## Topics on Final Exam

The final exam will take place Dec. 21, 7:00-9:00, WWH 312. If you are unable
to make this time, please let me know as soon as possible.
The exam will be closed book and closed notes. It will cover only subjects
that were discussed in lecture. The following will
* NOT* be on the exam.

- Minutiae of MATLAB. The MATLAB plotting functions.
- Gram-Schmidt orthogonalization algorithm
- Algorithm for inverting a matrix.
- Determinants
- Subjects discussed at the "makeup" lecture Wed. 11/18: Discrete Fourier
transform, eigenvalues and eigenvectors, singular value decomposition.
- Any questions that require any use of calculus.
- Any new subjects introduced in the last lecture 12/14.

My plan (subject to change) is that the exam will have two parts; a short
answer part of questions you should be able to answer quickly, and a number of
small (two or three line) MATLAB programming problems. I expect the MATLAB
code to be correct in spirit; I will not deduct points for trivial syntax
errors.

### List of topics

The following topics will be covered on the exam (again, I may make small
changes here, but this should be pretty much correct).
- MATLAB: Basic functionalities.
- Vectors.
- Basis operations
- Dot product. Orthogonality. Cosine formula.
- Basic applications, as discussed in the notes.
- Linear classifiers, as in the first assignment.

- Matrices
- Basic operations
- Multiply matrix times vector
- Matrix multiplication
- Linear transformations

- Vector spaces
- Vector spaces
- Linear independence
- Basis. Dimension
- Vector space sum. Complement. Orthogonal complement.
- Linear transformations: Rank, image, null space, inverse, right and left
inverse.
- Categories of systems of linear equations.

- Solving systems of linear equations
- Row-echelon form
- Gaussian elimination

- Geometry
- Points, lines, and planes
- 3 representational systems for lines and planes
- Problems: identity, conversion, incidence, generation, parallelism,
and intersection.
- Projection of a point onto a line or plane.

Distance from a point to a line or plane.

- Geometric transformations
- Natural and homogeneous coordinates
- Translation
- Rotation
- Rigid mappings
- Reflections
- Affine transformations

- Change of coordinate system

- Change of basis
- Probability
- Basic axioms
- Indepedence and conditional independence
- Bayes' Law
- Random Variables
- Expectation, variance, and standard deviation

- Distributions: Bernoulli, Binomial, Uniform, Gaussian, and long tail.
- Markov processes
- Transition matrix
- Hidden Markov model

- Monte Carlo methods

- Statistical inference from sample
- Maximum likelihood estimate
- Confidence intervals
- Resampling techniques.