CalcCheck</title>
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Live webpage: https://alhassy.github.io/CalcCheck/
Introduction to Discrete & Calculational Maths Sep 8
What is a calculational proof? What is discrete mathematics? How is math related to programming: “proofs-as-programs”.
Grammatical Analysis and Boolean Operators Sep 10
A proof is a “story”, and calculation hints are the “transitions” that make the story flow nicely. The formulae are the “sentences” and they are formed from operators, constants, and variables which act as “verbs”, “names”, and “pronouns”, respectively.
ℕumber arithmetic is learned by memorising parts of infinitely large addition and multiplication tables. In contrast, 𝔹oolean arithmetic has tiny 2×2 “truth tables”. As such, 𝔹 may be easier to learn than ℕ.
Ladies and Tigers, a teaser Sep 11
Continuing the discussion on Boolean operators and how they can be used to model puzzles.
Substitution Sep 15
Textual substitution is a way to implement function application, grafting on trees, and can be used for assignment commands in programming.
Inference rules, Proofs-are-programs, and Equivalence Part I Sep 17
Update: There will be no knights and knaves problems in the upcoming Sep 22 midterm; but possibly in a future midterm.
The inference rules act as the foundational justification for the equational proof style; the online lecture notes go into more detail.
Inference rules, Proofs-are-programs, and Equivalence Part II (with lofi music) Sep 18
Quickly show how a program can be shown to meet its specification, discuss equivalence and negation for the purposes of solving knights and knaves problems.
Sep 22 is the first midterm; it is online during class time.
Tabulation vs Calculation Sep 24
We review basic operations on the Booleans with a focus on how manipulating symbols can be more effective than constructing truth tables, or evaluating expressions by “plug and chug” simplifications.
We also discuss formalisations of English phrases as propositional expressions.
… more content at the webpage https://alhassy.github.io/CalcCheck/ …
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