CS/ECE 374: Stuff You Already Know
This page lists several basic mathematical concepts, data types, data structures, and algorithms that are typically covered in CS 173, CS 225, and earlier courses, with pointers to the corresponding Wikipedia entries. We assume you are already familiar with all of them. You can use any of these in your homework or exam solutions without providing further details or citing any source.
For a 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.)
Because familiarity with these topics is crucial for success in 374, we are strictly enforcing the prerequisites CS 173 (or Math 213) and CS 225. Students who do not already have credit for these courses—either directly, by proficiency exam, or by transfer from another institution—before the semester begins will be dropped.
Discrete Mathematics
-
Elementary algebra
-
Logarithm identities
-
Naive set theory
-
Binary relations, including functions, equivalence relations, and partial orders
-
Modular arithmetic
-
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
-
Recurrences
-
Graphs (both undirected and directed),
trees,
directed acyclic graphs
Abstract data types
Elementary data structures
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.
Elementary algorithms
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. We only care about worst-case running times in this class.