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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89
votes
7answers
11k views

Tablet for reading textbooks and writing math by hand?

I am a math student. I'd like to find out if tablets (iPads, Galaxy Note 10.1) are worth the cost. How good are tablets for the purposes of reading textbooks as PDF and writing mathematics with a ...
43
votes
4answers
5k views

Do you prove all theorems whilst studying?

When you come across a new theorem, do you always try to prove it first before reading the proof within the text? I'm a CS undergrad with a bit of an interest in maths. I've not gone very far in my ...
42
votes
9answers
6k views

How to effectively study math?

Maybe this is too general for here, but I am having a lot of difficulty studying math. Just got out of the military and I guess I am not use to this yet but when I run into a problem I have trouble ...
163
votes
28answers
17k views

Too old to start math

I'm sorry if this question goes against the meta for posting questions - I attached all the "beware, this is a soft-question" tags I could. This is a question I've been asking myself now for some ...
59
votes
6answers
8k views

Studying for the Putnam Exam

This is a question about studying for the Putnam examination (and, secondarily, other high-difficulty proof-based math competitions like the IMO). It is not about the history of the competition, the ...
25
votes
11answers
16k views

How to start with mathematics?

I fell in love with mathematics a bit too late when I've already taken decisions regarding my future, career-wise. Now I would like to learn math on my own but I'm a bit confused as where to start. My ...
151
votes
6answers
6k views

Best Sets of Lecture Notes and Articles

Let me start by apologizing if there is another thread on math.se that subsumes this. I was updating my answer to the question here during which I made the claim that "I spend a lot of time sifting ...
61
votes
3answers
2k views

Is there a definitive guide to speaking mathematics?

Is there a definitive guide to speaking mathematics to avoid ambiguity? I'm writing a program to generate text for a variety of mathematical expressions and would like to code it so that it adheres ...
31
votes
5answers
1k views

Book/tutorial recommendations: acquiring math-oriented reading proficiency in German

I'm interested in others' suggestions/recommendations for resources to help me acquire reading proficiency (of current math literature, as well as classic math texts) in German. I realize that ...
8
votes
4answers
3k views

Preparing For University and Advanced Mathematics

I am currently a college student, computer programming, who has developed an intense passion for mathematics. Following my graduation I wish to pursue a University degree in mathematics, the September ...
12
votes
2answers
3k views

When to give up on math? [closed]

How do I know when I should give up on math? I can't pass any of my math tests no matter much I study, I have tutors, attend office hours and I still can't do better than a D on any test. Most of the ...
3
votes
0answers
174 views

Vector spaces - Multiplying by zero scalar yields zero vector

Please rate and comment. I want to improve; constructive criticism is highly appreciated. Please take style into account as well. The following proof is solely based on vector space related axioms. ...
36
votes
13answers
3k views

Is there a good “bridge” between high school math and the more advanced topics?

I love math and would like to know more of it. However, whenever I try to pick up a book on what I consider to be "advanced" mathematical topics, I often have a hard time understanding some of the ...
17
votes
5answers
6k views

How to Improve Mathematical Thinking and General Problem Solving Skills?

I'm a sophomore in university and seriously feel that I'm bad at solving mathematical and algorithmic problems (be it discrete math, calculus or just puzzles). I noticed that I'm only good at solving ...
13
votes
3answers
2k views

What are the prerequisites for learning category theory?

Is category theory worth learning for the sake of learning it? Can it be used in applied mathematics/probability? I am currently perusing Categories for the Working Mathematician by Mac Lane.
5
votes
4answers
569 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 ...
4
votes
1answer
275 views

Seeking an effective pedagogy to learning limits, derivatives, and concepts in calculus

Recently I have been spending around 15-20 hours a week learning calculus, and I have to admit that the process, while I enjoy it, is seemingly slow going. I come back to limit questions, and I can ...
3
votes
5answers
516 views

Proof of uniqueness of identity element of addition of vector space

Please rate and comment. I want to improve; constructive criticism is highly appreciated. Please take style into account as well. Proof of uniqueness of identity element of addition of vector space ...
2
votes
0answers
61 views

How to model a real-world graphical structure into a mathematical formulation?

I am trying to learn how to model programming problems in a mathematical way. I am a software engineer, but have recently been running into road blocks where I can't solve some problems very ...
1
vote
0answers
60 views

Another proof of uniqueness of identity element of addition of vector space

Please rate and comment. I want to improve; constructive criticism is highly appreciated. Please take style into account as well. The following proof is solely based on vector space axioms. Axiom ...
270
votes
29answers
38k 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 ...
44
votes
7answers
6k views

Learning Lambda Calculus

What are some good online/free resources (tutorials, guides, exercises, and the like) for learning Lambda Calculus? Specifically, I am interested in the following areas: Untyped lambda calculus ...
44
votes
19answers
4k views

Mathematical subjects you wish you learned earlier

I am learning geometric algebra, and it is incredible how much it helps me understand other branches of mathematics. I wish I had been exposed to it earlier. Additionally I feel the same way about ...
58
votes
8answers
3k views

How to make notes when learning a new topic

At the moment I'm trying to teach myself Riemannian geometry by reading some books. I take notes by hand but I find that I forget it all and worse, either lose the sheets of paper or don't want to ...
27
votes
3answers
3k views

Math Major: How to read textbooks in better style or method ? And how to select best books?

