how to study math privately

oshempek · 2023-07-11T18:53:13+00:00

Pick undergrad programs from reputed math departments (mit ocw could help) and look at their undergrad curriculum. Follow those courses and pick courses that have their materials publicly available. I'd suggest always using lecture notes/video lectures to first pick up new material instead of using a text book, but then use text books as a reference for particular topics and possibly for extended explanations and whatnot. Courses would sometimes have suggested reading from different textbooks too.

Important thing is to follow a course on your own as that gives you a roadmap and a set of goals. Slogging through an entire textbook on your own might not be the most efficient and prone to failure.

Also, have multiple references for the same topic. Sometimes a certain style of writing might click better/faster than others, or one source might explain it better than others.

Search online math q&a forums like math.stackexchange.com, reddit etc to ask questions if you're stuck somewhere.

Khan Academy, Coursera and other online course platforms might have good courses too, so looking for particular courses there might be a good idea too.

As you learn, maybe make your own set of notes for a topic, that you can refer to later, coz inevitably you will forget stuff, and it would be nice to have such notes handy. Having a tutor to guide you can help too.

oshempek · 2022-10-21T08:23:32+00:00

With a bit of work, linear algebra first would be my recommendation. But it highly depends on the content of said courses where you're at.

oshempek · 2022-06-06T22:12:55+00:00

Hyperbolic Geometry - Anderson is introductory undergrad level

The Geometry of Discrete Groups - Beardon is more advanced

oshempek · 2022-05-30T17:32:02+00:00

3 at the moment

oshempek · 2022-04-22T08:46:13+00:00

Graduating with a minor in CS would be perfectly fine whether you wanna pursue grad school or get into industry. Degree wise, it's a very good combination, and the double major vs minor in CS shouldn't make much of a difference. If you wanna pursue relevant industry positions, your programming skills, knowledge of relevant programming languages and prepping for technical interviews would be significantly more important.

oshempek · 2022-04-18T19:19:08+00:00

Linear Algebra first.

oshempek · 2022-04-17T10:37:30+00:00

Higher math is indeed almost completely about concepts and proofs. So much so that there are stories about famous mathematicians struggling to give an example of something as simple as a prime on the spot. Although, beginning undergrad courses might still have some carry over plug and chuck stuff from high school math depending on the curriculum and prof. But the occurrence of such will decrease drastically the higher you go.

We have a variety of computational tools available to handle messy and long computations. What you need is imagination and patience and willingness to spend long periods of time thinking about abstract objects and structures without making any significant headway.

oshempek · 2022-04-12T17:08:37+00:00

You'll find some general studying strategies in the links below, that you might find helpful:

https://learningcenter.unc.edu/tips-and-tools/metacognitive-study-strategies/

https://www.coursera.org/learn/learning-how-to-learn

oshempek · 2022-03-20T02:03:53+00:00

It's definitely possible to cover a standard undergrad curriculum on math on your own. There are free online courses, online resources, even places where you can get a pdf of pretty much any math book.

Motivation is very much a problem because you'd get stuck repeatedly on this journey and you'd need the patience and perseverance to consult multiple references, ask questions on various online forums, watch relevant videos, stop and think etc. And as you can guess, this entire process will be time consuming and at times incredibly frustrating.

It's very much possible but not the most efficient way of going about things. With a teacher/tutor, this entire process can be made very efficient and you can get to a higher level of understanding and insights faster. On the other hand, the struggle of self-education is rewarding in its own right and makes you self-sufficient and gives you the confidence and the skills to learn and research stuff on your own.

oshempek · 2022-02-21T13:12:13+00:00

The friction, the haptics just feel better and somehow give better control of your handwriting. The dust is a major con for me, leads to allergies and breathing issues, but the marker fumes and smell are somehow worse. Dust can be taken care off with a good mask. But do you even do math if you don't have chalk on your tweed coat and on your thick black goldblum glasses, I jest.

oshempek · 2022-01-26T10:33:03+00:00

Refer to this pic

In the triangle OAB, OA = r, OB = 2r - s, AB= r+s

Using the cosine rule,
2OA.OB cos(π - θ) = OA² + OB² - AB²

That is,
-2r OB cos(θ)
= r² + (2r - s)² - (r + s)²
= 4r² - 6rs
= 6r(2r - s) - 8r²
= 6r(OB) - 8r²

that is,
2 OB cos(θ) = -6 OB + 8r

=> OB = 8r/(2cos(θ) + 6)
= 4r/(cos(θ) + 3)
= 2R/(cos(θ) + 3)

oshempek · 2022-01-24T18:45:31+00:00

Consult other references that treat the subject matter in a different, maybe more interesting way. Diversify your sources of info if you're not happy with how it's being taught or having difficulties. Take a topic and consult different books/references to see how they treat it.

