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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2answers
1k 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
201 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
140 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
173 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
555 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
102 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
345 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 ...
266
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 ...
1
vote
2answers
249 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
122 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
82 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 ...
1
vote
1answer
78 views

How can I prepare effectively for this test?

I live in Australia and I will be doing my final high school mathematics test in 5 months from today. The test is about the following topics: Differentiation and Integration and their applications ...
5
votes
3answers
226 views

learning/teaching approach to rigorous math with the goal of improving

I will state this now: yes, this is a subjective question. But I feel the answers people give may benefit students. I want to get better at doing non trivial proofs. Real analysis is standard ...
4
votes
4answers
345 views

The maths required for an economics degree

I have a degree in computer science and I wanted to do another degree in economics. However, my maths have been weak since high school always scoring slightly above passing rate. During my course of ...
5
votes
2answers
375 views

In what order should mathematical fields be learned? [closed]

This could be considered a broader version of this question, with all fields. I know that when high-level maths are reached, the fields being to split quickly (i.e. specializing in this type of ...
3
votes
4answers
135 views

What math will I need in order to learn Microsoft's UProve?

I'm studying Microsoft's UProve (independent studies at 35 years old) and forget most of the Math I learned in college. I intend to proceed and learn the contents of this chapter of this book but can ...
0
votes
1answer
353 views

What branch of mathematics improves logical thinking? [closed]

So, that's the question. I dare to generalize it even wider: what branch of mathematics improves the general thinking ability, intilligence, the way the person thinks, and makes it more logical? I'm ...
10
votes
2answers
2k views

Is it better to learn math before physics?

It seems that a persons ability to understand physics at a high level is limited primarily by their understanding of math. It also seems to be more efficient to learn the underlying math for a ...
3
votes
0answers
210 views

How does one study with many textbooks? [closed]

Suppose you wanted a good understanding of a subject, and so you start reading a recommended textbook. But it turns out that the textbook you have has a different perspective/omits certain topics, ...
5
votes
2answers
596 views

How can I make sure I never forget.

I am currently refreshing my Elementary Algebra using Schaum's Outlines. I find them useful as they are choc full of exercises (Which I now realize is the only way to master algebra). I am worried ...
6
votes
2answers
272 views

Rigour vs intuition

Researcher David Tall has written in chapter one of Advanced Mathematical Thinking that ...
2
votes
2answers
103 views

Infinite series help

Are there any hard and fast rules for finding the sum of an infinite series? What suggestions would you have for someone new to learning them? Memorize identities? Also, what are the best resources ...
18
votes
1answer
336 views

Learning Aid for Basic Theorems of Topological Vector Spaces in Functional Analysis

I am self-teaching myself the basics of functional analysis (e.g. topological vector spaces), and frankly I am starting to get a migraine sorting out/organizing in my head all of the ...
26
votes
3answers
707 views

Do free online collaborative solution manuals exist?

I'm not a mathematician by training and a rarely come in contact with mathematicians. For this reason I find solution manuals to be incredibly useful - reading them allows me to see how experienced ...
1
vote
1answer
55 views

From (almost) zero to knowledgeable in statistics

I work in (server) operations and it is not very uncommon for me to parse logs and try to make sense of some kind of metric. For some odd reason I have grown quite fond of it. Assume that I have ...
7
votes
1answer
526 views

Philosophy of learning mathematics (combinatorics)

How does one learn mathematics in depth and well? I think I may be studying mathematics incorrectly, or I could be doing it a lot more efficiently/effectively. Sometimes I feel like I need every ...
1
vote
3answers
522 views

Where to pick up learning math again?

In high school, I absolutely loved math classes. I took Calc in 11th grade, and then since have done just about nothing with math. Is there somewhere I go to see what math knowledge I still ...
6
votes
1answer
290 views

How to most efficiently remedy mathematical deficiencies

My spouse and I are currently both pursuing our undergraduate degrees. I'm double majoring in Computer Science & Mathematical Sciences and my spouse is double majoring in Economics & Finance. ...
57
votes
6answers
7k 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 ...
148
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 ...
6
votes
2answers
740 views

start mathematics from scratch

I'm sorry if this question goes against the site. I have completed my engineering in computer science; we were taught to get degrees only in our university :(. I love mathematics but time passed ...
5
votes
1answer
260 views

What should I be doing in a grad level math course?

