# Unit information: Linear Algebra and Geometry in 2015/16

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Unit name Linear Algebra and Geometry MATH11005 20 C/4 Teaching Block 4 (weeks 1-24) Dr. Misha Rudnev Not open An A in Mathematics A-level or equivalent. None School of Mathematics Faculty of Science

## Description

Unit aims

Mathematics 11005 aims to provide some basic tools and concepts for mathematics at the undergraduate level, to develop clear mathematical thinking and to introduce rigorous mathematical treatments of some fundamental topics in mathematics.

General Description of the Unit

Mathematics 11005 begins with the complex plane, conics, and hyperplanes in n-space, which leads to the straightforward ideas of vectors and matrices, and develops the abstract notion of vector spaces. This is one of the basic structures of pure mathematics; yet the methods of the course are also fundamental for applied mathematics and statistics.

Relation to Other Units

Mathematics 11005 provides foundations for all other units in the Mathematics Honours programmes.

Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/

## Intended learning outcomes

At the end of the unit, the students should:

• have developed some familiarity with abstract mathematical thinking;
• be familiar with geometric objects like lines, planes and hyperplanes, and their axiomatic generalisation into vector spaces and linear maps;
• be able to solve linear equations using elementary operations;
• be able to work with matrix algebra, including matrix inverses, determinants, and eigenvalues and eigenvectors.

Transferable Skills

Clear logical thinking; clear mathematical writing; problem solving; the assimilation of abstract and novel ideas.

## Teaching details

Lectures supported by lecture notes, problem sheets and small-group tutorials.

## Assessment Details

100% Examination

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

There are many good linear algebra texts. They come in different styles, some follow a more abstract approach, others emphasise applications and computational aspects. Some students may prefer the style of one book more than another.

The following is a selection of textbooks which cover a variety of styles:

• G. Strang, "Linear Algebra and its Applications".
• R. Allenby, "Linear Algebra"
• H. Anton and C. Rorres, "Elementary Linear Algebra"
• S. Lang, "Linear Algebra"
• S. Lipschutz and M. Lipson, "Linear Algebra"

The lectures will present the material in a different order from most textbooks.