Any recommended crash course on Maths? | Hacker News Reader

Any recommended crash course on Maths?

17 pointsfebin9 comments

My math is weak. I am finding difficult to understand research papers in the fields of AI, Blockchain, Quantum Computing, etc.

I tried khan academy videos, they are good, but there's so much. I want to understand the critical aspects that can help me dive and give the ability to figure things out.

Any hands-on materials would be great. I am reading "A Programmer's Introduction to Mathematics". But, I need more materials. Thank You!

P.S: I am a very impatient person by design.

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Being impatient is not something you are, but something you have become. Arguably, lots of social media exacerbate this issue. I would recommend you try to improve, as impatience will be very detrimental towards doing mathematics.

Without further details, it's hard to know what your current level is. Most math bootcamps cover algebra and calculus. A great high school level one is:

* Basic Mathematics by Lang

* Calculus Made Easy by Thompson

If that is too simplistic, try a Math 55 like approach:

* Linear Algebra Done Right by Axler

* Principles of Mathematical Analysis by Rudin

You can replace Axler by Finite-Dimensional Vector Spaces by Halmos. But it's harder. Sadly the latest edition of Axler has distracting pictures and boxes that have done away with some of it's TeX elegance.

You can also replace both books by Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, by Hubbard & Hubbard.

An alternative route is to do a bootcamp where logic and abstract algebra is the area of focus. I've never seen such a course offered to beginners, but I think it'd be great if you are later focusing on things like formal methods.

I can't agree enough about the Lang and Thompson suggestions. There are YouTube videos working through a lot of Lang's "Basic Mathematics" [1]. "Calculus Made Easy" is what got me through my first year of Calculus in 1981. I have read that modern Calculus textbooks are written for school board approval, or that of other Calculus teachers, whereas Thompson's book was written for the actual beginning student. Years later it rings true.

[1] https://www.youtube.com/watch?v=04MWqyhD61g

Thank you, totally agree with you on the impatience. I will go through this, thanks a lot.

Math professor here.

A book which I have found excellent is Epp's Discrete Mathematics with Applications. The book is very patient and explains things really well -- stuff like formal logic, induction and recursion, proofs, probability and combinatorics. Lots of good exercises too.

I used this as a textbook in a course required of all of our sophomore CS students. It lays an excellent foundation for more sophisticated material that follows.

The latest edition is absurdly expensive (as is the case with most textbooks), but used copies of previous editions are likely to be ubiquitous on Amazon and elsewhere.

Do you have a math reading list for an aspiring self-taught software engineer (assume I have no math background -- took calculus many years ago)? I was thinking of going from studying Calculus, then a book on proofs, then discrete math, then algorithms, maybe linear algebra too?

As mentioned in other answers, Thompson's Calculus Made Easy is an excellent informal book for calculus. Spivak and Apostol are nice at a much higher (rigorous and proof-based) level.

Most mainstream calculus books suck; they tend to hedge their bets between being advanced and proof-based on the one hand, and catering to students with a mediocre grasp of algebra on the other. Thomas' book is probably the best of this bunch.

Epp does proofs and discrete math, and a little bit of algorithms. The usual favorite for algorithms is Cormen et al.'s Introduction to algorithms, although I don't know it well.

For linear algebra, Axler (as someone else mentioned) is a very nice book. I really like Knop also (more beginner-friendly). Hefferon's Linear Algebra looks very nice, and is (legally!) free online. If you prefer a more applied/computational bent, try Strang.

Thank you for the response. Would reading Calculus to Epps then to some linear algebra & algorithms be most appropriate in a linear progression? Or would I be able to read some books concurrently?

Neither calculus nor Epp's book require any prereqs beyond high school algebra. Studying algorithms would definitely be easier if you'd gotten through Epp first.

For linear algebra, it depends heavily on your choice of book. To read Hefferon or (even more so) Axler, you'll want to have seen a fair amount of mathematical formalism, and read through some proofs. Knop is probably a good place to learn mathematical formalism; if you approach it with limited background it will be slow going but you'll learn a lot.

I got to have a look at the first few pages. This might be the book I just need. Thank You.

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