Recall that the core exams assess you on the core learning outcomes of the course, the fundamental skills that you should be able to confidentially perform quickly and efficiently.

Weeks 1–4

1. Author a formal proof of a property of a pure program.
2. Author a formal proof by structural induction.
3. Author a formal proof by mathematical induction.
4. Read a formal and proof and identify latent assumptions.
5. Author a formal proof of a property of impure program.

Weeks 5–9

1. Author a rigorous proof of the equality of two sets.
2. Author a rigorous proof utilizing classical reasoning (“proof by contradiction”).
3. Model real-world phenomena using the fundamental definitions of relations.
4. Author a rigorous proof of the countability of a given set.
5. Model real-world phenomena using the formal definitions of graphs and trees.

Week 10–13

1. Count the number of elements in an algebraic structure using combinatorial principles.
2. Accurately count the number of relevant operations that a (recursive) program performs.
3. Interpret a combinatorial formula as an algorithm for constructing an object when choice is involved.
4. Compute the probability of an event using fundamental combinatorial principles.
5. Apply random variables and expectation to model a probabilistic phenomena.