“Bibles” in Applied Math

Awhile ago, I and other VNQF members posted some of the most famous books in Quantitative Finance and related fields (including Partial Differential Equations, Numerical Methods, Optimization, Parallel Computing). Recently, I’ve posted a few classic books in Applied Math, based on the request of a member in the VEF’s VietnamBookDrive project. Even more recently, anh Ngo Quang Hung (and “đồng bọn”) have created a list of great textbooks in Computer Science.Here, I merely recompose the list of some bible books in Applied Math that I already did, but maybe more in depth and not limited to the scope of VEF. By Applied Math, I mean a wide spectrum from extremely mathematical topics (they’re essentially subsets of “Pure Math”) such as Partial Differential Equations to Computations (Numerical Analysis, Multiscale Modeling,…) to Probabilistic/Statistical Sciences to Computer Science and to a wide range of Applications (Physics, Chemistry, Biology, Engineering, Finance, Economics, Business, Medicines, etc.). Due to the breath and depth of this giant discipline, the list is by no mean complete and will be updated here continuously (possibly until I die).
Update: I’ll update this list on my blog so please check out that page instead.

3 Responses to ““Bibles” in Applied Math”

  1. Toan Says:

    Thanks a lot, Khoa, for this post. I am sure that many people will find this very helpful. Though, I’d like to make some comments on your choices for bible books in PDE. First, I don’t think people agrees that the PDE book of Evans is the bible in PDE, except possibly some grad may say so. This book contains many subjects but just basic, and has been used to teach in grad classes. But any one I asked agrees that the bible in PDE should be the book of Gilbarg-Trudinger, Elliptic PDE (It’s worth mentioning that there is a “parallel” version of this book by Liebermann, parabolic PDE). I don’t know the other two PDE books Khoa mentioned should be considered as the bibles (I never read those), but not seen for classes and for references as many as the others. There are also many other PDE books, considered significant…but for those who wants to study PDEs, as for a start, the book of Evans is suitable.

  2. Khoa Tran Says:

    Thanks anh Toan for your constructive comment.

    First of all, the word “bible” shouldn’t be taken rigorously at all. Moreover, though I tried to be as objective as possible, my personal taste is undoubtedly still visible.

    Secondly, each sub-field here (say, PDEs) is in fact a giant study in its own right. Thus, there are tons of significant books on the subject. This, combined with the breath/depth of my knowledge, only allows me talking about “sách nhập môn”. In this context, Evans’ book is by far the most popular used by American schools.

    And lastly, while I’m not a real PDEser, many bloggers here are. I’ll thus point readers to this comment page for PDE books. Also, many students will appreciate if the veterans here give a book-guide on studying PDEs.

  3. Toan Says:

    As for a “guide” of using PDE books, this is difficult to tell because it depends on one’s taste of using books. I hope some PDE experts here in this blog will share with us some advices.

    While waiting for some useful advice, I’d like to share my own experience. Let’s “mu’a ru*`u qua ma(.t tho*.” Hope it helps.

    – First I think one should read Evans’ book, as mentioned above. Don’t have to pay too much attention on some technical results. Just try to have an idea what the …PDE is and find out which kind of PDE one may want to study more or rather stop there, which is fine too.

    – Secondly, after one feels to want to study more on certain kind of PDEs, in my opinion, the following selected books are worth to have a careful look.

    + Conservation laws: The book of Bressan on Hyperbolic systems of conservation laws. After reading this book, one may want to look at the paper of Banchini and Bressan, appeared on Anal. of Math.

    + Elliptic eqs: Gilbarg-Trudinger’s book, the bible. For classical one, one may like Ladyzenskaja at al, elliptic version.

    + Parabolic eqs: Liebermann’s book. For classical one, Ladyzenskaja at al, parabolic version (my bible book). In fact, I don’t see that “much differences” between elliptic and parabolic.

    Of course, there are more books on topic one may want to look at. For instance, Variational method book of Struwe; Direct methods book of Guisti; Semigroup theory book of Pazy or Friedman;

    Last words, the above books are deserved to read carefully. Besides when you decide to study some topic, just check out “any book” on the field which your Library has and read them parallel….at least that’s my way – I don’t know if it helps.

    Once you really do research on some specific topic with your advisor, most of professors prefer you to learn by reading many papers….

    Good luck.

    Toan.


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