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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5
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2answers
1k 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
422 views

Rigour vs intuition

Researcher David Tall has written in chapter one of Advanced Mathematical Thinking that ...
2
votes
2answers
118 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 ...
20
votes
1answer
381 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 ...
28
votes
3answers
868 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
62 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
941 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
812 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 ...
73
votes
6answers
14k 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 ...
2
votes
2answers
169 views

Recommended topics for Chemical Engineering grad. [closed]

I'm a Chem. Eng. grad. I did well in my math courses and I really like math. I've started digging for some more to learn on my own. I like applying math but I'm most satisfied when I have a deep ...
208
votes
7answers
13k views

Best Sets of Lecture Notes and Articles [closed]

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
1k 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
295 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 ...
12
votes
4answers
228 views

Transitioning to Elementary School teaching and need some advice on bolstering my math skills

I'm an English major trying to make the transition to Elementary School teaching. For as long as I can remember, I've been extremely math-anxious and I've only done the bare-minimum level of Math work ...
4
votes
2answers
3k 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?
5
votes
1answer
209 views

Study advice: The meaning of 'doing mathematics' [closed]

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 ...
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 ...
5
votes
2answers
238 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 ...
11
votes
4answers
676 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
2k 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
284 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 ...
7
votes
5answers
3k views

Relearning Mathematics

First post, I'll try to make it clear and concise. I've been spending the past few weeks watching all sorts of space and science documentaries and it's ignited my eagerness to learn more about these ...
15
votes
4answers
1k 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 ...
2
votes
2answers
402 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 ...
2
votes
3answers
108 views

easy activity to train finding pattern ability? [closed]

I realize that my math learning go wrong way. Wikipedia says math is finding pattern, formulating conjectures, and proving it. but my math learning didn't focus on them. memorizing formula doesn't ...
8
votes
3answers
3k 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
372 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
661 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
191 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
294 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 ...
10
votes
2answers
2k 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 ...
26
votes
8answers
4k views

Math every mathematician should know [closed]

This question is meant as a companion to previously asked questions like Proofs every mathematician should know. More and more I'm beginning to see that there is just too much math to learn. ...
53
votes
9answers
4k views

Is memory unimportant in doing mathematics?

The title says it all. I often heard people say something like memory is unimportant in doing mathematics. However, when I tried to solve mathematical problems, I often used known theorems whose ...
187
votes
28answers
26k views

Too old to start math [closed]

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 ...
2
votes
2answers
178 views

Numeric synaesthesia: uses of and advice for learning math.

It turns out that my adolescent son might have numeric synaesthesia-- numbers have specific colors and possibly other distinguishing characteristics for him. He has shown that he can commit long ...
20
votes
5answers
10k 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 ...
1
vote
4answers
426 views

Which books /tutorials will be good for these topics for AI computer science student

I have found from the internet that I need to know these topics for understanding Artificial Intelligence: Matrix algebra: most machine learning models are represented as matrices and vectors. ...
4
votes
1answer
99 views

the nature of numbers?

I am currently relearning basic math - including; fractions, decimals and percentages. I am learning from various different sources, and what gets me is that they only teach math in forms of methods. ...
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 ...
1
vote
1answer
70 views

Noise sensitivity of Boolean functions

Is there any Boolean function from $\{-1,1\}^n$ to $\{-1,1\}$ such that whose noise sensitivity is greater than delta, where Delta is the probability of each bit is flipped in n-tupple.
23
votes
4answers
1k views

What are the dangers of visual exposition of mathematics?

I've heard several times (such as this one) that it's dangerous to learn/prove/teach mathematics through images. I've also read somewhere that showing mathematics through images helps one's intuition ...
85
votes
10answers
10k views

Math and mental fatigue [closed]

Just a soft-question that has been bugging me for a long time: How does one deal with mental fatigue when studying math? I am interested in Mathematics, but when studying say Galois Theory and ...
9
votes
6answers
10k views

Math Textbooks for High School

I'm a high school student who is trying to figure out a complete course of self study for each year of high school. Is there a way to self learn grades of math without devoting too much time? For ...
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 ...
11
votes
4answers
2k views

Mathematics base for data mining and artificial intelligence algorithms. [closed]

Could you give me some clarification about data mining and artificial intelligence algorithms? What mathematics base they used for? Could you give me starting point, in mathematics, to understand ...
81
votes
23answers
29k views

Complete course of self-study [closed]

I am about $16$ years old and I have just started studying some college mathematics. I may never manage to get into a proper or good university (I do not trust fate) but I want to really study ...
47
votes
3answers
5k views

Motivation and methods for self-study [closed]

First, a little background: Beginning with calculus in my first semester of college, I fell in love with mathematics. That was the point at which the concepts became interesting to me, and I started ...
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 ...
13
votes
3answers
11k views

I want to start mathematics from scratch. What should I begin with?

I've just finished high school but I don't feel my knowledge of mathematics is good enough. I'd like to start again from scratch, possibly adding a bit (a lot) of problem solving to it. What is the ...
2
votes
0answers
434 views

Schaum's Outlines for self-study

I wish to learn Physics via self-study. I realize that I have a long way to go as far as Mathematics prerequisites: I will need to begin with Precalculus(I took that course many years ago, so I am ...