Mathematics

What Hacker News says

1. biofoxMar 2025
   There are two books which do a fantastic job of this:

   Mathematics: From the Birth of Numbers, by Jan Gullberg

   and

   Mathematics: A Cultural Approach, by Morris Klein

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2. photochemsynDec 2022
   Mathematics From The Birth of Numbers (Jan Gullberg, 1997)

   It's a pretty large tome, but covers all the basics and is a great reference. It goes well with Khan Academy videos for example.

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3. photochemsynMay 2022
   Coincidentally I'm doing the same thing right now. The plan I'm pursuing is to design a multi-month course in a particular mathematical subject I feel I need to learn, as if I was going to teach it to someone else. I would need a course syllabus as a framework for the material (in my case, this is something called complex analysis, because I need to understand how it all works, and unfortunately neglected it in the past).

   Step One: Find some good source material. Many people have suggested Khan Academy, in my particular case I've discovered this excellent Herb Gross lecture series, 'Calculus of Complex Variables' provided via MITOpenCourseWare. Then, review all the source material and make a list of the topics:

   Part I: Complex Variables:

   The Complex Numbers; Functions of a Complex Variable; Conformal Mappings; Sequences and Series; Integrating Complex Functions;

   Part II: Differential Equations:

   The Concept of a General Solution; Linear Differential Equations; Solving the Linear Equations L(y) = 0 with Constant Coefficients; Undetermined Coefficients; Variations of Parameters; Power Series Solutions; Laplace Transforms;

   Part III: Linear Algebra:

   Vectors Spaces; Spanning Vectors; Constructing Bases; Linear Transformations; Determinants; Eigenvectors; Dot Products; Orthogonal Functions;

   Step Two: Plot a timeline. Here I'll give myself one week per lecture. I'll set aside 1-2 hours per day, at least four days a week, to work on the material. This might be inadequate. Staying motivated without having some external pressure will be a bit of a problem, but noting that from the beginning helps.

   Step Three: Devise problem sets to test my understanding of the material. Here is where having a good teacher on hand would be invaluable, but that's not an option, so I'll have to find example problems. One option is to find a complex analysis textbook somewhere, and also find its solution manual, and use the problems provided there. Having the solutions around to check results can be very useful. A websearch like "complex analysis problems and solutions site:.edu" turns up a lot of results, just look for the simplest introductory ones (i.e. not the advanced proofs!).

   So, I think this is the way to go for self-learning in math. If you have a more introductory level subject, say Linear Algebra (w/o complex), or Differential Calculus, just try to do the same thing.

   P.S. I find Jan Gullberg's "Mathematics, From The Birth of Numbers" to be a great overview of the whole mathematical world, kind of like a guidebook: https://www.goodreads.com/book/show/383087.Mathematics

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4. DrPhishOct 2021
   Mathematics: From the birth of numbers by Jan gullberg

   A worthwhile investment

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5. bobmaxupJul 2020
   Jan Gullberg - Mathematics: From the Birth of Numbers

   https://www.amazon.com/gp/product/039304002X

   Amazon.com Review What does mathematics mean? Is it numbers or arithmetic, proofs or equations? Jan Gullberg starts his massive historical overview with some insight into why human beings find it necessary to "reckon," or count, and what math means to us. From there to the last chapter, on differential equations, is a very long, but surprisingly engrossing journey. Mathematics covers how symbolic logic fits into cultures around the world, and gives fascinating biographical tidbits on mathematicians from Archimedes to Wiles. It's a big book, copiously illustrated with goofy little line drawings and cartoon reprints. But the real appeal (at least for math buffs) lies in the scads of problems--with solutions--illustrating the concepts. It really invites readers to sit down with a cup of tea, pencil and paper, and (ahem) a calculator and start solving. Remember the first time you "got it" in math class? With Mathematics you can recapture that bliss, and maybe learn something new, too. Everyone from schoolkids to professors (and maybe even die-hard mathphobes) can find something useful, informative, or entertaining here. --Therese Littleton

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6. chrismarlow9Jul 2020
   I'm reading a book called Mathematics from the Birth of Numbers by Jan Gullberg and it covers these systems from various cultures in depth. Great book and easy to read even for the non mathematician. It reads like a cross between a history book and a technical reference. This is literally the first topic in the book.
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