Resources

Curated pointers only — add a resource here when you actually start using it, not speculatively.

• Book files live in your existing library at /home/ed/Insync/e.f.bird@outlook.com/OneDrive/__Personal/__Study/Books/Math Books/.
• Math Landscapes links go to the MSC2020 reference site (cloned locally at /home/ed/MEGA/math_landscapes/, live at mathlandscapes.com). Use these to look up how a topic sits in the wider classification — not as a study source.
• Chapter/page numbers below were pulled directly from each PDF’s table of contents (via pdftotext), so they’re real — but sanity-check against the file itself, since editions/scans can differ.
• External links are given where the source is freely available and the link is a well-known, stable one (official book site, publisher page, DOI). Where no reliable free link exists, that’s noted instead of guessing a URL.

1. Discrete math, logic, formal grammars

Serves VCD correctness — Strand 1.

Math Landscapes - 03 — Mathematical Logic and Foundations - 03Bxx — General Logic - 68Qxx — Theory of Computing (formal languages/grammars/automata) - 68Rxx — Discrete Math in relation to CS

Books

• Graham, Knuth & Patashnik — Concrete Mathematics (concrete_mathematics-unknown_author.pdf)
  • No official free link — this is the library PDF.
  • Chapters to use:
    • Ch. 1, Recurrent Problems — p. 1
    • Ch. 2, Sums — p. 21
    • Ch. 5, Binomial Coefficients — p. 153
    • Ch. 8, Discrete Probability — p. 367
    • Ch. 9, Asymptotics — p. 425
  • Best single source for the proof/recurrence/asymptotics style needed for VCD work.
• Sindre Sogge Heggen — First Principles of Mathematics (first_principles_of_math-sindre_sogge_heggen.pdf)
  • Logic, sets, and proof-technique fundamentals — use only if a refresher is needed before Concrete Mathematics (see PLAN.md Phase 1).
• Michael Sipser — Introduction to the Theory of Computation, 3rd ed. (Sipser_Introduction.to.the.Theory.of.Computation.3E.pdf)
  • No official free link — this is the library PDF.
  • The standard reference for formal language theory, context-free grammars, and automata. Covers the regular/context-free/computability hierarchy directly relevant to VCD’s formal-language work.

2. Algorithms & complexity

Serves VCD complexity characterisation — Strand 1.

Math Landscapes - 68Wxx — Algorithms and Complexity

Books

• Graham, Knuth & Patashnik — Concrete Mathematics (as above)
  • Ch. 9, Asymptotics — p. 425 — direct match for multi-parameter worst-case analysis.
• Kleinberg & Tardos — Algorithm Design (algorithm-design-by-jon-kleinberg-eva-tardos_compress.pdf)
  • Proof-technique-focused algorithms text; the primary reference for formal complexity-proof technique beyond Concrete Mathematics when VCD design work needs it.

3. Probability & statistics

Priority topic within this area: comparative judgement (Bradley-Terry, Thurstone) — serves CJ-Bench, Strand 3. Splits into a math core (3a) and an applied methodology literature (3b) — see below.

Math Landscapes - 60 — Probability Theory and Stochastic Processes - 62 — Statistics - 62Fxx — Parametric Inference - 62Gxx — Nonparametric Inference (bootstrap) - 62Cxx — Decision Theory

Books

• Illowsky & Dean (OpenStax) — Introductory Statistics 2e (statistics/introductory_statistics_2e-barbara_illowsky,_susan_dean.pdf)
  • Free online: openstax.org/details/books/introductory-statistics-2e
  • Chapters to use:
    • Ch. 3, Probability Topics
    • Ch. 7, The Central Limit Theorem
    • Ch. 8, Confidence Intervals
    • Ch. 9–10, Hypothesis Testing
    • Ch. 12, Linear Regression
  • Covers the CI/bootstrap/significance-testing trio named directly in the proposal’s Evaluation Plan.

3a. Math core (statistics / psychometrics)

Paired-comparison models, MLE of latent scale values, ranking theory — where Bradley-Terry, Thurstone, and Kendall belong as mathematics.

Gap: none of the library books cover Bradley-Terry, Thurstone’s law of comparative judgement, or Kendall’s ranking coefficients directly — sourcing the primary papers is the priority.

