
Ask HN: 'Crash Courses' for Mathematics Related to DL, ML and Data Analysis - mayankkaizen
I am specifically looking for free pdf or online materials for mathematics needed in ML, DL and Data analysis which doesn&#x27;t necessarily go in depth. My primary aim to have a good top level view and if possible get hold of the most basics stuffs as soon as possible.
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sdiq
First, please read and internalize dsacco's comment.

In the meantime, the following might help. But from experience, if your math
is already shaky, you would certainly need to look for resources covering
everything listed in a more in depth manner.

Basic calculus refresher -
[http://www.stat.wisc.edu/~ifischer/calculus.pdf](http://www.stat.wisc.edu/~ifischer/calculus.pdf)

Learning from Data -
[http://www.inf.ed.ac.uk/teaching/courses/fmcs1/readings/matl...](http://www.inf.ed.ac.uk/teaching/courses/fmcs1/readings/matlab-
barber.pdf)

Basic probability theory -
[http://homepages.inf.ed.ac.uk/sgwater/teaching/general/proba...](http://homepages.inf.ed.ac.uk/sgwater/teaching/general/probability.pdf)

Mathematics for Machine Learning -
[https://pdfs.semanticscholar.org/910e/3118b50f426e5e840561e1...](https://pdfs.semanticscholar.org/910e/3118b50f426e5e840561e1f9f1fdd67e5724.pdf)

Math for Machine Learning -
[https://www.umiacs.umd.edu/~hal/courses/2013S_ML/math4ml.pdf](https://www.umiacs.umd.edu/~hal/courses/2013S_ML/math4ml.pdf)

~~~
mayankkaizen
Yes I have read his comment and added a reply there. To reiterate my point, I
asked for crash courses not because I wanted to make quick progress but
because I wanted to have an idea of what kind of mathematics is needed. In a
way I was looking for some syllabus with some description added.

Thank you for posting these links. I'll definitely go through these.

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dsacco
I’m sorry to say this because I observe that we get these questions somewhat
frequently, but I don’t think what you’re asking for - in the format, goals
and speed you’d like it - is a thing.

That’s a pretty discouraging statement, so let me try to be more helpful. The
mathematics comprising contemporary machine learning and data analysis
primarily consists of linear algebra, calculus, mathematical statistics and,
at the high end, probability theory. There are boutique efforts to use things
like topology but that’s non-standard.

As it stands, your question is underspecified, which is what I repeat for most
of these questions. The answers you receive here are going to variously
interpret what you’re actually looking for and prescribe based on the author’s
interpretation and intuition. It would be more useful if you explained exactly
what your goals are. Here’s precisely the problem: you apparently don’t know
these mathematics already, but you’re asking for something that “doesn’t
necessarily go into depth.” How much depth is too much, and how would you know
that exactly given your present unknown unknowns? If you explain what you
actually want to achieve, we might be able to

1\. Tell you that you don’t actually need that “top level view” to achieve
what you’d like,

2\. Tell you that such a top level view is not nearly enough for what you’d
like to do, or

3\. Tell you that a top level view is coherent, and optimize the best
materials for you to learn from based on what you want to do.

It would also help us make recommendations if you explained what your current
level of mathematical background looks like. Have you taken linear algebra at
least once? Exactly how basic do our resources have to be? Different textbooks
written for different audiences can variously explain the same concept in two
pages or 10 pages, and they can emphasize different things.

I’d like to help, and I probably can, but it would go a long way if you could
tell us what your end goal is instead of what you interpret as the next step
towards that goal. Then we can provide resources based on your mathematical
maturity.

~~~
jxub
Topology for ML sounds amazing. Got any papers/links?

~~~
dsacco
Sure, try this:
[http://math.ucr.edu/home/baez/information/](http://math.ucr.edu/home/baez/information/).

In a nutshell, you take probability distributions and project them onto
topological manifolds, such that the distribution consists of points on the
manifold. You can find more by searching for key words like "information
geometry" or "differential geometry machine learning".

~~~
mlevental
there's also the stuff that ayasdi and carlsson were/are doing but i never
really saw the point of that (e.g. just compute connected components instead
persistent homology).

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imakecomments
Any PreCalculus text -> Stewart Calculus -> Strang + Axler Linear Algebra -> a
Calculus based Statistics & Probability book. Do the problems in the books.
Read each chapter. If you do that you'll know Calculus and Linear Algebra
better than most. If you want to then move up from there study Real Analysis
and higher level math like Measure theory (but this may not be necessary for
your purposes).

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sushanthiray
Take a look at the Coursera specialization: Mathematics for Machine Learning
[1]. The specialization isn't free but you can certainly apply for financial
aid.

