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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40
votes
7answers
11k 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 ...
23
votes
2answers
2k views

How to think deeply in mathematics way? [closed]

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 ...
15
votes
3answers
3k 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 ...
20
votes
4answers
2k views

Perspectives on Riemann Surfaces

So, I have come to a somewhat impasse concerning my class selection for next term, and I have exhausted all the 'biased' sources. So, I was wondering if anyone in this fantastic mathematical community ...
26
votes
2answers
1k views

Efficient ways to read and learn a new topic [closed]

I started reading the book "Topology without tears" by Sidney A Morris and lecture notes on "Elementary Number Theory" by WWL.Chen. To get the maximum out of the book and understand the material ...
11
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 ...
23
votes
8answers
1k views

Looking to attain fluency in mathematics, not academic mastery

I'm a business/international relations person and a lot of my job is flying around. I have had a lot of downtime recently, and couldn't find a sustainable hobby to fill in that time. Until I found ...
6
votes
5answers
1k views

Materials for self-study (problems and answers)

I'm hoping to self-study Geometry, Algebra, Calculus, Vector Calculus, Linear Algebra, Probability and Statistics, and other intermediate maths. I've found the best way for me to learn is to work on ...
15
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 ...
11
votes
4answers
675 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" ...
10
votes
8answers
10k 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. ...
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, ...
10
votes
5answers
2k views

Advice for benefits to directly use analysis textbook to replace calculus

Main purpose: For self-learning performance, neither for exam nor degree courses. Calculus textbook using now[1]: Calculus I, Weinstein&Marsden, UTM, Springer Question Description: I've been ...
8
votes
5answers
3k views

How do you rebuild your Math skills after college? [closed]

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 ...
6
votes
2answers
607 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 ...
11
votes
0answers
203 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 ...
9
votes
2answers
3k views

How do I get good at Math?

How do I get good at math? I'm a freshman in college, and I've always done OK in math. I never had any good teachers in High school, and I always have done the bare minimum. Over the course of this ...
3
votes
5answers
808 views

Preparing for first year CS

I'm in Italian guy almost in my 30. I have a regular job as a programmer. When in school I've never been much interested nor good in math and even at the university I've been studying languages, hence ...
6
votes
4answers
1k views

Self-learning Mathematics

My question is very elementary, but I hope that you will endure it. I am currently in a CS Master's program and I notice that my skills in mathematics are lacking. My calculus course was 10 years ...
5
votes
3answers
480 views

Map of Mathematical Logic [closed]

My undergraduate University does not offer advanced courses on logic, I know truth tables, Boolean algebra, propositional calculus. However I want to pursue Mathematical Logic on the long term as a ...
4
votes
3answers
2k views

Help in self-studying mathematics.

Is this a reasonable list for who seek to learn mathematics by "self learning" program? and is it a well sorted list to follow? http://www.math.niu.edu/~rusin/known-math/index/index.html
10
votes
1answer
683 views

Undergrad Student Trying to Figure Out What to Study

this is my first time on stack exchange and I am seeking advice for my future studies. Some background first; I am a undergraduate student pursuing a degree in mathematics and I hope to pursue ...
6
votes
6answers
8k views

Steps to Re-Learn Mathematic the right way

I was always branded weak mathematics back at school though i loved it. The reason was that I was not having many basics in maths. Due to this problem I stopped learning Maths after my 10th grade. But ...
5
votes
2answers
2k 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 ...
5
votes
1answer
2k views

Can I go through Hartshorne without knowing much analysis?

I know intro abstract algebra and some real analysis. Is this enough to study algebraic geometry from the book of Hartshorne?
4
votes
6answers
232 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 ...
4
votes
2answers
379 views

Study program for algebra for an math-phobic person

I have a female friend (Mid 20's) who wants to get an associates degree, who has an absolute phobia of math, and algebra in particular. I'm trying to find a good program that can help her to study ...
3
votes
1answer
264 views

I'm searching for some books with guidance into mathematical study. [closed]

Yesterday, I've found this. It's a PDF file with this purpose, from Oxford. Some weeks ago I've also found two books tha seems to fill this purpose: Prelude to Mathematics; I Want to Be a ...
2
votes
2answers
401 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 ...
3
votes
1answer
920 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 ...
4
votes
5answers
540 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 ...
3
votes
1answer
568 views

Study Order for high school math

Here in Brasil math is "divided" on fundamental, average and superior, where superior is the math that you learn on universities, like calculus, integrals, limits, derivates, etc. My question 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. ...
2
votes
1answer
864 views

Vector spaces - Multiplying by zero vector 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 axioms. Axiom ...
2
votes
3answers
130 views

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

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 ...
2
votes
2answers
110 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, ...
2
votes
3answers
369 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?
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
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
95 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
116 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) ...