# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2010/2011

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DRPS : Course Catalogue : School of Mathematics : Mathematics

# Undergraduate Course: Geometry & Convergence (MATH08003)

 School School of Mathematics College College of Science and Engineering Course type Standard Availability Available to all students Credit level (Normal year taken) SCQF Level 8 (Year 1 Undergraduate) Credits 10 Home subject area Mathematics Other subject area Specialist Mathematics & Statistics (Year 1) Course website https://info.maths.ed.ac.uk/teaching.html Taught in Gaelic? No Course description 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.
 Pre-requisites It is RECOMMENDED that students have passed Practical Calculus (MATH08001) AND Solving Equations (MATH08002) Co-requisites Prohibited Combinations Students MUST NOT also be taking Mathematics for Informatics 2a (MINF08002) OR Mathematics for Informatics 2b (MATH08047) OR Applicable Mathematics 2 (MATH08031) OR Mathematical Methods 2 (MATH08032) OR Other requirements None Additional Costs None
 Pre-requisites None Displayed in Visiting Students Prospectus? Yes
 Delivery period: 2010/11 Semester 2, Available to all students (SV1) WebCT enabled:  Yes Quota:  272 Location Activity Description Weeks Monday Tuesday Wednesday Thursday Friday Central Lecture 1-11 12:10 - 13:00 Central Lecture 1-11 12:10 - 13:00 First Class Week 1, Monday, 12:10 - 13:00, Zone: Central. David Hume Tower, Lecture Theatre C Additional information Tutorials: Tu at 9:00, 10:00, 1110 and 1210. Exam Information Exam Diet Paper Name Hours:Minutes Stationery Requirements Comments Main Exam Diet S2 (April/May) 2:00 None. No YAF. Resit Exam Diet (August) 2:00 None. No YAF.
 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.
 Coursework (which may include a Project): 15%; Degree Examination: 85%. Visiting Student Variant Assessment Coursework (which may include a Project): 40% Examination: 60%.
 None
 Academic description Not entered Syllabus Not entered Transferable skills Not entered Reading list Not entered Study Abroad Not entered Study Pattern Not entered Keywords GCo
 Course organiser Dr Toby Bailey Tel: (0131 6)50 5068 Email: t.n.bailey@ed.ac.uk Course secretary Miss Louise Durie Tel: (0131 6)50 5050 Email: L.Durie@ed.ac.uk
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