I'm a bachelor student of Math major. The question is about the better way to select and read maths text- or non-text- books, without considering the course and exam. (Because we follow the lecture ...
38
votes
7answers
8k views

I can't do math?

So after failing another math test today I have realized that I can't do math on my own. For whatever reason when I get to a test I just can't do math without extra resources. I think this is because ...
21
votes
2answers
2k views

How to think deeply in mathematics way?

Most of the time, I solve a problem by doing the following steps: 1. Look for a related theorem. 2. Look for a related formula. 3. Find a similar problem or sub-problem. 4. Try to adapt the one that I ...
11
votes
3answers
2k views

Best way to learn Algebraic Geometry?

I've been reading the book Commutative Algebra with a view towards Algebraic Geometry. I was wondering is the best way to learn algebraic geometry through commutative algebra? As the book I'm ...
10
votes
13answers
2k views

False beliefs in mathematics (conceptual errors made despite, or because of, mathematical education)

Over on mathoverflow, there is a popular CW question titled: Examples of common false beliefs in mathematics. I thought it would be nice to have a parallel question on this site to serve as a ...
8
votes
8answers
7k views

Where to go after calculus?

Ok this is a bit of an unanswerable question, but hopefully someone will answer. As I have been going through college & high school there has been a kind of "path" through which you learn math. ...
16
votes
7answers
4k views

How to study for analysis?

I am currently a first year undergraduate majoring in mathematics. I'm taking an introductory analysis course and find it very hard compared to other math couses. I know that the topics covered in the ...
16
votes
4answers
1k views

Grasping mathematics

First, I'm not trying to make this sound like a "poor-me" story. I understand fully that every decision I've made leading to this is my fault. I am genuinely looking for advice. So, I am a high ...
10
votes
4answers
595 views

How can I explain topology to my grandmother?

I was recently look at a post on tex.stackexchange about explaining $\LaTeX$ to the OP's grandmother. I was wondering, could the same thing be done for topology? Except in this case the "grandmother" ...
5
votes
2answers
471 views

Organization of the Learning Process

Sorry for off topic. I'll delete this topic immediately when community decides it's useless, however if anyone finds it's interesting, share your opinion with us. I just want to know your opinion ...
6
votes
4answers
2k views

How do you rebuild your Math skills after college?

I minored in Math in college (B.S. Software Engineering), and went through advanced Calc, Differential Equations, etc. But about 6 months after I graduated I had lost all my formulas. Now, about 5 ...
4
votes
1answer
214 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 ...
11
votes
3answers
3k views

Why is it that when proving trig identities, one must work both sides independently?

Suppose that you have to prove the trig identity: $$\frac{\sin\theta - \sin^3\theta}{\cos^2\theta}=\sin\theta$$ I have always been told that I should manipulate the left and right sides of the ...
4
votes
6answers
227 views

Help me to remember $\operatorname{cosh}^{2}(y) -\operatorname{sinh}^{2}(y)=1$, some easy verification and deduction?

I can faintly visualize some way of deducing this formula with exponential functions but forgot it. How do you remember it? Suppose you just forget whether it is plus-or-minus there, how do you find ...
3
votes
1answer
674 views

learning maths for statistics

Apologies if I have posted this in the wrong place first off. My work has taken me into a unexpectantly large amount of statistics. In order to really understand what I am doing I need to understand ...
2
votes
2answers
322 views

Studying Schedule [closed]

Currently I am studying, on my own, multivariate calculus, math statistical analysis, and physics. My question is, when you personally study multiple math and physics subjects, do you study a little ...
7
votes
2answers
100 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, ...
4
votes
3answers
105 views

Intuition - Divisibility results - If c divides some integers, then c divides any linear combination of them.

Not querying about proofs here. I don't want to memorize, thence are there intuitions or illustrations for them? As a student, how else can I remember these results? Origin - Elementary Number ...
4
votes
2answers
796 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 ...
3
votes
5answers
333 views

good resources for getting started with algorithms

I am reasonably mathematically competent and use algorithms regularly in computing, however I have started reading through 'introduction to algorithms' but find I need to understand a few more basics ...
2
votes
3answers
347 views

Should I write out stuff? [closed]

When I go through textbooks should I write out solutions to the exercises? Or is it fine if I just do it in my head? I mean either way you are still doing the problems right?
0
votes
1answer
51 views

Intuition or wisdom for stability and instability properties of locally linear system. Boyce, p513, Table 9.3.1

Our instructor requires us to memorize this table for our differential equations exam. So I wonder if anyone has some deeper intuition or observation to help with this? For example, I noticed ...
0
votes
5answers
114 views

What is the algorithm for solving an equation like this one?

The solutions of the equation : $\sqrt{x+2\sqrt{x-1}} + \sqrt{x-2 \sqrt{x-1}} = 2$ are: A) $x=1$; B) $x=2$; C) $x\in [1,2]$; D) $x\in \begin{bmatrix} \frac{3}{2},2 \end{bmatrix}$; E) ...