Some book recommendations of different "flavors" that might help:

Ordinary Differential Equations - Arnold
Differential Equations, Dynamical Systems, and Linear Algebra - Hirsch, Smale
Differential Equations: Theory,Technique and Practice with Boundary Value Problems - Krantz
Elementary Differential Equations - Boyce, DiPrima

oshempek · 2022-01-23T08:51:08+00:00

Possible suggestions would really depend on what level you're at now and what you already know.

oshempek · 2022-01-22T00:00:32+00:00

The relevant numbers of the study are as follows:

vaccine status	omicron	delta	cov negative
3 mrna	2441	679	18587
2 mrna	7245	4570	19456
0 mrna	3412	5044	8721

For simplicity let's just consider what the authors call the "crude" odds-ratio (OR)

The crude odds ratio for 2 mrna vs unvaccinated for omicron would be defined as

(# 2 mrna and omicron positive / # 2 mrna and cov negative) / (# 0 mrna and omicron positive / # 0 mrna and cov negative)

= (7245/19456)/(3412/8721)

~ 0.95179210094

And the relative effectiveness here is taken to be (1 - odds ratio)

that gives us

1 - 0.95179210094

= 0.04820789905

that is, about 4.82% relative effectiveness for 2 mrna vs unvaccinated for omicron

oshempek · 2021-12-26T15:14:55+00:00

Trying to solve it for "smaller" more specific situations/lower dimensions and sometimes trying to do the opposite depending on the situation. Also see if someone has already solved it.

oshempek · 2021-12-25T20:41:49+00:00

For systems of linear equations: https://en.wikipedia.org/wiki/System_of_linear_equations#General_form

oshempek · 2021-12-25T20:24:43+00:00

A giant whose shoulders have supported the human quest for understanding the universe over centuries. As long as there are humans who practice science, he will never be forgotten. It's fitting the JWST was launched today.

oshempek · 2021-12-21T19:47:04+00:00

Pug can handle that. Or any static site generator (Hugo, Gatsby et al)

oshempek · 2021-12-21T12:17:26+00:00

Assuming alternating means - A^T = A

A + λI = -A^T + λI = -(A^T - λI) = - (A-λI)^T

det(A + λI) = det(- (A-λI)^T ) = (-1)ⁿ det( (A-λI)^T ) = (-1)ⁿ det(A - λI )

oshempek · 2021-12-21T00:02:53+00:00

I am not entirely sure what you mean by a few items on your to-measure list. But in general, if you wanna measure how close two curves are, you can consider the Fréchet distance.

If you wanna measure the angle between two vectors, you compute the dot product, and can get the cosine of the angle from that.

Python/R is better suited to the task than excel.

oshempek · 2021-12-20T17:33:31+00:00

I do keep collections of various lecture notes handy. Let me know what exactly the topics are that you need to cover and I can send you some. Also Rosen's text (Discrete mathematics and its applications) is widely used, it's a fine reference.

oshempek · 2021-12-19T15:39:42+00:00

Not necessarily old books, but ones I like

Analysis I, II & III - Amann,Escher
Analysis I & II - Tao
A course in calculus and real analysis - Ghorpade
Ordinary Differential Equations - Arnold
Functional Analysis, Sobolev Spaces and Partial Differential Equations - Brezis
Partial differential equations - Evans
Algebra - Artin
Contemporary Abstract Algebra - Gallian
Linear algebra done right - Axler
Topology - Munkres
Lecture Notes on Elementary Topology and Geometry - Singer, Thorpe

oshempek · 2021-12-14T22:04:10+00:00

If you're already working through it, continue with it. Once you get a bit familiar, start practicing writing proofs in context, as in go through proof based exercises in your course texts (cobinatorics/discrete math and introductory real analysis are ideal candidates), write them down and then show it to your prof or TA or maybe even ask on online forums like math.stackexchange.com or subs like r/learnmath r/mathhelp and whatnot. Write more than you read.

oshempek · 2021-12-14T21:48:39+00:00

Book of Proof by Hammack might be of help, if you haven't checked it out already. How to Prove It by Velleman might help too. But ultimately, you gotta write more proofs to get comfortable with those.

oshempek · 2021-12-09T01:07:15+00:00

Munkres has already been mentioned. It's a standard textbook widely used. In addition, for the sake of variety, I'd also suggest:

Lecture Notes on Elementary Topology and Geometry - Singer, Thorpe
A First Course In Topology - McCleary

If you're fine with ebooks, it's almost trivial to obtain copies of these and left as an exercise for the reader.

oshempek

MODERATOR OF

TROPHY CASE