Hacker News new | comments | show | ask | jobs | submit login

This is awesome. At some point in the next five years I plan on taking a sabbatical and focusing almost exclusively on redoing my math education and moving deeper into advanced topics than I did as an undergraduate.

Is there anyone who has done something similar who might share some suggestions for success?




A good entry point are one of these books which start from the very beginning of math in Egypt/Greece and teach the fundamentals of math through a narrative as humans discovered the various parts:

"Mathematics for the Nonmathematician" https://www.amazon.com/Mathematics-Nonmathematician-Morris-K...

or

"Mathematics for the Million" https://www.amazon.com/Mathematics-Million-Master-Magic-Numb...

Of the two I prefered Kline's book but they are both good, albeit a bit heavy on geometery as that was a big focus of early math research.

Another great starting point is "Book of Proofs" and "Introduction to Mathematical Reasoning" to give you a deeper sense of how to approach the subject.

https://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472...

https://www.amazon.com/Introduction-Mathematical-Reasoning-N...

From there I went down this path (the order of which is up to you, each has tons of good source material):

-> Proofs/Logic

-> Algebra

-> Linear Algebra

-> Calculus

-> Abstract Algebra

-> Set Theory

-> Group Theory

-> Category Theory

-> Statistics/Probability

-> Discrete Mathematics

I never did well with learning math in a classroom but I've grown to love math through this process. There are lots of applications in programming as well. It makes approaching the deeper parts of Haskell/FP, data science, and machine learning much more accessible. I particularly liked the higher level Abstract Algebra stuff over the more grinding equations of calculus/linear algebra as it was more similar to programming.


> I particularly liked the higher level Abstract Algebra stuff over the more grinding equations of calculus/linear algebra as it was more similar to programming.

Linear Algebra Done Right takes a more abstract approach so there is minimal computational pain.


Thanks, I'll check it out the book.

I prefer the more abstract stuff as I can do most of the computation via Sage (which is a great learning tool). Plus there are some amazing scientific calculator apps for Android and iOS these days which let you compose and calculate full complicated equations.

Of course it helps to work out equations to understand them but far too many math books push you towards rote memorization and test prep, meaning lots of exercises with endless equations, which is far from my goal here.

I'd say there is a market here for a math book/video series combined with Sage for teaching programmers and data scientists math. But there are so many math books already I'm afraid it would get lost in the noise.


The author of Book of Proof referenced here also offers a free online Creative Commons-licensed version: http://www.people.vcu.edu/~rhammack/BookOfProof/

But the dead tree version is also very reasonably priced.


I so badly want to do this. I did pretty well in my undergrad math degree, making it through some grad level classes in logic and topology. Then I got a job in business.

Fast forward 15 years and I've forgotten so much that I look at old notebooks and can't understand a fucking thing I wrote back then.

It depresses me to no end.

And I kind of despair that with the obligations I'm locked into right now, it will be nearly impossible to dedicate the time I would need to relearn it all.


Suggestion: Just try to sock away 1 hour a week. Select a topic that you remember being good at. Then just pick one chapter from one of the free books listed, and have at it.

The mind map in your head will start reconnecting fairly quickly I imagine.

I personally find the sheer quantity and range of these free pdfs daunting, so as a renegade physics graduate I'm focusing on Hammack's The Book of Proof this summer. As you did Maths at University, you might not need elementary stuff like that having already learned the strategies for abstract proof.


Thanks, good idea. One hour per week seems do-able and if it's review of things that I had a solid grasp of earlier, hopefully they come back quickly.


I have quite a few adult readers using my book to refresh and re-learn basic calculus and mechanics. You might consider checking it out[1]. It's not free, but very affordable.

[1] https://www.amazon.com/dp/0992001005/noBSguide preview: https://minireference.com/static/excerpts/noBSguide_v5_previ...


Ha, this looks great, thanks. I have no problem paying for good content.


I am the same, relearning a lot of linear algebra. It's a great book and my choice, so far, for this process. It does jump around a bit in some places but I have found, if something is not explained I keep on reading and some time later he comes back to it. Highly recommended.


This book looks amazing! Exactly what I've been looking for as a refresher. Thanks.


My suggestions would be to form study groups and seek out study partners. And if you are willing to take the lead when you meet, you'll learn more through (quasi-)teaching.

MOOCs and books provide the materials but not the motivation or the opportunities for synthesis through verbalization and interaction.

For what it's worth, I'm basically in the midst of a sabbatical in order to study math.


I'm having similar thoughts. I've started this journey by trying to complete all exercises on khanacademy.org.


Same, I started at the pre-school math lessons and worked forward from there.

Progress is sporadic, due to having a newborn in the house, but patching all the holes in my math knowledge feels good.


Likewise. I started with pre-algebra level stuff and I just login when I have some free time and watch more videos and do more exercises. I figure every time I jump on there and do some of it, I'm improving that foundation.

I've also been running through the series of Youtube videos on Calculus I by Professor Leonard. The plan is to go through his entire sequence (Calc I, II and III) and then move on to Linear Algebra (I've already been dabbling in that as well, mostly with the 3blue1brown videos).

It's not easy, but I think it's worth the effort to build up that math base. It increases the scope of things you can read, study and understand, which is pretty valuable.


I've felt a similar sense of loss about losing knowledge picked up while in academia. I think that to re-learn properly, however, you need to find a way to apply the knowledge "in anger". There's a reason why we did endless problem-sets in school.

After a few fits and starts at re-learning I've found the only things that stick are things that I end-up using (albeit sometimes in a forced way). Nothing wrong with a nostalgic perusal of classic well-written texts, but these kinds of things were never intended for just reading. You gotta apply it to really know it.


Yeah. Find a pro that you can talk to. Nothing beats having a teacher for this stuff. Getting a leg-up can help you progress a hundred times faster. Even for the professionals learning mathematics is difficult, and people try to learn from other people. Of course, you also need plenty of suffering over the textbook and hours staring at the ceiling... Also, it helps if you actually have a concrete project in mind, not just "learn more cool formulas and stuff."


I think you can make up for the lack of a teacher to a certain extent by choosing slower-paced and more verbose source materials. For instance, Hammack's Book of Proof, and the Khan Academy curriculum (both mentioned elsethread) -- as opposed to, say, the dense exposition of Spivak's Calculus. The Spivak problems are incredibly well-composed, but will often stump the student. Not so the straightforward problems of Hammack and Khan.

I definitely agree that human interaction is needed, though (as noted in my other response) -- but it could be either a teacher or other students.


I choked on linalg for years, trying to read one textbook. The formal kind. Found a 5$ suggestion on Reddit (Gareth Williams), I made more progress in the following week than ever before.

Doesn't matter how as long as you do the work. If a book leaves you dry, try another one asap.


> Is there anyone who has done something similar who might share some suggestions for success?

I guess you're an engineer in academia, but it might help to specify, since that affects what suggestions are relevant.


Since i went into fp and recursive function, i felt the need and drive to do this as well.

I'd love a group




Guidelines | FAQ | Support | API | Security | Lists | Bookmarklet | DMCA | Apply to YC | Contact

Search: