MA1S12: Mathematics for Scientists
(discrete mathematics portion)
You should each be scheduled for on A tutorial group (and one B group - but that is for Calculus).
- A1
- Monday at 14:00 in 20 Westland Row Seninar Room (David Whyte)
- A3
- Monday at 14:00 in M21 (Eric Mehes)
- A5
- Wednesday at 13:00 in Salmon (Roisin Braddell)
- A2
- Thursday at 16:00 in Salmon (Eric Mehes)
- A4
- Thursday at 16:00 in Synge (Roisin Braddell)
- A6
- Friday at 13:00 in Synge (Robert Murtagh)
- A7
- Friday at 13:00 in EELT2 (David Whyte)
Solutions to tutorial sheets
- Tutorial Sheet 1 [January 20 - 24]
- Calculating determinants by cofactor expansion along the first row and using Gaussian elimination.
- Tutorial Sheet 2 [January 28 - 31]
- 3 by 3 determinants as scalar triple products and (signed) volumes. Cofactor expansion along rows other than the first.
- Tutorial Sheet 3 [February 3 - 7]
- Adjugate matrix, Cramers rule, use of determinant to find equations.
- Tutorial sheet 4 [February 10 - 14]
- Orthogonal matrices, matrices for rotations (using change of basis matrix $P$ to another orthonormal frame). version A, version B, version C.
- Tutorial sheet 5 [February 17 - 21]
- More on rotation matrices, Gram-Schmidt. version A, version B, version C.
- Tutorial sheet 6 [March 3 - 7]
- Eigenvalues, eigenvectors ard orthogonal diagonalaistion of symmetric matrices. version A, version B, version C.
- Tutorial sheet 7 [March 10 - 14]
- Eigenvalues, eigenvectors ard diagonalaistion of matrices. Matrix exponentials. version A, version B, version C.
- Tutorial sheet 8 [March 19 - 24]
- Least squares fit. Linear ODEs of second order (homogeneous) and systems of first order linear (contant coefficient) ODEs. version A, version B.
- Tutorial sheet 9 [March 26 - 31]
- Probabilities. Theoretical measn and standard deviation of a random variable. Binomial distribution. version A, version B, version C.
- Tutorial/exercise sheet 10 [March 31]
- Poisson and normal distributions. Student's $t$-test. (Solutions.)