Primary papers (all cited in the proposal — read in the original, no textbook substitute exists in the current library):

• Thurstone, L. L. (1927). A Law of Comparative Judgment. Psychological Review, 34(4), 273–286. DOI: 10.1037/h0070288
• Bradley, R. A. & Terry, M. E. (1952). Rank Analysis of Incomplete Block Designs: I. The Method of Paired Comparisons. Biometrika, 39(3/4), 324–345. DOI: 10.2307/2334029
• Kendall, M. G. & Babington Smith, B. (1939). The Problem of m Rankings. Annals of Mathematical Statistics, 10(3), 275–287. (search via publisher/JSTOR — no single stable free link confirmed)

Supporting book

• Agresti, A. — Categorical Data Analysis (Categorical_Data_Analysis.pdf)
  • Has a solid Bradley-Terry chapter with worked examples; fallback synthesis text.
• David, H. A. — The Method of Paired Comparisons (1988) — hard to source (obscure monograph, not digitised via usual routes). Worth an interlibrary loan request via NTU if a more rigorous, paired-comparison-specific treatment is later needed.
• Bond, T. & Fox, C. — Applying the Rasch Model — adjacent (item-response-theory / measurement theory) but Rasch-specific, not a direct substitute.

3b. Assessment methodology (education / research methods)

Not math or CS: the applied literature on using comparative judgement validly to mark student work — panel/rater reliability, Swiss-pairing/adaptive comparison scheduling, validity vs. traditional marking. Lives in educational-measurement journals and CJ-platform literature (e.g. No More Marking, RM Compare), not math departments — mostly journal articles (BERA, Sage, Taylor & Francis), so university/ILL database access is the likely route, not a book search.

• Verhavert, S. et al. (2019). Meta-analysis on CJ reliability — already in the proposal’s reference list; the meta-analytic entry point.
• Alistair Pollitt — pioneered CJ’s use in exam marking; likely anchor author for this shelf.
  • “Comparative judgement for assessment.” International Journal of Technology and Design Education (2012).
  • “The method of Adaptive Comparative Judgement.” Assessment in Education (2012) — coined ACJ, standard citation for this shelf.
• Tim Newton — writes on reliability/validity of CJ vs. traditional marking, adjacent to Pollitt’s work.
• Bramley, T. (Cambridge Assessment) — “Paired comparison methods,” chapter in Examining the Comparability of Examination Standards (2007) — closest thing to a book-chapter treatment, from an exam-board context.
• No More Marking (Chris Wheadon) — practitioner whitepapers (not peer-reviewed) on Swiss-pairing/adaptive comparison scheduling; useful for the scheduling-algorithm side rather than validity theory.
• Newton, P. & Shaw, S. — Validity in Educational and Psychological Assessment (2014) — general textbook fallback if a single book anchor is wanted; covers validity-vs-traditional-marking framing generally, CJ as one case among several, not CJ-specific.

Before rebuilding from scratch, review prior wiki work (math core / 3a side): - reference/estimate-bradley-terry-strengths-from-paired-comparison-data.md - reference/choose-wald-vs-wilson-vs-exact-for-a-proportion-interval.md

4. Optimisation

Constrained MDPs, Pareto efficiency, DPO/RLHF background — serves MOA-Edu, Strand 2.

Math Landscapes - 49 — Calculus of Variations and Optimal Control - 49Sxx — Variational Principles in Optimization - 90 — Operations Research / Mathematical Programming - 90Cxx — Mathematical Programming

Gap: no dedicated optimisation/MDP/RL textbook found in the library. The proposal’s own citations are the best entry points.

Primary papers

• Altman, E. (1999). Constrained Markov Decision Processes.
• Achiam, J. et al. (2017). Constrained Policy Optimization.
• Rafailov, R. et al. (2023). Direct Preference Optimization (DPO). arXiv: 2305.18290

Worth sourcing a general convex-optimisation or RL text (e.g. Boyd & Vandenberghe’s Convex Optimization, free at stanford.edu/~boyd/cvxbook, or Sutton & Barto’s Reinforcement Learning: An Introduction, free at incompleteideas.net/book/the-book.html) if this becomes a sustained study block.

5. Linear algebra & calculus

Instrumental — read only as deep as needed to follow the ML papers underlying all strands. Don’t let this expand into a full course unless a specific paper demands it.

Math Landscapes - 15 — Linear and Multilinear Algebra, Matrix Theory

Books

• Hefferon, J. — Linear Algebra (linear_algebra/linear_algebra-jim_hefferon.pdf)
  • Free official version: hefferon.net/linearalgebra
  • Chapters to use: Ch. 1 Linear Systems, Ch. 2 Vector Spaces, Ch. 3 Maps Between Spaces, Ch. 4 Determinants, Ch. 5 Similarity.
  • Proof-based, good for building real understanding rather than just computation.
• Deisenroth, Faisal & Ong — Mathematics for Machine Learning (mathematics_for_machine_learning-marc_peter_deisenroth,_a._aldo_faisal,_cheng_soon_ong.pdf)
  • Free official version: mml-book.github.io
  • The most directly relevant single book in the library: written specifically to bridge linear algebra/calculus/probability into the ML literature this proposal builds on. Good default when the question is “how much math do I need to read this paper,” rather than deep coverage of any one area.