Ask HN: Books to learn applied maths?

[nocoder]

I am looking for books that can help me learn maths from a applied point of view. I have studied statistics & I am comfortable with graduate level maths. I like books that start from applied point of view & then move in to theory. Something like the Halliday, Resnick, Walker book on Physics, do you know anything similar for maths? I understand that maths is part of many disciplines so I don't mind if the books go into many different realms

[dagw]

You're talking about a pretty massive field. That being said The Nature of Mathematical Modeling by Neil Gershenfeld might be what you're looking for. Each chapter is a short (15-25 page) introduction to one common tool in applied mathematics. In that space you'll get an overview of when you might want to use that technique, a brief description of the basic mathematical theory underlying the method and a few examples of how it can be applied.

Of course you won't learn enough about any topic to be able to actually tackle any but the most trivial of problems, but you will come away with a good understanding of which technique you should use for which kind of problem and have a good enough of a basis to be able to understand the more advanced books on the given topics. Each chapter also ends with a recommendation of 3-4 books which you can check out if you want to dig deeper into that particular topic.

[nocoder → dagw]

Thanks for this. I checked out the book ToC and found it interesting. One question, does this book assume the knowledge of the tool to start with?

[dagw → nocoder]

No. The book does assume you know and are comfortable with your calculus and linear algebra, but each topic is covered from the start as it where.

[nocoder → dagw]

Thanks. That's helpful

[MTsardakas]

Howison's Practical Applied Mathematics has many illuminating examples of maths being applied in a variety of fields. A good introduction to modelling techniques with a nice balance between theory and examples is Applied Mathematics by Logan.

[nocoder → MTsardakas]

Thanks for this. I checked them out and they sound very interesting, do you recommend that I begin with one of them or is it fine to read them concurrently?

[MTsardakas → nocoder]

It depends! If you want to see unusual examples of applied maths or a bit of thinking out of the box, focusing on techniques and not theory, start with Howison's. Logan builds theory alongside applications and is, therefore, heavier on maths. If you're confident with graduate level physics though you should be fine with both.

[wayn3]

applied maths is a big field. is there anything in particular that is interesting to you?

halliday is a book on experimental physics. it takes a phenomenological approach because thats how experimental physics works. theres nothing "applied" about it.

[nocoder → wayn3]

My bad, I studied it long back & did not realize that it was experimental physics. What I meant was I really liked the approach in the book, it made understanding concepts really easy for me. I don't do it really well understanding from theoretical principles & working upwards, instead going from application to theory works for me. As far as my interest goes, I am interested in mathematical modelling of social & biological systems, i know this might again be too broad but inputs will be appreciated.