This list of topics is not necessarily complete. Everything covered through Euler's theorem (Monday 10/24) will be in scope. Material covered since the first prelim, and material covered on the homework will be given heavier emphasis.

Some related questions from previous semesters are here, (solutions).

- Probability
- Basic definitions: sample space, event, probability measure
- Condiitonal probability: definition
- Probability trees
- Independence, mutual independence vs. pairwise independence
- Bayes' Theorem and law of total probability
- Random variables: definition, independent random variables
- Probability distributions: uniform distribution, binomial distribution
- Expectation: definition, linearity of expectation
- Markov's inequality, Chebyshev's inequality, variance

- Number theory
- use euclidean division in definitions and proofs
- base b representation:
- definitions, algorithms for base-b arithmetic, know existness and uniqueness

- apply algorithms contained in inductive proofs
- e.g. eucidean division, base-b representation, Bezout coefficients

- determine whether functions defined using equivalence classes are well-defined or not
- definitions:
- quotient, remainder,
*a*|*b*, linear combination, equivalence class, unit

- quotient, remainder,
- theorems:
- division algorithm, base b representation, euclid's gcd algorithm, Bezout coefficients, Euler's theorem, modular arithmetic operations are well-defined