[1]: [https://www.coursera.org/specializations/mathematics-
machine...](https://www.coursera.org/specializations/mathematics-machine-
learning)

~~~
astrodev
Yes! It's a new course that will be open for enrolment soon. I think it's
exactly what most people here are looking for.

There is the financial aid and normally there is the option to watch the
lectures and see the assignment for free. On the other hand, the cost of the
courses rarely exceeds $50.

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ivan_ah
Check out my books on CALCULUS+MECHANICS, and LINEAR ALGEBRA:
[https://minireference.com/](https://minireference.com/) They are not free,
but not expensive. It's like 2 years worth of undergraduate maths packed into
two small books.

Previews are free though, and might be useful if all you need is an overview:
[https://minireference.com/static/excerpts/noBSguide_v5_previ...](https://minireference.com/static/excerpts/noBSguide_v5_preview.pdf)
[https://minireference.com/static/excerpts/noBSguide2LA_previ...](https://minireference.com/static/excerpts/noBSguide2LA_preview.pdf)

This is also good: [http://ml-cheatsheet.readthedocs.io/en/latest/](http://ml-
cheatsheet.readthedocs.io/en/latest/)

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BiancaDelRio
[http://www.cs.cornell.edu/jeh/book.pdf](http://www.cs.cornell.edu/jeh/book.pdf)

~~~
WalterGR
Foundations of Data Science

Avrim Blum, John Hopcroft, and Ravindran Kannan

Copyright 2015

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usgroup
Undergrad lin algebra and calculus ... start there! Although there is no
skimmable view of those worth a damn. You need 2-3 months @ 8 hours a day.

Stats thereafter is pie, ML low hanging fruit will come easily.

Good inference and learning from data on the other hand is experience: expect
years, no shortcuts. In fact, suffer. It’ll make the journey as informative as
possible.

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gtani
Similar quesion, aimed at math majors:
[https://www.reddit.com/r/math/comments/81px9v/what_are_some_...](https://www.reddit.com/r/math/comments/81px9v/what_are_some_good_mathematical_books_should_i/)

Really, if you're not going to go to e.g. community college where you can do a
lot of this (LA, prob/stats, calc) your best shot is to find study groups in
Data science meetups, etc which are plentiful in major cities since many
people have the same impulse. Truthfully, self study rarely gets far if people
never went beyond Calc 2.

Here's a blog about one guy's adventure, read the part where he talks about
Shores' LA text(not a bad book by the way but yes, lots of typos):
[https://news.ycombinator.com/item?id=8996024](https://news.ycombinator.com/item?id=8996024)

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mithunmanohar1
Week 1 Linear Algebra [https://ocw.mit.edu/courses/mathematics/18-06-linear-
algebra...](https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-
spring-2010/)

Week 2 Calculus
[https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53...](https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr)

Week 3 Probability [https://www.edx.org/course/introduction-probability-
science-...](https://www.edx.org/course/introduction-probability-science-
mitx-6-041x-2)

Week 4 Algorithms
[https://www.coursera.org/courses?languages=en&query=Algorith...](https://www.coursera.org/courses?languages=en&query=Algorithm%20design%20and%20analysis)

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bjourne
Read these books!

* [http://www-bcf.usc.edu/~gareth/ISL/ISLR%20First%20Printing.p...](http://www-bcf.usc.edu/~gareth/ISL/ISLR%20First%20Printing.pdf) * [http://web4.cs.ucl.ac.uk/staff/s.prince/book/book.pdf](http://web4.cs.ucl.ac.uk/staff/s.prince/book/book.pdf) * [http://users.isr.ist.utl.pt/~wurmd/Livros/school/Bishop%20-%...](http://users.isr.ist.utl.pt/~wurmd/Livros/school/Bishop%20-%20Pattern%20Recognition%20And%20Machine%20Learning%20-%20Springer%20%202006.pdf)

I am not an expert in ML. I have heard experts in ML call the above books
introductory.

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mindcrash
This got trending on Github today. It might help:

[https://github.com/llSourcell/Learn_Machine_Learning_in_3_Mo...](https://github.com/llSourcell/Learn_Machine_Learning_in_3_Months)

First month covers the basics (calculus, algebra, probability, algorithms)

Second month is focused around coding (Data science in Python) and putting the
things learned in the first month in a ML context (Siraj's Math of
Intelligence course on YouTube)

Third month is all around Deep Learning.

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zengid
This article on matrix calculus seems pretty good for someone familiar with ML
and DL concepts but not on the maths:

[http://parrt.cs.usfca.edu/doc/matrix-
calculus/index.html#sec...](http://parrt.cs.usfca.edu/doc/matrix-
calculus/index.html#sec3)

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abhinavkits501
[https://developers.google.com/machine-learning/crash-
course/...](https://developers.google.com/machine-learning/crash-course/ml-
intro)

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uptownfunk
the strang lectures on LA, any decent calculus book (khan academy or something
maybe too) and then i would jump into ISLR and the karpathy Stanford lectures
on DL, the rest you learn as you go adhoc.

~~~
usgroup
One can't over emphasise: LA and Calc. Do that!

The rest will be a cake walk.

But you need LA from matrices to spectral decomposition and Calc from
differentiation to Laplace transforms; so no easy feat. You'll need a fair
amount of "give a damn" to put yourself through it.

