
Any recommended crash course on Maths? - febin
My math is weak. I am finding difficult to understand research papers in the fields of AI, Blockchain, Quantum Computing, etc.<p>I tried khan academy videos, they are good, but there&#x27;s so much. I want to understand the critical aspects that can help me dive and give the ability to figure things out.<p>Any hands-on materials would be great. I am reading &quot;A Programmer&#x27;s Introduction to Mathematics&quot;. But, I need more materials. Thank You!<p>P.S: I am a very impatient person by design.
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nextos
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.

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eggy
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](https://www.youtube.com/watch?v=04MWqyhD61g)

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impendia
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.

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LeicesterCity
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?

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impendia
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.

~~~
LeicesterCity
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?

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impendia
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.

