Questions about the process of learning mathematics, both inside and outside a formal environment, including learning strategies, recommendations for learning particular subjects, and studying habits.

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2
votes
2answers
34 views

Staying focused on proofs. Occilation of feelings towards Math [on hold]

I enjoy Mathematics and I am doing a degree in it. I am in my third year. I find that some parts of my texts are really boring, others extremely fun and the occasional proof is painful to stay ...
2
votes
0answers
20 views

Learning from Alternative Sources

I have a very general question about people's experiences with learning math. I can think of a couple of times where I had the following situation. I was seeking to learning about topic A. However, ...
1
vote
0answers
18 views

Is it more useful to study lots of methods/theorems or work with details?

Suppose one has to learn a new subject on book that contains hundreds of pages and hundreds of problems. Is it more useful to learn book by reading it and skipping those parts I don't understand and ...
14
votes
5answers
605 views

OK at Applied Math but Fail Pure Math?

Summary. Name Applied Math as AM, and Pure Math as PM. I want to succeed in PM but what am I doing wrongly? Am I too dumb, or is my brain unfit, for PM? Should I just stick to AM? Here, I read the ...
0
votes
0answers
9 views

Concept Learning algorithm in Artificial Intelligence

Im going through Machine Learning in Artificial intelligence(Artificial Intelligence by George F Luger-Page 398) . Im going through the candidate elimination algorithm. There is this specific to ...
48
votes
13answers
3k views

How to stop forgetting proofs - for a first course in Real Analysis?

I am taking my first course in analysis. I like the subject. I study it almost on a daily basis. I try to prove theorems on my own without even looking at the hints. If I really get stuck I just read ...
0
votes
1answer
46 views

How to find a sequence?

Is this a serie or a sequence (or both), and how can be found an equation for such? $3$ - $6$ - $15$ - $45$ - $153$ - $561$ - $2145$
0
votes
3answers
53 views

Sum with three notations around it.

Have seen the below notation (How to calculate number of triangles and points after dividing a triangle n times?) and need to break it down into plain english so to speak. This just so I can catch up. ...
1
vote
1answer
73 views

How to calculate number of triangles and points after dividing a triangle n times?

When having a triangle and dividing it n times, how to get the number of triangles and points? ...
0
votes
1answer
73 views

Which topology textbook has the greatest amount of ancillary support available on the Internet?

I'm considering to begin upon the study of topology and am wondering which book would the best option. I've even started reading Munkres and G. F. Simmons, but the problem is neither book has any ...
2
votes
1answer
74 views

Learning concepts in mathematics

Apologies for the soft question, but I was wondering whether it is a good idea, in mathematics, to learn/study things simply for the sake of studying it. A very good example comes from category ...
0
votes
0answers
24 views

Fractal Generation Project: How to Continue after L-Systems?

Three months ago, we defined a programming project for some gifted middle school students: Writing code to generate simple fractals. Two of them have finished writing Pascal programs already! The ...
38
votes
2answers
621 views

Effective Research Notes

Note-taking for research is vital to your success as a mathematician. As I look back at some of my handwritten notes, I realized how poor they were. I had thought to myself, "What happened?" I was ...
0
votes
0answers
58 views

AoPS Intermediate Algebra vs. Higher Algebra by Hall and Knight? And some more questions about learning math.

Ok. I'm learning algebra at the level of AoPS algebra 2, and I want to quickly progress through math. Allow me to explain the situation. I am highly interested in artificial intelligence/computer ...
7
votes
2answers
362 views

How can I pick up analysis quickly?

I have a 2-3 week recess from university for winter break. In this time, I would like to learn analysis, starting with Walter Rudin's Principles of Mathematical Analysis, and then, if at all possible, ...
7
votes
0answers
106 views

How to listen math lectures?

Many times, the lectures goes beyond the head and not easy to follow, (at least with me),mainly in the workshop/conferences, though the audience are eager to learn something from it. Also, most of ...
13
votes
2answers
171 views

Strategies to study apart from “books cover to cover.”

