Discrete Structures II

Course Description

Discrete Structures II continues the mathematical foundations sequence with graph theory, trees, and further combinatorics, building the exact toolkit the second-year algorithms and data structures courses assume students already have.

Learning Outcomes

Model a problem using graphs or trees and justify the choice of representation.
Apply basic graph algorithms by hand and reason about their correctness.
Use combinatorial counting to analyze the size of a problem space.
Connect discrete mathematics concepts directly to algorithm design.

Weekly Topics

Examines graph fundamentals from a practical angle, using a case drawn from real systems to motivate the concepts.

Builds directly on the previous week to extend graph traversal, with an emphasis on where the earlier techniques stop working.

Combines a short lecture on trees with an in-class exercise students carry into the week's assignment.

Focuses on common mistakes and misconceptions around weighted graphs, using student work from the previous assignment as material.

Introduces shortest paths (conceptual) and immediately puts it to use in a small design or implementation task.

Situates advanced counting within the broader arc of the course, showing how it connects to what comes next.

Uses a guest dataset or scenario to explore mid-semester review in a setting closer to professional practice.

Introduces permutations & combinations through short lectures and worked examples, building the vocabulary the rest of the course relies on.

Works through probability basics in a lab-driven session, with guided exercises students complete and discuss in small groups.

Covers recurrence relations revisited in depth, connecting the underlying theory to a concrete example the class builds together.

Examines algorithmic complexity preview from a practical angle, using a case drawn from real systems to motivate the concepts.

Builds directly on the previous week to extend applied modeling, with an emphasis on where the earlier techniques stop working.

Combines a short lecture on revision with an in-class exercise students carry into the week's assignment.

Assessment

Assignments — 20%

Practical Work — 20%

Mid-Semester — 20%

Final Examination — 40%

Prerequisite Map

Related Courses

Core100 Level

CSC103

Discrete Structures I

Discrete Structures I builds the mathematical vocabulary computer science depends on: logic, sets, functions, and basic proof technique. Rather than treating this as abstract mathematics for its own sake, the course consistently ties each idea back to a computing problem — why a search terminates, why an argument about correctness holds, why two representations of the same information are equivalent.

Kenji Watanabe 3 cr

Core200 Level

CSC201

Data Structures & Algorithms

Data Structures & Algorithms is where students stop asking only "does this work?" and start asking "how well does this work, and why?" The course covers the core data structures used throughout the rest of the curriculum — stacks, queues, trees, hash tables, graphs — alongside the analytical tools to reason about their time and space costs. Every structure is motivated by a problem it solves better than the alternatives.

Kenji Watanabe 4 cr