1S2: Discrete Mathematics I for Scientists
Solutions to tutorial sheets
Will appear here.
- Tutorial Sheet 1 [October 22 - 26]
- The first tutorial [or exercise] sheet (on systems of linear equations) is available here in PDF format. And here with solutions.
- Tutorial Sheet 2 [October 30 - November 5]
- More on Gaussian elimination. Start of vectors.
- Tutorial Sheet 3 [November 7 - 12]
- Coordinates in space, lengths of vectors, distances.
- Tutorial Sheet 4 [November 14 - 19]
- Dot products, projections, equation of a plane.
- Tutorial Sheet 5 [November 21 - 26]
- Lines and planes in space.
- Tutorial Sheet 6 [November 29 - December 3]
- Manipulation of vectors (or points) in n-space; matrix operations (addition, mulliplication by scalars, matrix multiplication).
- Tutorial Sheet 7 [January 7 - 11]
- Matrix version of systems of linear equations; inverses of matrices.
- Tutorial Sheet 8 [January 14 - 18]
- Calculations with doagonal and triangular matrices. Inverse of a product.
- Tutorial Sheet 9 [January 21 - 25]
- Trace and transpose. Determinants by cofactors.
- Tutorial Sheet 10 January 28 - February 1]
- Determinants, applications to areas and volumes.
- Tutorial Sheet 11 February 4 - 8]
- Cross products. Application of determinants to finding equations.
- Tutorial Sheet 12 February 11 - 15]
- Vertex matrix of a graph. Counting in bases 2, 8 and 16.
- Tutorial Sheet 13 February 18 - 22]
- Conversion between binary, octal and hex numbers. 32 bit representations.
- Tutorial Sheet 14 February 25 - 29]
- Conversion of fractions to binary. Orthogonal matrices (products and determinants of them).
- Tutorial Sheet 15 March 3 - 8]
- 3 by 3 rotation matrices (are orthogonal, have determinant 1, inverse is rotation by minus the angle, determinant of change of basis matrix P).
- Tutorial Sheet 16 March 31 - April 4]
- 3 by 3 rotation matrices (same as orthogonal of determinant 1; find angle and axis given matrix). Gram-Schmidt method for othonormalisation.
- Tutorial Sheet 17 April 7 - 11]
- Eigenvalues, eigenvectors, diagonalisation.
- Tutorial Sheet 18 April 14 - 18]
- Powers and exponentials of diagonalisable matrices. Systems of linear first order differential equations.
- Tutorial Sheet 19 April 21 - 25]
- Systems of linear first order differential equations. Least squares fit.
- Tutorial Sheet 20 April 28 - May 2]
- Probability.