I have never really liked reading a book from cover to cover (because I usually get bored). Most of what I've learned so far has been picked up from forums like this one, or occasional reading from ...
2
votes
4answers
74 views

Research Projects for 7th Grade Students

I'm going to define some math research projects for 7th grade students. The projects can be both purely mathematical and interdisciplinary. By the way, the students can write simple Pascal codes. I ...
2
votes
1answer
41 views

Why is it so difficult to obtain the spectral properties related to infinite matrices, especially when they are not symmetric?

I believe most of the spectral theory is revolving around the bounded self-adjoint linear operators being analogous to real symmetric infinite matrices. Whereas, there are cases when the matrices are ...
6
votes
1answer
119 views

How to get university level Mathematics education on my own?

As far as Mathematics go, I have a highschool level education. I wonder how I could learn more about Mathematics to be on the level of those who had Mathematics level education at a university. Is ...
1
vote
2answers
93 views

How to learn math? [closed]

I am 19 years old and I'm computer programmer and Software Engendering college Student, And I am smart (mean: I am not stupid) and know programing better than other, I think math is like programming. ...
0
votes
0answers
41 views

Where can I get detailed and comprehensive notes of a functional analysis course taught using the book by Erwine Kryszeg?

Where on the Internet can I find detailed and comprehensive lecture notes of an elementary functional analysis course taught using the book Introductory Functional Analysis with Applications by Erwine ...
1
vote
0answers
30 views

Is it more useful to study lot or accurately?

I would like to have a job in mathematics. Is it more useful to study many courses with average/little better than average grades or less courses with better/(almost) maximal grades to have a job?
2
votes
0answers
68 views

From newbie to professional, the path.

I left school long time ago because of family stuffs and with this I left many subjects behind and since then I try to find something to do and when I discovered the computer and what I can do with it ...
1
vote
1answer
85 views

In war with exercise, any future for me?

I love theory with theorems, definitions & proofs, but i don't like exercise, I need more context around it. Is there a different way of practicing theory except given exercises, maybe some ...
2
votes
1answer
56 views

How to organize myself around calculus?

Calculus is the biggest topic i have encounter in math. Book that i am using is great, clear as can be, but so many definitions and theorems. I will like to have all most crucial def/thr as ...
0
votes
0answers
31 views

Why does $\int f(x)(y-r(x))\;dP(y,x) = 0$?

My question is, why does: $$\int f(x)(y-r(x))\;dP(y,x) = 0,$$ where $r(x) = \int y \;dP(y|x)$ and $P$ is a probability distribution function. It was also given (in my book) that: $$\int ...
3
votes
2answers
50 views

Simple everyday math

I am looking for a book that contains (instead of crossword puzzles) math problems beginning with simple addition, subtraction, multiplication and division and progresses to more difficult area ...
0
votes
0answers
18 views

Looking for Comprehensive Integration Techniques Tutorial

I am trying to improve my skills and I usually learn best by attempting problems just barely above my skill level then reading the solution. Does anyone know where I can find structured integration ...
4
votes
1answer
231 views

Is this study plan sufficiently general, or overly specialized? [closed]

My current study plan is in order below. I will be completing these textbooks in this order one at a time. I have been told that I don't have textbooks in my plan that approach topology in a general ...
20
votes
2answers
259 views

How can a beginner researcher or Ph.D. student efficiently and effectively learn new concepts while staying motivated?

I hope this question is appropriate for MSE. The situation is that someone is reading a book (e.g. a monograph), possibly helpful in his/her research, and the content is sufficiently extensive or ...
0
votes
1answer
28 views

How can i learn when to use which multiplication rule: Probability

Hey guys im studying for a math exam and was wondering if anyone has some easy techniques to remember in what kind of scenario to use these equations. These are I believe called multiplication rules. ...
3
votes
1answer
59 views

Is probability theory useful in electrical engineering

I have a two week holiday after finishing this semester and I was hoping to study something. Ideally, I would like to study something that I can benefit from in any upcoming courses I take. I'm ...
2
votes
0answers
53 views

Can any one recommend a way to “quickly” learn a subject?

