CS/ECE 374 A: 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.

Because familiarity with these topics is crucial for success in 374, we are strictly enforcing the CS 173 and CS 225 prerequisites. Students who do not already have credit for both CS 173 and CS 225 (either from taking the course, passing the proficiency exam, or transferring credit from an equivalent course at another institution) cannot register for 374 without an override from the CS department. Instructors cannot offer prerequisite overrides.

A previous version of this page stated these prerequisites incorrectly, reflecting policy from previous semesters that has since been changed. I believe the current statement is consistent with department, college, and campus policy as of Fall 2019, but if there is an inconsistency, this page is incorrect.

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.)

• CS 173:
  • Building Blocks for Theoretical Computer Science by Margaret Fleck, written specifically for CS 173.
  • Mathematics for Computer Science by Eric Lehman, Tom Leighton, and Albert Meyer, written for the Mathematics for Computer Science course at MIT.
• CS 225:
  • Open Data Structures by Pat Morin
  • datastructures by Don Sheehy

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
  • Jeff's notes on induction
• Recurrences
  • Solving simple divide-and-conquer recurrences via recursion trees (or at least the Master Theorem)
  • Jeff's notes on solving recurrences
• Graphs (both undirected and directed), trees, directed acyclic graphs

Abstract data types

• scalars (booleans, characters, integers, reals, etc.)
• records
• pointers / references
• strings
• arrays / vectors (indexed sequences)
• stacks (LIFO lists)
• queues (FIFO lists)
• deques (double-ended queues)
• priority queues
• dictionaries
• graphs (directed and undirected)

Elementary data structures

• binary numbers, including 2's complement representation of negative integers
• arrays
• linked lists (singly and doubly linked, linear and circular)
• hash tables
• binary trees: worst-case depth O(n)
• binary heaps
• binary search trees
• balanced search trees: worst-case depth O(log n)
  • At least one of the following: B-trees (such as 2-3-trees or (a,b)-trees), AVL trees, red-black trees, skip lists
• adjacency matrices
• adjacency lists
• The difference between this list and the previous list

Elementary algorithms

• elementary arithmetic á la Al-Khwarizmi and Fibinacci
• sequential search
• binary search
• comparison-based sorting:
  • insertion sort, selection sort, (standard) quicksort: O(n²) time
  • mergesort, heapsort: O(n log n) time
• radix sort: O(nw) time
• binary tree traversal: pre-order, post-order, in-order, level-order
• depth-first search (at least for rooted trees)
• breadth-first search (at least for rooted trees)