CS 473: Stuff You Already Know
This page lists several basic mathematical concepts, data types, data structures, and algorithms that are typically covered in CS 173 and CS 225, and covered in more detail in CS 374, with pointers to the corresponding Wikipedia entries.
We assume that everyone
taking CS 473 is already familiar with everything on this
list, or at least has the intellectual maturity to learn it on the
fly. You can use any of these in your homework or exam solutions without providing further details or citing any source.
For detailed review of any of these topics, we strongly recommend using an actual textbook or one of the following online resources. (Beware that Wikipedia occasionally makes some very strange choices.)
For a solid introduction to most of these topics, I strongly recommend
Eric Lehman and Tom Leighton's
for Computer Science course at MIT.
Naive set theory
Binary relations, including functions, equivalence relations, and partial orders
- Elementary discrete probability: Uniform vs. nonuniform distributions, expectation, variance, conditional probability
Asymptotic notation (o, O, Θ, Ω, ω); comparing asymptotic growth rates
Evaluating simple summations (at least asymptotically)
Propositional logic (T, F, ¬, ∧, ∨, ⇒, ⇔) and first-order predicate logic (∀, ∃)
Basic proof techniques: direct, indirect, exhaustive case analysis, contradiction
★ Induction ★ (or equivalently, proof by minimal counterexample), especially strong induction and structural induction
Graphs (both undirected and directed),
directed acyclic graphs
Abstract data types
You may use any of these data structures in your homeworks and exams without providing further details or citing any source. If you use a small modification of one of these data structures, just describe your changes; don't regurgitate the original data structure details.
You may use any of these algorithms in your homeworks and exams without providing further details or citing any source. If you use a small modification of one of these algorithms, just describe your changes; don't regurgitate the original algorithm details.
It is useful to have some basic background in theory of computation.
Theory of Computation/Complexity