I would love to read a well written book on a subject - provided that I have the time. But sometimes we do not need to become experts on a particular field but still need the basics. For example, a ...
2
votes
1answer
84 views

How can I learn to recognize the obvious questions?

I have heard and seen several references to "obvious questions", "obvious axioms" and other "obvious" things (I am not referring to obvious results!). Now, in a seminar I am taking, at the end of each ...
4
votes
1answer
73 views

I love maths, but my school is limited in its teachings. [closed]

I'm not sure how well this question will be received but, I feel there is no harm in asking. I'm 17 soon to be 18. I was in my applied maths course, but not anymore, not due to difficulty, but I can ...
0
votes
1answer
377 views

James R. Munkres' TOPOLOGY, 2nd edition: How to check my work?

I'm trying to learn, or revise, some topology from James R. Munkres' TOPOLOGY, 2nd edition. I'm working alone; that is, I'm self-learning. It is quite fun. But the problem is how do I check if I've ...
1
vote
0answers
81 views

How to deal with a lack of ability to apply ideas in math?

I am currently studying Theoretical Computer Science, but as a Computer Science student who does not have a formal background in mathematics, past A Level (High School), I find that the ideas I learn ...
0
votes
2answers
57 views

Optimizing a box

I'm learning the use of derivatives and I have found a problem: Supposing we want to build a box of $4000\, \textrm{cm}^3$ of volume without top and a square base. Which are the measures so we ...
1
vote
2answers
54 views

Is it possible to gain intuition into these trig compound angle formulas - and in general, final year high school math?

Does anyone have any insight into the trig sum and difference formulas? The formulas in themselves are very elegant, but I don't really like the proofs that have been given, even the geometric proofs. ...
13
votes
0answers
305 views

IMO programs of different nations?

We have a good team in the IMO, and this year I can, and probably will, be part of it. Since we as a country do not have a public training programme, I have to consult the training programms of ...
0
votes
2answers
68 views

Find the equation of the parabola given the tangent to a point and another point.

I have a problem with derivatives, I've been trying to solve but I was not able to do it. A parabola is tangent to the line $3x-y+6 = 0$ in the point $(0,6)$ and goes through the point $(1,0)$. ...
0
votes
3answers
119 views

I want to study higher mathematics. Where do I start?

Since last year, I've been interested in higher mathematics and don't really know where to start and don't know what knowledge I still need to obtain, before being able to understand the concepts. ...
0
votes
0answers
24 views

Books or notes focusing more on the intersection between manifolds and topology?

I try to prepare for the qualify exams, and find that the problems of geometry part are quite interesting. In the past, I just learned some elementary things on manifolds and algebraic topology ...
4
votes
0answers
64 views

How can I retain the mathematics that I've supposedly learnt?

So my question simply is "What is the best method to make sure you retain what you have learnt?" Okay so I've tried learning mathematics up to where I should be at in the past. Every time though I ...
4
votes
0answers
75 views

How to select good exercises?

I'm studying on Rudin "Principles of of Mathematical Analysis" which I begin to find as a good and complete reference. I wonder how many exercises shall I do at the end of each chapter ? In case of ...
0
votes
3answers
36 views

Is this derivative correct?

I'm newbie at Calculus, so I'm doing some exercises of derivates, I know by the formula: $f(x) = \sqrt u$ $\frac {df(x)}{dx} = \frac{u'}{2 \sqrt u}$ that the derivate of the next function is: ...
1
vote
2answers
81 views

Path to 3d Mathematics programming, where to start?

This might read like duplicate of this question https://math.stackexchange.com/search?q=where+to+start However since that one wasn't answered, and I have a more specific problem in regards to ...
2
votes
0answers
80 views

How to Read Michael Artin's Algebra

I am currently reading Algebra by Michael Artin (for self study). I'm finding the book pretty interesting, but I'm still not sure how I should study the book. For example, should I try to prove every ...
5
votes
1answer
126 views

How important is the “prestige” of your university for undergraduate mathematics?

I go to a university in Canada. It's not really considered a top university (it is one of the best universities in the province but is ranked really low nationally). I study mathematics here and ...