Topics on Final Exam
The final exam will take place Dec. 16, 5:00-7:00, 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.
- 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
List of topics
The following topics will be covered on the exam.
- 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,
- Projection of a point onto a line or plane.
Distance from a point to a line or plane.
- Geometric transformations
- Natural and homogeneous coordinates
- Rigid mappings
- Affine transformations
- 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
- 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)
- 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
- Probabilistic problems