Welcome to Linear Algebra! This course is designed for first year honours maths and joint honours students. It is part of the double module Core A.

Some useful resouces are

• The official department page for the course where you can find lots of useful information about the course, including lecture times, tutorial times and groups and past exam papers. Note that tutorials begin in week 2 which means from Thursday 10th October.

• The faculty of science module description.

• The the page from the course booklet. This has details of the recommeded books, an overview of the course and the syllabus.

• You may want to brush up your skills .

Core A Linear Algebra Problems

• 1H Linear Algebra Problem Sheet, Michaelmas 2002 in postscript or pdf.

• 1H Linear Algebra Problem Sheet, Epiphany 2003 in postscript or pdf.

Set problems

I will be setting work in the lecture every Tuesday.
• Work set on 8th October : to hand in 2(i), (ii), (iv); for tutorials 1, 2(iii), (vii).

• Work set on 15th October : to hand in 6, 8; for tutorials 4, 9.

• Work set on 22nd October : to hand in 12(i), (ii), (vii); for tutorials 12(iv), (v), (viii).

• Work set on 29th October : to hand in 13(i), 23(i), (v); for tutorials 13(iv), 23(vi), 24.

• Work set on 5th November : to hand in 28(i), (iv), 29; for tutorials 28(ii), (iii), 31.

• Work set on 12th November : to hand in 32(a), 46(i), (ii); for tutorials 32(b), 33, 38.

• Work set on 19th November : to hand in 49(i), 53; for tutorials 50, 52.

• Work set on 26th November : to hand in 39, 62(i); for tutorials 47, 51, 63(i).

• Work set on 3rd December : to hand in 62(iv), (v), 70; for tutorials 62(iii), 64.

• Work set on 28th January : to hand in 3, 4; for tutorials 1, 2.

• Work set on 4th February : to hand in 5, 9; for tutorials 7, 8.

• Work set on 11th February : to hand in 11, 19; for tutorials 16, 20.

• Work set on 18th February : to hand in 22, 27; for tutorials 23, 28.

• Work set on 25th February : to hand in 39, 48(a), (b) [last part is optional]; for tutorials 40, 43.

• Work set on 4th March : to hand in 44, 46; for tutorials 41, 45.

• Work set on 11th March : to hand in 49(i), (iii), 56(a); for tutorials 49(ii), 55.

• Work set on 18th March : to hand in 60, 61; for tutorials 57, 62.

Handouts.

• Basic Ideas of Linear Algebra

• Gauss-Jordan Elimination (postscript) or Gauss-Jordan Elimination (PDF)

  Follow this link for interactive Gauss-Jordan elimination .

• Matrices and determinants (postscript) or Matrices and determinants (PDF) .

• Determinants

• Linear Geometry in 3-space

• The Vector Cross Product

• Axioms for the Vector Space R^n

• Spanning Sets

• Dimension of Vector Subspaces of R^n

• The Dot Product in R^n

• Rotations in 3-space

• Axioms for a general Vector Space over R

• Dimensions of sums and interesections of vector subspaces

• The matrix of a linear transformation

• Isomorphisms of vector spaces

• Change of basis

• An example of reducing a matrix to canonical form

• Row rank equals column rank

• A diagonalization theorem

• Solving ODEs using diagonalization

• The Cayley Hamilton Theorem

• Orthogonal complements, projections and reflections

Links.

• Interactive Gauss-Jordan elimination .

• Linear algebra toolkit .

• MIT open courseware .

• Department of Mathematical Sciences home page.
• The University of Durham home page

If you have Netscape you should be able to view the linked sheets on screen by following the link. If this does not work, try adding the lines: