Geometry & Convergence (U01457)

? 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. Iteration to solve equations. Use of 'seq' and 'do' loops in Maple. (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

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

? Prohibited combinations : MAT-1-mi2, MAT-1-am2, MAT-1-mm2, MAT-2-am2A, MAT-2-mm2A

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)

? Contact Teaching Time : 2 hour(s) 30 minutes per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
07/01/2008	12:10	13:00	Lecture Theatre C, David Hume Tower	Central

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	12:10	13:00	Central
Lecture	Thursday	12:10	13:00	Central

? Additional Class Information : Tutorials: Tu at 1110 and 1210.

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. Understanding the 'sequence', 'set' and 'list' datatypes in Maple.
10. Ability to write simple 'do' loops in Maple.
11. Familiarity with the concept of iteration of a function.
12. Intuitive understanding of the idea of convergence of sequences and series.