Further Reading: Capstone — Applying Discrete Mathematics

The capstone touches the whole book, so this list is organized by track plus a final group on the skill the capstone is really about — turning proven mathematics into a system you can defend. Read the section for whichever track you chose; skim the others for a second pass. All sources are Tier-1 (canonical, verifiable) or Tier-2 (a real, well-known work or idea attributed carefully).

On integration itself (read this first, whatever your track)

Lehman, Leighton & Meyer, Mathematics for Computer Science (MIT 6.042J), the synthesis chapters Freely available. The single best companion to this book's whole project: it develops discrete math as the foundation of computing, with the same "prove it, then build on it" spirit. Its closing material on putting the pieces together is the right frame of mind for a capstone.

Cormen, Leiserson, Rivest & Stein (CLRS), Introduction to Algorithms (4th ed.), the chapter introductions The chapter and part introductions (not the algorithms themselves) are a master class in motivating a technique before formalizing it — exactly the §39.7 "lead with the problem and the model" discipline. Read them as models for your own write-up.

Track A — RSA and number theory

Katz & Lindell, Introduction to Modern Cryptography (3rd ed.), the public-key chapters The rigorous standard reference for why RSA is secure (and the precise sense in which it is). It is also the place to learn why a hand-rolled mod_pow must never guard real secrets — the gap between "the round-trip is proven correct" and "the system is secure" that §39.7 insists you keep straight.

Rosen, Discrete Mathematics and Its Applications (8th ed.), the number-theory and cryptography sections (Ch. 4) Re-derives gcd, modular arithmetic, Euler/Fermat, and RSA at the level this book used. The natural place to firm up any step of the Track A correctness argument you found slippery.

Knuth, The Art of Computer Programming, Vol. 2: Seminumerical Algorithms (Tier 2 — a real, canonical work; the specific section on modular arithmetic and primality is the relevant one.) The deep reference on doing arithmetic with very large integers efficiently — the machinery a production RSA needs and your toy version omits.

Track B — graphs and network analysis

West, Introduction to Graph Theory (2nd ed.) The standard rigorous graph-theory text. Read the sections on connectivity and distance to formalize the exact objects this case work used — components, diameter, and cut vertices (articulation points), which Case Study 1 reasoned about by hand.

CLRS, Introduction to Algorithms (4th ed.), the elementary-graph-algorithms chapter The canonical treatment of BFS and DFS with the proof that BFS computes shortest distances — the very theorem Track B cites rather than re-proves. Also covers connected components and the breadth/depth-first machinery your analyzer iterates.

Easley & Kleinberg, Networks, Crowds, and Markets (Cambridge) (Tier 2 — a real, widely used text; freely readable online.) The bridge from graph theory to social networks: small-world structure ("six degrees"), centrality, and community detection, with the real-world modeling judgment Track B's analyzer demands.

Russell & Norvig, Artificial Intelligence: A Modern Approach, the constraint-satisfaction chapter (Tier 2 — a real, standard AI text.) The definitive textbook treatment of CSPs and backtracking search, including constraint propagation (the "naked single" speedup §39.5 lists as an extension) and why tight constraints make a worst-case-hard problem easy in practice.

Sipser, Introduction to the Theory of Computation (3rd ed.), the NP-completeness chapter The rigorous source for the claim §39.5 makes in passing: generalized $n\times n$ Sudoku is NP-complete, and the gap between worst-case hardness and typical-case ease. Read it to understand why your tiny $9\times 9$ solver is fast even though its general class is hard.

Track D — coding theory and finite fields

Rosen, Discrete Mathematics and Its Applications (8th ed.), the coding-theory material Develops Hamming distance, the minimum-distance bound, and Hamming codes at the level §39.6 used. The right place to re-derive the single-error-correction argument if the triangle-inequality step felt quick.

Lehman, Leighton & Meyer, Mathematics for Computer Science, the sections on finite fields / GF(2) Freely available. Builds the algebra (Chapter 24's territory) underneath codes — exactly what you need to understand why the Reed–Solomon codes in QR codes and CDs require a finite field, the "capstone of the capstone" §39.6 points toward.

Hamming, "Error Detecting and Error Correcting Codes," Bell System Technical Journal (1950) (Tier 2 — the real, foundational paper; widely reprinted.) Richard Hamming's original paper inventing the codes that bear his name. Short, readable, and a model of an engineer reasoning from a concrete frustration (a weekend computer crash) to a clean piece of mathematics.

On presenting technical work (for every track's write-up)

Knuth, Larrabee & Roberts, Mathematical Writing (MAA / Stanford notes) (Tier 2 — real, freely available course notes.) The classic short guide to writing mathematics clearly. Directly relevant to §39.7: how to state a claim, structure an argument, and not overclaim.

Dijkstra, "Testing shows the presence, not the absence, of bugs" (and surrounding essays) (Tier 2 — a genuine, widely quoted Dijkstra remark.) The one-line case for the whole book's theme two, and the §39.7 distinction between demonstration (tests) and guarantee (proof). Worth internalizing before you write the "Evidence" section of any capstone.

Suggested order

  1. Before building: skim the MIT 6.042 synthesis material and one CLRS chapter introduction to get into "model first, then build" mode.
  2. While building your track: read that track's first listed source alongside the chapter section — it re-derives the load-bearing theorem you will cite.
  3. Before writing the report: read the two "presenting technical work" entries; they are short and they directly shape the §39.7 write-up.
  4. For a second pass / Deep Dive: read the second source for your track (West, Sipser, or the finite-fields material) and the corresponding track-B/C/D extension reference.