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
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1answer
43 views

Matrix multiplication memorisation

So I'm writing an exam about matrices in a few weeks time, and I'd like to know if anybody has any tips about multiplying matrices.
0
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1answer
30 views

Requirements for learning and understanding trigonometry?

Im reaching a point in programing where I need to create basic shapes which I simply cant since my math skills are very bad. After finding out that the skills required are trigonometry I read a few ...
31
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10answers
2k views

How do mathematicians find formulas?

How do mathematicians find formulas? For instance, the area of a triangle is $$\mathrm{area}=\frac{\mathrm{base}\times \mathrm{height}}{2}.\tag{1}$$ When I study maths, the book I am using tells ...
1
vote
2answers
38 views

Representative Pedagogical Examples of Groups, Real Functions, Modules, etc.

In the preface of Munkres's Topology, he writes, Fortunately, one does not need too many counterexamples for a first course; there is a fairly short list that will suffice for most purposes. Let ...
0
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0answers
26 views

Does Thompson's Calculus hit all the essentials needed?

I found out in my preliminary research for my undergraduate degree that I need a bit of undergraduate-level mathematics for my topic at the very minimum to start with, up to ODEs. So I found a ...
8
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2answers
98 views

Learning modern differential geometry before curves and surfaces

What might one miss by learning modern differential geometry without first learning about curves and surfaces? I'm currently reading this book on differential geometry which starts with manifolds and ...
8
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1answer
71 views

Importance of Exercises in Mathematics for Self-Studying

I am a high school student wanting to major in Mathematics in the future. I started to like Mathematics recently, starting a year ago and I watched some interesting math videos on YouTube for fun (ex: ...
11
votes
4answers
2k views

Is it necessary for one to understand analysis?

Is it necessary for one to understand analysis in order to pursue a career in mathematics? Basically, I am very weak at analysis. But the problem is that most of the topics listed in the syllabus ...
5
votes
1answer
96 views

Being a good listener in math

I'm reasonably good at learning from textbooks, but I often find that when people explain mathematical ideas to me in person I don't understand what they are saying. I sense that there is actually a ...
11
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1answer
99 views

How to stay productive while you are studying math?

Not sure that this question is a good fit for this site, but I will try. When I am working through a chapter of a mathematical book first two hours are normally very productive (easily remember ...
2
votes
1answer
52 views

Mathematics Learning Process: Plan of Attack [closed]

I have been intrested in a lot of topics concerning Mathematics for the past few months: I ordered some textbooks from Germany which cover essential Algebra and Geometry, and they are excellent. ...
0
votes
1answer
36 views

Knowing how to draw Venn Diagrams to post question effectively [closed]

I want to draw Venn Diagrams to illustrate something in a question section using $\rm\LaTeX$, but I cannot do this. Can anyone suggest a tool for drawing Venn Diagrams?
4
votes
2answers
97 views

Quality of Videos Lectures and Lectures vs Textbooks

I am a student trying to learn different subjects by watching video lectures and reading on my own time. I was wondering if the lectures from ICTP and nptelhrd are a great use of my time. I tried ICTP ...
9
votes
4answers
787 views

Forgotten old results break my motivation

I'll begin graduate school next year and I am very impatient to learn new things such as theories, ways of thinking and so on (I enjoyed reading about category theory on my own and I find Galois ...
13
votes
13answers
4k views

How to explain the formula for the sum of a geometric series without calculus?

How to explain to a middle-school student the notion of a geometric series without any calculus (i.e. limits)? For example I want to convince my student that $$1 + \frac{1}{4} + \frac{1}{4^2} + ...
2
votes
0answers
51 views

What is the best way to master my algebra skills without taking an algebra class?

I was in advanced math my entire life. I got through all the math I needed for my original degree. 8 years later here I am changing degrees and I need more math. I just took calculus I and I passed ...
4
votes
4answers
1k 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
vote
1answer
107 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
37 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
73 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
64 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 ...
57
votes
11answers
4k 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
37 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
50 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
111 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 ...
0
votes
0answers
12 views

Pre-requisites for learning multivariable calculus

I've been interested in learning about multivariable calculus now. What topics do you suggest that I familiarise myself with before I dive into it? Also if possible, can you provide any recommended ...
6
votes
0answers
162 views

Most efficient way to learn mathematics

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
63 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
106 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
41 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
22 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 ...
0
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0answers
33 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 ...
51
votes
13answers
4k 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
55 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
80 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
84 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
84 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 ...
40
votes
2answers
688 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
1answer
104 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 ...
8
votes
2answers
402 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, ...
8
votes
1answer
137 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 ...
14
votes
2answers
188 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
103 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
46 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
124 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
124 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
89 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
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
60 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
52 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 ...