Mathematical Foundations of Computing

Topics

• Use logical notation to define and reason about statements expressed in informal language.
• Write mathematical proofs using clear and precise reasoning; recognize when to use various proof techniques; find errors in faulty proofs.
• Precisely state induction hypotheses and write inductive proofs; write and use inductive definitions.
• Reason about fundamental mathematical concepts such as sets, functions, relations, graphs and their properties.| Apply combinatorial reasoning to solve counting problems arising in real-world applications; use the pigeonhole principle to prove statements.
• Use probability concepts and notation such as conditional probability, Bayes rule, random variables, and tail bounds to model and analyze real-world applications; compute associated quantitaties such as probabilities, expectations, variance, covariance, and correlation.
• Prove properties of regular languages and automata; design automata and regular expressions accepting or denoting a certain regular language; prove that a language is not regular.

Official roster learning outcomes