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12 points

·
1st Oct 2018

Proceeding with knowledge gaps is something everyone has to do. In your case, you're going to have to improvise a lot. What I tend to do is put a black box on any confusing detail and write it off as "this blackbox let's me do X." If a definition is confusing for me, I replace the definition with an example that I understand and leave it be. (Some definitions have this sort of infinite regression to it; to understand this definition, you need to understand these other 3 definitions, which requires you to understand these 9 definitions and so on.)

Normally people have to take classes and pass an exam so you have at least 1 year to build that knowledge.

I don't recommend trying to learn what took others years to learn in 1 month, that's just unrealistic. Talk to your advisor; a lot of times you don't need to know the subject 100%, just some parts of it.

For analysis, you might not need to know everything about it, just maybe what a Hilbert space is and some standard results. For complex, honestly I think that class was more to teach people how to do analysis (the proofs are very elegant and it really give you experience on how one ought to go about proving something in classical analysis), as far as results goes, I only know the residue theorem and Riemann mapping theorem. For algebra, I guess I know what all the structures are... but don't remember much else.

Oh, there's this book that supposedly give a good outline on math you need to know.

3 points

·
14th Sep 2018

Munkres is a great resource to learn topology if you want to actually learn the material and as for complex I don't have a good suggestion for it, but since you're trying to study for the GRE I would suggest checking out All the Mathematics You Missed but Need to Know For Graduate School by Thomas Garrity. The link I added leads to the amazon page where you can buy it for pretty cheap. It's a great book that contains the two subjects that you want to study and many more topics. I myself am using it to study for the GRE and am finding it very helpful in learning the subjects I haven't touched.

2 points

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28th Apr 2015

I hear this book is good for a refresher, though you may need to dig up some old math texts, borrow, or somehow acquire them to delve into topics you really forgot everything in.

Good to have you back learning math. As some math guy/gal said, if you are unhappy, do math to become happy.

1 point

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12th Oct 2019

All the Mathematics You Missed - Thomas Garrity

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I've been reading through this over the last few days. Seems like it might be what you're after. Does a nice overview of all the major topics covered in in a standard undergrad curriculum.

1 point

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8th Jan 2017

Maybe start with a book like this and when you hit a wall, you get the relevant textbook and do exercises.

One of my undergrad profs said that "The only way to learn mathematics is to DO mathematics."

1 point

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10th Aug 2015

This book suggests some knowledge of algorithms and complexity could be useful to the incoming mathematics graduate student (with book recommendations).

You could pick up a copy and use it to guide your independent studying so you cover all your bases.

3 points

·
4th Sep 2020

Have you seen this?

2 points

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8th Dec 2020

Are you specifically wondering about the math knowledge required for a data science master's program? I have thoughts on that, albeit based on fairly limited personal experience.

For a broader comparison (say, how much math do you know compared to the typical math grad student), there's a book called All the Mathematics You Missed (But Need to Know for Graduate School). Though I haven't read the book, I think just scanning through the table of contents and checking off the things you know would give you a good idea of your level of knowledge. Alternatively, this is the sort of knowledge you'd expect to be covered in the GRE math subject test, so getting some practice tests for that might give you a clue.

2 points

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18th Feb 2015

You'd be better off studying to do well on the Math subject GRE and possibly aiming as high as doing well on the qualifying exams before even getting accepted.

If you master the material in these two books (and perhaps <em>Putnam and Beyond</em> if you're set on Putnam-type problems), you should be good enough for graduate school.

1 point

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11th Mar 2021

Not Dover, but relevant: https://www.amazon.com/All-Mathematics-Missed-Thomas-Garrity/dp/0521797071

1 point

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3rd Oct 2018

https://www.amazon.com/All-Mathematics-You-Missed-Graduate/dp/0521797071

http://web.evanchen.cc/napkin.html

and books by Ian Stewart/David Tall and Courant/Robbins *What is Math*,

1 point

·
7th Mar 2018

Wikipedia...

(https://www.amazon.com/All-Mathematics-You-Missed-Graduate/dp/0521797071 - you can try this, but Wikipedia has more info...)

1 point

·
9th Oct 2016

Try reading:

https://www.amazon.com/All-Mathematics-You-Missed-Graduate/dp/0521797071/

or

https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163/

or

https://www.amazon.com/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809/

or

https://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192/

I promise that not a single angel will lose his/hers/its wings.

1 point

·
7th Nov 2015

This book has good summaries of the topics you should be familiar with for grad school as well as book recommendations from which one can learn them.

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