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Brains can work that way. It is a skill, and this skill even has a name: mathematical maturity. Basically, after you've been exposed to a lot of mathematics yo
by mej10 9y ago
Brains can work that way. It is a skill, and this skill even has a name: mathematical maturity.
Basically, after you've been exposed to a lot of mathematics you develop a skill where you can just accept abstract definitions and go with it.
- agentultra 9y agoI would expect no less even in an introductory text. Mathematics is meant to be precise and formal mathematics even more so. Prosaic pedagogy might suit a liberal arts introduction but it won't help the reader to convince themselves that the statements and theorems proposed are true and valid. The syntactic approach is really useful as a programmer. A Logical Approach to Discrete Math[0] teaches programmers how to develop proofs in this style using logic and syntactic substitution. Once shown how easy it is to achieve rigour it is hoped that work-a-day programmers can formulate their own proofs and develop stronger specifications using mathematical tools. I'm not a formally trained mathematician and am completely self-taught as a programmer but with some background in set and graph theory I found it approachable. It's certainly a good companion text to learning more practical systems like TLA+ or Lean. [0] https://www.amazon.ca/Logical-Approach-Discrete-Math/dp/0387941150 https://www.amazon.ca/Logical-Approach-Discrete-Math/dp/0387...
- skybrian 9y agoGreat that it works for you, but it won't convince anyone of anything if they don't understand what it means or why they should care. As a writer or a teacher, if you want to reach a broad audience, give some simple, concrete examples, then explain the abstraction that covers them all. Assuming mathematical maturity won't help you reach your audience.