Undergraduate Analysis

What Hacker News says

1. kingofalltradesMar 2024
   First step into math is to learn how math people think. Here below is an intro textbook meant to do just that[0]. It's a high quality, free introduction. You don't need to know much past 6th/7th grade level math which amounts to knowing how to do arithmetic with fractions and decimals and maybe an ability to in/equalities in one variable. I will also add a couple of google links that might be more relevant to what you might be trying to do[1][2].

   [0] Book of Proof by Richard Hammack https://www.people.vcu.edu/~rhammack/BookOfProof/

   [1] Linear Algebra: Step by Step by Kuldeep Singh https://www.google.com/books/edition/Linear_Algebra/BJNoAgAA...

   [2] Number Theory: Step by Step by Kuldeep Singh https://www.google.com/books/edition/Number_Theory/YZr9DwAAQ...

   [3] Undergraduate Analysis: A Working Textbook by Aisling McCluskey and Brian McMaster

   https://books.google.com/books?id=7U9HtAEACAAJ&printsec=copy...

   There's even more relevant book for you[4]

   [4] Foundations of Applied Mathematics by Jeffrey Humpherys, Tyler J. Jarvis, Emily J. Evans

   https://books.google.com/books?id=CEc3DwAAQBAJ&pg=PR3&source...

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2. practalOct 2024
   I am looking at the whole development of this thread with amusement, but I also find it somewhat shocking.

   I see that you are desperately trying to distinguish "foundational" and "analysis" contexts from each other. If you are writing a book about analysis, it might be helpful to clarify that in this context you reserve "function" for mappings into ℂ or ℝ, for example [1] defines "function" exclusively as a mapping from a set S to ℝ (without any further requirements on S such as being a subset of ℝⁿ). Note that even under this restricted definition of function, a distribution still is a function.

   In a general mathematical context, "function" and "mapping" are usually used synonymously. It is just not the case that such use is restricted to "foundations" only.

   It seems to me that squabbles about issues like this are becoming more frequent here on HN, and I am wondering why that is. One hypothesis I have is that there is an influx of people here who learn mathematics through the lens of programs and type theory, and that limits their exposure to "normal" mathematics.

   [1] Undergraduate Analysis, Second Edition, by Serge Lang

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3. stiffMar 2018
   Springer has problem books with full solutions:

   https://www.amazon.com/Problem-Book-Analysis-Books-Mathemati... https://www.amazon.com/Problems-Solutions-Undergraduate-Anal...

   The second one is for Lang's "Undergraduate Analysis" book.

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