#### CS 601: Mathematics for Computer Science

###### Linear Algebra:

- Fields.
- Vectors spaces, examples,Rn, Cn; subspaces.
- Linear independence, dependence and dimension.
- Linear transformations.
- Matrices, matrix algebra, determinants. Properties of matrices and determinants.
- Systems of linear equations.
- Eigenvalues, eigenvectors, eigenspaces, diagonalization and the spectral theorem.
- Factorization and singular value decomposition.

###### Probability:

- Sample spaces, events, axioms of probability.
- Conditional probability and independence.
- Random variables. Discrete and continuous random variables, densities and distributions.
- Expectation and its properties.
- Normal distribution and its properties.
- Law of large numbers, central limit theorem.
- Bounds on deviations: Chebyshev, Markov, Hoeffding, Chernoff.
- Introduction to Markov chains, random walks.

###### Logic:

- What is a proof? And proof methods.
- Propositional logic syntax and semantics.
- Tautologies, axiom system and deduction.
- Proof of soundness and completeness.
- First order logic syntax and semantics.
- Converting natural language into FoL wffs.
- Structures, models, satisfaction and validity.
- Axiomatization, soundness and completeness.
- Refutation and logic programming.