate students.

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Year 1), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 1st year

? Delivery Period : Semester 2 (Blocks 3-4)

? Additional Class Information : The course is taught entirely as a distance learning course with no scheduled contact hours. WebCT will be the teaching medium with course texts and a dedicated tutor.

Summary of Intended Learning Outcomes

1. Ability to compute dot, cross and triple vector products.
2. Ability to perform vector algebra manipulations using expansion of a x (b x c) and properties of the various products.
3. Ability to use vector methods to attack elementary problems in geometry.
4. Familiarity with the idea of a matrix giving a transformation of R^2 or R^3.
5. Familiarity with rotation and reflection matrices in the plane.
6. Familiarity with the standard form of conics and their graphs.
7. Ability to construct proofs by induction in concrete problems.
8. Familiarity with AP's, GP's and their sums.
9. Intuitive understanding of the idea of convergence of sequences and series.