The foundations of mathematics
by Ian Stewart, David Orme Tall · first published 1977
100% recommend
Why HN recommends it
Bridges the gap from computing with formulas to writing proofs, giving readers a sense of university-style mathematics; suits self-learners, students starting upper-level maths, and adults returning to the subject.
Summarised by Claude from recommending comments
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Others here have offered some great suggestions already, so I will offer one a little off the beaten path: Foundations of Mathematics https://www.amazon.com/Foundations-Mathematics-Ian-Stewart/d... This book is meant to help one transition from performing math in an algorithmic manner to generating proofs based on logic and also…
on “Ask HN: Resources to learn real analysis?” ↗…through such a tough subject that it has to be a good book? I mean, do people normaly study from more than one text?! > ...to give people a flavour of university style mathematics I've just started The Foundations of Mathematics by Ian Stewart & David Tall. So far it's really promising.
on “A non-standard book list for software developers” ↗After reading all the comments I am sharing my choices 1. The foundations of mathematics by Stewart and Tall 2. Problem Solving Strategies by Arthur Engels 3. Journey into Mathematics by Rotman 4. Concrete Mathematics by Knuth et al.
on “Ask HN: Serious mathematics books that can replace a good teacher?” ↗The Foundations of Mathematics - Ian Stewart. I wouldn't say it taught me the most, but more like it opened the door so I could learn the most out of everything after it.
on “Ask HN: Which mathematics books taught you the most in your career?” ↗…I've bought it for friends and family with a wide range of maths backgrounds (graduate mathematicians to not-since-school-forty-years-ago). Also "Alice and Numberland", Baylis and Haggarty; and "The Foundations of Mathematics", Stewart and Tall. These are both pitched somewhere between high school and university level and bridge the gap well.
on “Learning Math” ↗I would suggest to start with reading The Foundations of Mathematics by Stewart and Tall: https://global.oup.com/ukhe/product/the-foundations-of-mathe... This will give you an understanding of which topics make sense to you and which you can barely follow. From that,…
on “Ask HN: How to learn math from zero for adults?” ↗