I have an undergrad degree in an engineering field and switched to applied math for a PhD. In engineering, I have had my share of good and bad professors but I knew what I had to be doing during a ...
2
votes
2answers
1k views

Math resources for electrical engineering?

I am considering electrical engineering as my field of study. However, my math knowledge might not be as good as it should be. What math books/resources would you recommend me to read?
4
votes
1answer
161 views

Study advice: The meaning of 'doing mathematics'

I am a former computer engineering student that switched to mathematics this semester. The only math I have is basic calculus and linear algebra, both thought in a "engineering way". Now I really want ...
6
votes
4answers
1k 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 ...
5
votes
1answer
188 views

Flexible distance learning Mathematics programme

I am looking for a flexible Mathematics degree programme from a reputable institution. By flexible here I mean: Able to take the programme at one's own pace The option to complete the programme at ...
10
votes
4answers
592 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" ...
2
votes
5answers
664 views

How to learn differentiation?

I am having a confusion in learning differentiation. Can you please point me to some video tutorials which explains differentiation basics clearly for beginners?
5
votes
2answers
241 views

How does one best balance learning from a “problem based book” with supplementary material?

We all know that when learning math, one has to do more than just simply read - one must try to solve problems and work actively with the material. Many books try to force the reader to participate ...
15
votes
4answers
978 views

How to get more creative in Calculus

I'm currently doing Calculus I (one variable and some max- min problems with two variables as well), and I can follow most proofs and understand most of all chapters in the book. It seems tough that ...
1
vote
0answers
256 views

khan academy and learning

I want to finish all the exercises in the map from addition to differential calculus, I'd say I'm about half way done. is there anything I should be aware of? What is khan academy missing? say if i ...
2
votes
2answers
319 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 ...
6
votes
3answers
2k views

Advice on Understanding Vector Spaces and Subspaces

currently I am studying Vector spaces and sub spaces. I enjoyed working with matrices and using the Gaussian-Jordon elimination and I also had no problems with cofactor expansion and determinants in ...
9
votes
3answers
276 views

Links to Online Videos of Good-Quality Lectures by Mathematicians

I am not trying to do anything new here, but I would like to start an activity that has been going on at Math Overflow. Hopefully, people here at the Math StackExchange can also enjoy the good stuff. ...
7
votes
1answer
403 views

Empirical distribution vs. the true one: How fast $KL( \hat{P}_n || Q)$ converges to $KL( P || Q)$?

Let $X_1,X_2,\dots$ be i.i.d. samples drawn from a discrete space $\mathcal{X}$ according to probability distribution $P$, and denote the resulting empirical distribution based on n samples by ...
3
votes
1answer
114 views

Exercise #26 from “Abel's Theorem in Problems and Solutions” by Alekseev

Exercise: Prove, that for every element $a$ of the group: $(a^m)^{-1}=(a^{-1})^m$, where $m$ is natural. On the #23 was proven that $$(a_1 \centerdot \ldots \centerdot a_n)^{-1} = a_n^{-1} ...
6
votes
2answers
257 views

How to 'analyze' problems in analysis; Computing $\int_0^{2\pi}\frac{1}{(a+b\cos(\theta))^2}d\theta$

If $a, b \in \mathbb{R}$ with $a > b > 0$, compute this ungodly thing; $$\int_0^{2\pi}\frac{1}{(a+b\cos(\theta))^2}d\theta$$ I'm really not a fan of complex analysis... I can't visualize ...
8
votes
2answers
1k views

Intuition on the Orbit-Stabilizer Theorem

The Orbit-Stabilizer says that, given a group $G$ which acts on a set $X$, then there exists a bijection between the orbit of an element $x\in X$ and the set of left cosets of the stabilizer group of ...
27
votes
8answers
3k views

Math every mathematician should know [closed]

Sorry in advance if this question doesn't belong here. I know it walks the line of what kinds of questions should be asked, but I'm really interested in what the community here has to say on it. ...