Proofs and Discrete Structures: Reading Guide
Use Mathematics for Computer Science as the primary text and Rosen's Discrete Mathematics and Its Applications for a second explanation or targeted exercises. You do not need to read either book front-to-back for this module. These are topic assignments; book landing links are not mislabeled as exact section destinations.
Bounded core reading
After a lesson attempt, read only the assigned topic and reconstruct one argument with the book closed. Record the edition, actual section and exercise identifier. Extraction can corrupt symbols; consult the source PDF when notation is ambiguous.
| After | MCS topic and local chunk locator | Stop when you can |
|---|---|---|
| Logic | Logical formulas: implication, equivalence/validity and predicates; chapter 3 index, especially chunk 017 | Explain an exhaustive truth table and negate a mixed-quantifier claim |
| Proof methods | Proving an implication; iff/cases/contradiction; chunks 005–007 | Reconstruct a proof and identify every hypothesis |
| Sets/functions | Sets and functions, especially chunk 031 | Explain typed maps, empty cases and a preimage proof |
| Relations/orders | Binary relations 032; partial orders 122; equivalence relations 124 | Produce a failure witness and prove representative independence |
| Induction | Ordinary induction 038–039; strong induction 040–041; compare principles 042 | Justify base coverage and the smaller-instance hypothesis |
| Recursive data | Recursive definitions and structural induction 058 | Prove a constructor property and distinguish recursion from runtime stack limits |
Local book roots, relative to the workspace: Books/Mathematics for Computer Science/contents/
and Books/Discrete Mathematics and Its Applications/contents/. Each has an index.
In Rosen, chunk 004 is a table-of-contents fragment, not a usable sets lesson;
substantive sets material appears around 062–070, functions around 071 onward,
and predicates/quantifiers around 034–039. Verify the actual topic heading in
the edition before choosing a problem; do not infer it from a chunk number alone.
Optional depth with an output
- Proof fluency: use another Rosen proof exercise after a diagnosed gap. Submit a fresh proof and a method comparison, rather than more reading notes.
- Induction foundations: read the generation-rule versus recursive-function discussion in Cornell's notes. Show why building a finite set in different orders requires consistent outputs.
- Broader proof writing: the local
Resources/Catalogue-master/Discrete/contains Morash's Bridge to Abstract Mathematics and Language, Proof and Logic. These are inventory candidates, not fully reviewed assignments. Inspect an edition's contents and select a short proof-writing topic only for a named gap. - Additional MCS copies:
Resources/pdfs/Mathematics for Computer Science (2012).pdfand(2018).pdfare available. Do not mix their numbering without checking.
Optional depth adds time. For the full-book path, this module's assignment is a checkpoint within separately budgeted whole-book reading. The current upgrade inspected local indexes and selected excerpts; it does not claim to have audited every book or PDF in Books, reading or Resources.