Reference and Selective Reading
You do not need to read the source books front-to-back for this module. Use the concept pages and practice pages first. Open these local chunks only when you need alternate exposition, more worked examples, or a deeper exercise lane.
Source Roles
| Source | Role | Why it is here |
|---|---|---|
| Mathematics for Computer Science | Primary teaching source | Strongest for counting rules, combinatorial proofs, graph structure, and planarity with CS framing |
| Discrete Mathematics and Its Applications | Selective support and exercise source | Better for catalog depth, alternate graph terminology, and extra counting examples |
Read Only If Stuck
Counting Models
- MCS: Counting One Thing by Counting Another / Counting Sequences
- MCS: The Generalized Product Rule
- MCS: The Division Rule
- Rosen: The Basics of Counting
Binomial and Constrained Counting
- MCS: Counting Subsets
- MCS: Sequences with Repetitions
- MCS: The Pigeonhole Principle
- MCS: Inclusion-Exclusion
- MCS: Combinatorial Proofs
- Rosen: Binomial Coefficients and Identities
Recurrences and Generating Functions
- MCS: Counting with Generating Functions (Part 1)
- MCS: Counting with Generating Functions (Part 2)
- MCS: Solving Linear Recurrences
- Rosen: Applications of Recurrence Relations
Graph Language and Core Structure
- MCS: Vertex Degrees / Walks and Paths
- MCS: Adjacency Matrices / Walk Relations
- MCS: Vertex Adjacency and Degrees
- MCS: Isomorphism
- MCS: Walks in Simple Graphs
- MCS: Connectivity
- Rosen: Graphs and Graph Models
- Rosen: Graph Terminology and Special Types of Graphs
Trees, Coloring, Matchings, and Planarity
- MCS: Forests and Trees (Part 1)
- MCS: Forests and Trees
- MCS: Bipartite Graphs and Matchings (Part 1)
- MCS: Coloring (Part 1)
- MCS: Special Walks and Tours
- MCS: Definitions of Planar Graphs (Part 1)
- MCS: Euler's Formula / Bounding the Number of Edges in a Planar Graph / Returning to K5 and K3;3
- MCS: Coloring Planar Graphs
- Rosen: Connectivity
- Rosen: Introduction to Trees
- Rosen: Minimum Spanning Trees
Optional Deep Dive
- MCS: Counting Practice: Poker Hands
- MCS: Generating Functions Problems and References (Part 1)
- MCS: Simple Graphs Problems and References (Part 1)
- MCS: Another Characterization for Planar Graphs
- Rosen: Generating Permutations and Combinations
- Rosen: Shortest-Path Problems
Concept-to-Source Map
| Primary concept | Best source if stuck | Why this source |
|---|---|---|
| Counting by structure, not by guessing | MCS: Counting One Thing by Counting Another | Best entry into product, division, and bijection reasoning |
| Inclusion-exclusion as overlap accounting | MCS: Inclusion-Exclusion | Compact and operational |
| Stars and bars, distributions, and integer solutions | MCS: Sequences with Repetitions | Gives the right encoding perspective |
| Recurrences arise from structural decomposition | Rosen: Applications of Recurrence Relations | Strong on turning stories into recurrences |
| Graphs as models of constraint and interaction | Rosen: Graphs and Graph Models | Best model-first exposition |
| Trees are minimally connected and maximally acyclic | MCS: Forests and Trees | Clean equivalence-based treatment |
| Coloring, bipartite graphs, and matching structure | MCS: Bipartite Graphs and Matchings | Connects graph structure to assignment problems |
| Planarity, Euler's formula, and forbidden structure | MCS: Euler's Formula / Bounding the Number of Edges in a Planar Graph | Best short route from embedding to obstruction |