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
- Any questions that require any use of calculus.
- Hidden Markov models
- Any new subjects introduced in the last lecture 12/14.

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.

- MATLAB: Basic functionalities. (Notes, Chap. 1)
- Vectors. (Chap 2, except section 2.7 on plotting)
- Basic operations
- Dot product. Orthogonality. Cosine formula.
- Basic applications, as discussed in the notes.
- Linear classifiers, as in the first assignment.

- Matrices (Chap 3)
- Basic operations
- Multiply matrix times vector
- Matrix multiplication
- Linear transformations

- Vector spaces (Chap. 4 part I; that is, sections 4.1-4.7)
- Vector spaces
- Linear independence
- Basis. Dimension
- Vector space sum. Complement. Orthogonal complement.
- Linear transformations: Rank, image, null space, inverse.
- Categories of systems of linear equations.

- Solving systems of linear equations. (Chap 5, sections 5.1, 5.2, 5.4)
- Row-echelon form
- Gaussian elimination
- MATLAB. You should know the built-in functions M\C, rank(M), null(M). You don't need to know the 6 different things M\C does.

- Geometry (Chap 6, except 6.4.7 and 6.4.8).
- 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

- Points, lines, and planes
- Change of basis (Chap 7, sec 7.1-7.3, 7.7, 7.8)
- Change of coordinate system
- Singular value decomposition

- Probability (Chap. 8)
- Sample spaces
- Axioms
- Bayes' Law
- Independence and conditional independence
- Random Variables

- Numerical Random Variables (Chap 9)
- Marginal distribution
- Expectation, variance, and standard deviation
- Distributions: Bernoulli, Binomial, Inverse power law, Uniform, and Gaussian. You do not have to memorize the formulas for expected value and standard deviation for these.

- Markov models (Chap 10, sections 10.1, 10.2)
- Definition
- Transition matrix
- Stationary distribution

- Confidence Intervals (Chap 11, first two pages, before section 11.1)
- Monte Carlo methods (Chap 12.1-12.3, 12.6)
- Finding Area
- Counting
- Probabilistic problems