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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3
votes
1answer
131 views

Learning to understand proofs faster?

There are many books, written by highly decorated academics, which feature proofs that I can hardly comprehend in an acceptable amount of time. Roughly each week, it happens that I find myself having ...
1
vote
0answers
44 views

Any quick mental mathematics techniques?

I recently came across a very easy way to find the squares of fairly large numbers ($1$-$100$, but could be extended indefinitely), by using a simple formula. It does require you to know the square ...
1
vote
1answer
68 views

How to get better at inequality problems?

I really like inequality problems, but I've found that I have severe difficulties with ones that should be simple. I can prove something simple like this For positive $a, b, c$ with $a + b + c = 6$ ...
0
votes
1answer
60 views

Nature of Points and Lines in Euclidean Geometry

It may be true that very few middle school student can grasp the meaning of lines and points in Euclidean geometry prior to a direct instruction. For example, it's possible that such a conversation ...
0
votes
1answer
69 views

TV Shows for Popularization of Mathematics

There are many TV shows and programs which are dedicated to popularization and of physics, biology, etc. I'm looking for such media about mathematics. Thanks.
11
votes
2answers
139 views

Dealing with Fatigue [closed]

If all goes well, I am on the route to start a PhD in Mathematics next Fall. I worked very hard my undergrad years with little or no break and no travels. It is something I really regret. Now I have ...
5
votes
1answer
103 views

Software for basic math notes at 5th to 10th grade level (10 to 15 years old)

So I've looked around, here and otherwise, but sadly can't seem to find quite what I'm looking for. I don't know if it even exists, I figured it was worth trying to ask, though. I've found plenty of ...
1
vote
1answer
40 views

Math Mindeset: Historical Learning vs Generality of Concepts

I started math four months ago with modules like measure theory and topology. It was unavoidable to notice how many concepts are more general than what I thought before. For example the ...
6
votes
4answers
840 views

Teaching irrational numbers?

I'm interested in teaching the irrational numbers to high-school students, and I need your ideas on how to do in an 'optimal' and innovative way. And my question is: What should the teacher know ...
1
vote
0answers
54 views

Studies on how the wording employed on the explanation of mathematical concepts helps students to learn?

I remember that I had to learn division in my childhood, I could handle all the other mathematical concepts that were presented until then but division was a real pain to learn, somehow the idea of ...
3
votes
1answer
228 views

Math Shock in graduate program

People call it Culture shock but I call it Math Shock... let me explain my Problem... First I am graduate student in a good university in USA ( I get scholarship from my country). Before I lived in ...
-1
votes
1answer
45 views

Learning way and Resource for Complete math Subject. [closed]

I want to learn [self learning] Mathematics from basic.What is the order [like 1) arithmetic,2) Geometry,Etc..] to learn the maths? and what is the best resource to that particular subject?
1
vote
1answer
89 views

Can I go “out of the order” of learning math?

So I want to clear something up before I go any further with calculus. Is it wrong to actually skip ahead in math? You see, I'm in 8th grade taking algebra 1 honors(Though I personally think I should ...
7
votes
2answers
99 views

Information on crucial results concealed as exercises or neglected in a textbook

First, where can students find lists, information, or resources on the crucial results, inequalities, theorems, etc... which a textbook might not explictly feature or even bring up at all? Second, ...
1
vote
0answers
15 views

Looking for intuition for picking strategy on how many pages to flip

This question is going to sound more CS'y because that is my background. It also might be a bit vague but that is because I am not sure what the right thought process is in how to formulate it. I ...
5
votes
0answers
159 views

Study group for working through Spivak/Wilson [closed]

I'm planning on working through Spivak's Calculus or Wilson's "Introduction to Graph Theory" and was wondering if anyone here might be interested in joining a study group for it. There's no ...
2
votes
2answers
210 views

Ring theory : Completely lost and overwhelmed

Over the past 3( 9 sessions) weeks my professor has covered entire Part 3 - Rings from Gallian's Abstract Algebra which includes Introduction to Rings Motivation and Definition Examples of ...
3
votes
3answers
118 views

Question on Rudin sequences?

