Chapter Zero

What Hacker News says

1. PenyngtonSep 2023
   I've personally read An Introduction to Mathematical Reasoning: Numbers, Sets and Functions Paperback by Peter Eccles and Chapter Zero by Carol Schumacher and would recommend them both.

   Sadly, this is not an easy thing to learn and requires a lot of work and most importantly discipline. You mustn't let yourself be at all complacent. It's very easy when doing exercises by yourself to believe that you've "got the idea" and you can "see how it works", but the key is to actually write _everything_ down, so that there is no room for handwaving at all. This is not easy to force yourself to do, but it is necessary.

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2. pgeertsemaMay 2023
   2 books that are worthwhile: "A mathematical bridge" (an introduction to the lie of the land in higher math) and "Chapter Zero" (a review of material not taught in school, but wich is so basic that most textbooksjust assume you know, e.g. bijections and proof by induction)
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3. causalmodelsFeb 2022
   > Given my situation, how would you try to convince me that I should learn math

   Learning math has been the only time that I have ever been truly humbled by the aesthetic beauty of an idea. I didn't intend on studying math, I wanted to be an english major, but the woman I was dating at the time was somewhat of a math prodigy and I wanted to understand her world more // impress her. This may seem silly to some of the more mathematically mature people here, but the moment I fully understood Cantor's theorem it felt like my mind was dunked into this sublime understanding that left me in a daze for a week. Russell sums this up pretty well,

   """ Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry. """

   > how would I teach myself the actually interesting parts without getting bogged down by doing lengthy calculations that a computer could do. The standard curriculum is so heavy on the latter and mostly absent of the former.

   This wont be much of a problem if you're interested in pure math as numbers bigger than 10 are rare in that domain. I would recommend picking up an intro to proofs type book like [1]. The reviews are mixed but I would take that with a grain of salt as I suspect many of them were written by bitter students.

   [1] https://www.amazon.com/Chapter-Zero-Fundamental-Abstract-Mat...

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4. timwisemanApr 2012
   Wikipedia is a fantastic resource, but it is first and foremost an Encyclopedia, a reference. It has many times helped me refresh my memory or helped explain something I read first in another context. But it is not a good place to learn a brand new subject.

   There are many good resources to learn math, most in the form of books (some of which have digital versions). Personally, I find it best to find a subtopic that interests me and dive in. Though I will say that I would recommend "Chapter Zero" to most people wanting to get back into math after a long break.

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5. ubasuNov 2010
   Here's my list:

   Basic

   1. Chapter Zero (Carol Schumacher) 2. Naive Set Theory (Paul Halmos)

   Linear Algebra

   1. Finite-Dimensional Vector Space (Paul Halmos) 2. Linear Algebra Done Right (Steven Axler)

   Real Analysis

   1. Real Mathematical Analysis (Charles Pugh) 2. Introduction to Analysis (Maxwell Rosenlicht)

   Algebra

   1. A first course in abstract algebra (John Fraleigh)

   These books are better for self-directed reading compared to some of the classics like Rudin or Herstein. These should keep you busy for a while.

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6. timwisemanAug 2010
   I do not know if it is exactly what you want, but Chapter Zero ( http://www.amazon.com/Chapter-Zero-Fundamental-Abstract-Math... )comes close. It talks about a lot of the foundational mathematics that and symbolism that is often never taught to non-math majors, but it does so in an easily understood way.

   Proofs and Refutations by Lakatos also touches on this topic, though it is not the primary or sole discussion there.

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