School of Mathematics
MA1S11: Mathematics I for Scientists
(discrete mathematics portion)
Solutions to tutorial sheets
Tutorial/Exercise Sheet 1 [due October 1]
The first sheet (on vectors in the plane).
Solution available here (in
PDF format).
Tutorial Sheet 2 [October 2 - 5]
Vectors in space (as arrows), length, dot product, angles. Equation of a sphere.
Tutorial Sheet 3 [October 9 - 12]
Vectors in space: projections, planes, lines.
Tutorial Sheet 4 [October 16 - 19]
Vectors in space: cross products, some applications to planes and lines.
Tutorial Sheet 5 [October 23 - 26]
Cartesian equations for lines. Algebra in $\mathbb{R}^n$. Hyperplanes.
Tutorial Sheet 6 [October 30 - November 2]
Augmented matrices (for systems of linear equations).
Gaussian elimination.
Tutorial Sheet 7 [November 13 - 16]
Gauss-Jordan elimination.
Tutorial Sheet 8 [November 20 - 23]
Matrix multiplication, inverses.
Tutorial Sheet 9 [November 27 - 30]
Triangular matrices, transpose, trace, nilpotence.
Tutorial Sheet 10 [December 4--7]
Vertex matrices for graphs. Trace, transpose of a product, triangular matrices.
Tutorial Sheet 11 [December 11--14]
Binary, octal and heaxadecimal.
Exercise Sheet [due January 14, 2013 via email]
Using spreadsheets via Google Drive.