In baby Rudin, Rudin shows that $$\lim_{n \to \infty}\sqrt[n]{p} = 1.$$ In the proof of limit he tries to prove that the limit is $1$. So he takes $x_n = \sqrt[n]{p} - 1$. I have never noticed this ...
2
votes
0answers
134 views

Dynamic Geometry Software for Straight-edge and Compass Constructions

Geogebra is a very good dynamic geometry software. It has so many default tools, e.g. parallel line, angle bisector, tangent to the circle, inscribed and circumscribed circles, etc. But I want the ...
3
votes
1answer
87 views

How does one learn math from square one? [closed]

Ok, I know this is vague, but assume I never really had a good working knowledge of math in any area. I want to pursue X related work, which calls for X, Z, E, A, L, C, Q, etc. math. I realize that ...
1
vote
1answer
68 views

Suggestions for complicated math concepts that a child can understand

My son really loves math (so do both his parents, for that matter), and does well at it in school. I will give him math puzzles or tricks now & again, as well as introducing him to Khan Academy ...
8
votes
2answers
214 views

Advice in Bachelor Degree

First of all, I´m very sorry for my bad english, especially writing. Ok, for differents problems i´m studing a Bachelor degree in Mathematics. These degree is online. Now, the problem with my school ...
3
votes
1answer
91 views

Is there a math news website or publication (for mathematicians)?

I'm an undergraduate math and physics major aiming to pursue a Ph.D. in either pure math or theoretical physics. I don't read traditional newspaper or news websites, since in my opinion they are ...
4
votes
2answers
647 views

How to study abstract algebra

I am taking Abstract Algebra course at the university. We are doing chapters 1-20 from Gallian's abstract algebra text book. I am just doing assigned homework everyweek ( About 5 questions from each ...
2
votes
3answers
49 views

Commutativity or Distributivity - Which One to Use to DEFINE Multiplication of Negative Numbers?

It's easy to calculate $3 \times (-4)$, using the meaning of multiplication: $3 \times (-4)=(-4)+(-4)+(-4)=-12$. But it's not the case about $(-4)\times 3$! To DEFINE $(-4)\times 3$ we can choose ...
6
votes
1answer
176 views

Is the computer changing the way we teach and learn math in schools?

Back in school, what I got taught during school was labeled 'math', but it was actually 'rote arithmetics.' This seems to also be the case of many other people. Some came to hate it and never came ...
3
votes
1answer
109 views

New ways to light the fire again

Recently I've been studying a lot of analytic geometry and this subject made my motivation drop. The thing is, the courses aren't stopping and I'm beginning to lose the passion I had before. I need ...
9
votes
2answers
919 views

Learning Abstract Algebra for a graduate degree

I would like to do a graduate degree in mathematics, and I have a full year before I will be able to do so (for personal reasons). I mainly have my weekends available to study. I am interested in ...
14
votes
2answers
463 views

How to do math and help people

I am currently an junior math and statistics student at the University of Florida. For my whole life I have really enjoyed math and really do find a calling in mathematics. Math classes are the only ...
1
vote
1answer
487 views

Best way to learn from THEOREM-PROOF format?

I've always loved the theorem-proof format in textbooks, e.g. Hardy and Wright's Introduction to the theory of numbers. However, the problem is that I can't remember anything I read in this format ...
6
votes
2answers
304 views

Which books to study category theory?

I am an amateur math researcher in the field of general topology. I've set the purpose to learn enough category theory for my research. After reading Steve Awodey, "Category Theory", 2010, is it ...
1
vote
1answer
214 views

What is the order of math topics that people learn math in?

You know how they say to learn algebra first, then learn geometry, then trig, then calculus...etc? So after that, is there an order of what to learn next? If so, I'd like to know what comes after ...
2
votes
1answer
178 views

Math writing solutions

I will begin to learn in the university next month and I would like to know what is the best way to write math except from handwriting? I am not sure if to use a mathematical software, digital pen or ...
5
votes
6answers
171 views

When learning maths, should I review past topics?

