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.

learn more… | top users | synonyms

0
votes
1answer
61 views

Severe problems with math undestanding

Recently (although still in high school) I've been at university, more precisely at information science engineering as apprenticeship. I want to become an operating system programmer but I severely ...
2
votes
0answers
33 views

How should I learn the Mathematical Proofs?

S.E advisers, What is the most efficient way to learn the basic proof methodologies, which are essential for studying the mathematical analysis and number theory? I am very interested in studying ...
1
vote
1answer
37 views

The Monty Hall problem - convincing a skeptic

I have lost count of the number of times that I have been debating the solution of the Monty Hall problem with someone. Recently I had a long conversation with a colleague, who didn't seem to buy ...
2
votes
2answers
58 views

Explaining intersections to a 6th grader

$A=\{1,2,3,4,5\}$ $B=\emptyset$ How to explain to a learner from 6th grade the result for $A \cap B$ ? For a 6th grade student, it could be difficult to understand why the result is $\emptyset$. ...
0
votes
1answer
20 views

graph theory, economics and learning prerequisites

I'm a undergraduate student of economics and I"d like to know which classes I have to take to get in in graph theory with the purpose to apply it to economic theory. Undergraduate math is sufficient ...
-1
votes
0answers
18 views

Is the usage of subscript for describing multiple variables ambiguous?

Suppose we have variables $x_1, x_2, \ldots, x_n$. For brevity, I often declare such variables as $x_{1,2,\ldots,n}$, but I've been wondering, whether this syntax is ambiguous with respect to tensors ...
0
votes
0answers
16 views

Sample complexity of coin bias problem

I am reading a paper involving learning in Multi-armed bandit case (its okay if you don't know what that is. Just trying to give context here.) To give sample complexity lower bound, they reduce their ...
0
votes
1answer
66 views

Math without notation

Are there any researchers that try to develop learning materials to teach the core mathematics knowledge without using notation (and instead just plain English -- preferably without images)?
10
votes
0answers
127 views

Is it a good approach to heavily depend on visualization to learn math?

I am a third year undergraduate and I am a beginner on these "real mathematics" (no pun intended). Before contacting the "real math", my math level should be considered to be "good", although I was ...
2
votes
0answers
63 views

How to learn problem solving strategy for Measure Theory?

I have taken both graduate level Algebra and Measure theory courses but found the latter much more difficult for me. I have put a lot effort on learning it by reading a few reference books and ...
2
votes
1answer
44 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
votes
1answer
44 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 ...
34
votes
10answers
2k views

How do mathematicians find formulas? [closed]

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
44 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
votes
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
votes
2answers
127 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
votes
1answer
112 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: ...
12
votes
4answers
1k 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
105 views

Being a good listener in math [on hold]

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
votes
1answer
110 views

How to stay productive while you are studying math? [closed]

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
67 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. ...
4
votes
1answer
115 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
797 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
3k 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
58 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
112 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
39 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
82 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
69 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 ...
58
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
38 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
56 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
121 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
15 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
192 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
votes
1answer
69 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
112 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
47 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
votes
0answers
57 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 ...
52
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
3answers
56 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
85 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
86 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
86 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 ...
41
votes
2answers
703 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 ...
8
votes
2answers
429 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, ...
9
votes
1answer
147 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
198 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 ...