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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4
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4answers
2k views

Why is “All horses have the same color” considered a false proof by induction? [duplicate]

Upon reading of All horses have the same color "paradox", I began to wonder a couple of things. First of all, to me the inductive step seems flawed. Just because I have $n$ white horses, does not ...
1
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1answer
133 views

In balancing effort and advancement in what concerns learning

What's new besides showing modern advancements in modern mathematics as well as eloquently written notes also contains some good advice to young people like me in this room (career advice:!). in ...
3
votes
0answers
53 views

Advice on methods to capture lecture board and add notes [closed]

I am looking for a method to save the lecture materials, and examples without hand copying from the boards during the lectures. Unfortunately some courses don't have the material available, and ...
1
vote
2answers
131 views

Memorising lots of maths theorems/lemmas

In a few weeks I'll have my summer exams in a Senior Freshman Mathematics course. Two of my modules have a huge number of theorems, lemmas and definitions - over 200 definitions and 250 proofs by my ...
0
votes
1answer
120 views

What are the prerequisites for learning abstract algebra?

Well, I want to learn abstract algebra. So, I get across this http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra. But I'm not sure whether I've understanding of prerequisites ...
65
votes
11answers
7k views

How do people who study intensely abstract mathematics “imagine” or understand the concepts they are studying or being taught? [closed]

This question is probably to the actual people who study such mathematics, rather than any "third-party". I haven't studied any such mathematics, but I can imagine that some (probably most of it) of ...
1
vote
3answers
39 views

Logs in equations

I am working on an excel project and had a few questions. I need to solve $\log(x)/\log(2)=-0.145509439$. I already know the answer, which is $0.90406$, but I do not know how to solve the equation.
0
votes
2answers
81 views

What mathematics should I study to understand Neural Nets / Machine Learning?

I am strongly fascinated by neural nets, and perhaps other forms of machine learning. There are so many (potential) applications: teaching a robot with shaft encoders to drive along different ...
0
votes
1answer
153 views

How to re-learn math: books or websites?

To re-learn math, both websites and books provide visual content (text and some of them shows illustrations). So are websites an alternative to books (content quality-wise)? My goal is to re-learn ...
5
votes
1answer
567 views

Most efficient way to learn mathematics [closed]

So there's a lot of advice on how to learn mathematics most efficiently, and it mostly revolves around doing problems, asking questions, and considering all possible generalizations. However, I was ...
0
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1answer
105 views

what is required for a person to do well on imo

What kind of skill is required to solve IMO or Putnam sort of problems. Does one have to be a genius or just learn some tricks.
2
votes
2answers
135 views

Is there a math website to study math from a mathematician point of view (ie proof oriented?)

I´m a student of the University of Puebla, Mexico, and I think that we lack of exigence there so I want to study math on internet to improve my education. I have already looked sites like edX, but I ...
2
votes
1answer
64 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
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0answers
31 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 ...
56
votes
13answers
5k 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
3answers
57 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
193 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
104 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
103 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 ...
42
votes
2answers
826 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 ...
11
votes
2answers
629 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, ...
11
votes
1answer
182 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 ...
15
votes
2answers
260 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
186 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 ...
3
votes
1answer
76 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
144 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 ...
2
votes
2answers
221 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. ...
1
vote
1answer
96 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
75 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 ...
3
votes
2answers
68 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
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0answers
35 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
348 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
378 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 ...
1
vote
1answer
37 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
135 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
80 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 ...
3
votes
1answer
118 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
103 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 ...
1
vote
1answer
3k 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
91 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
65 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
142 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. ...
16
votes
1answer
463 views

IMO programs of different nations?

We in Albania have a good team in the IMO, and this year I will probably be part of it. Since Albania does not have a public training programme, I have to consult the training programmes of other ...
0
votes
2answers
2k 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
752 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. ...
5
votes
1answer
219 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
93 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
41 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
140 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 ...
4
votes
0answers
703 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 ...