So I've been learning maths from online video lectures and books for some time now and, as is probably quite natural, I have forgotten some of the stuff I've already read through. That'd be mostly ...
0
votes
1answer
57 views

relevant pure math for optimization

I'm interested in optimization generally. I don't know enough to break it down to sub-fields that I would work on. Probability and statistics seem relevant. What about calculus of ...
3
votes
0answers
118 views

Where to start?

I want to learn Mathematics but I don't know where to start. Sometimes I really get frustrated as I am a Software Engineering graduate (currently working) and I feel like I don't know anything about ...
7
votes
1answer
138 views

Is it a bad idea to study modern algebraic geometry without having any background in smooth manifolds?

I have a chance to take a course in algebraic geometry developed in the scheme theoretic setting and am considering my options. I have taken graduate courses in general and commutative algebra and ...
0
votes
3answers
190 views

Recommended math background for game theory

I recently got interested in some game theory applications to poker. I want to try some of them out programmatically, but a lot of the math is a bit confusing. I learn math on my own fairly quick and ...
2
votes
2answers
952 views

MOOCs for college-level discrete math?

Specifically I am looking for short lectures (and quizzes) on specific topics. (like Khan Academy offers) Topics I am learning about include; Intro logic-theory + set-theory Notation, negation, ...
4
votes
2answers
196 views

Training to actively learn, think and use mathematics studied and construct everything on ones own

Someone said this: "Memorizing the entire Swedish dictionary will never make you mastering Swedish. Same to Maths, the only way is to actively think & use basics you absorbed so far to practice ...
4
votes
4answers
138 views

Resources to help an 8yo struggling with math

Friends of mine asked me for suggestion for one of their children (age 8) who had bad scores at the local Star test (the family is based in California). Both parents work, so they have also limited ...
4
votes
2answers
172 views

How to determine the big questions in a field of mathematics?

During my self-study (and soon to continue at a university) of mathematics, one thing I have been interested in is how to to effectively learn the material. An answer to a question provided by ...
1
vote
0answers
69 views

Recommend me math textbooks from prealgebra to undergrad level. [duplicate]

So I've been reading through math.stack exchange and physics forums and r/learn math to find a comprehensive list of math textbooks to learn math from the ground up. I'm more wanting to do so to ...
5
votes
4answers
535 views

Books for a beginner

I am a student of 11th grade and i have completed the syallabus of both 11th and 12th grade maths with complete understanding and it was possible coz of the love for this subject that i have. I don't ...
3
votes
1answer
101 views

About having everything well under control [closed]

When I started doing maths I "rediscovered" some elemental things and listed them on a notebook. All things I learned were in there, like Pythagorean theorem, sine and cosine definitions, some ...
4
votes
5answers
330 views

How important is a teacher / tutor?

I am doing fine in my classes and enjoy math. That is not the issue. During my spare time, I am doing more advanced stuff than my class is currently doing. My question is though, would I benefit more ...
264
votes
29answers
37k views

My sister absolutely refuses to learn math [closed]

My 13-year-old sister has a problem which, given the way math is currently taught, I doubt is anything but all too common. She has a low grade in her math course and only ever attempts to memorize ...
1
vote
2answers
240 views

Study regimen for discrete mathematics? - Lack high-school maths…

I have just gotten into college, and will be studying mathematics from next semester. (this course) Unfortunately I did not study mathematics for the last 2-3 years of high-school mathematics. What ...
6
votes
0answers
120 views

How much of the content from past classes do people remember? [closed]

I'm currently a third year math student and I am preparing to take my GRE subject test. As I study for the test I feel as if I have forgotten much of the content from classes that I've taken in the ...
0
votes
1answer
81 views

Problem with lowercase versus uppercase.

I often attack problems on two levels, a verbal level and a visual level. At a visual level, I try to imagine how everything is related - I arrange the ingredients of the problem into a two (or ...