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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55
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 ...
195
votes
28answers
27k 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 ...
21
votes
5answers
12k 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
446 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
100 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
9k 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
73 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.
25
votes
4answers
2k 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 ...
90
votes
10answers
12k 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
11k 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 ...
86
votes
23answers
33k 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 ...
48
votes
3answers
6k 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
265 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
12k 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
488 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 ...
13
votes
2answers
21k views

Tips for an adult to learn math — from the beginning. [closed]

First let me start with I am an adult and I can't do simple maths. I some how got through all of my math courses in University (after several attempts) but I honestly couldn't tell you how... I ...
7
votes
1answer
185 views

What is a good communication platform, which supports something like TeX-code?

I moved away and am now planning to communicate with a friend over the internet and talk about mathematical subjects (e.g. via Skype). However the text blocks like "\int_G\omega..." in a chat window ...
70
votes
9answers
4k views

How to make notes when learning a new topic [closed]

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 ...
3
votes
3answers
472 views

For Maths Major, advice for perfect book to learn Algorithms and Date Structures

Purpose: Self-Learning, NOT for course or exam Prerequisite: Done a course in basic data structures and algorithms, but too basic, not many things. Major: Bachelor, Mathematics My Opinion: Prefer ...
1
vote
1answer
787 views

Where can I find (download) a book about basics of discrete mathematics?

I am a beginner in this craft. Do you know where can I download a good book about basics of discrete mathematics?
54
votes
6answers
3k views

Am I too young to learn more advanced math and get a teacher?

I am still 15 years old, but I am very interested in pure math. I have been teaching myself though books, from the internet and from others for the past year or so. I haven't mastered all the topics ...
0
votes
5answers
117 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) $x=\...
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
1
vote
0answers
302 views

Programmer understanding academic writings on maths

I would like to know in which order I should learn different areas of maths so I can have a robust overview of all the theory in case I need something for a computer programming problem. So I've ...
40
votes
6answers
4k views

Are the exercises necessary to understand the subject of a mathematical textbook?

When I am reading a mathematical textbook, I tend to skip most of the exercises. Generally I don't like exercises, particularly artificial ones. Instead, I concentrate on understanding proofs of ...
2
votes
1answer
1k views

Self-studying preparation for finance PhD program

This is my first "soft question" so I hope it is alright. I graduated from a well-respected institution a few years back with an undergraduate degree in Finance and Economics. From there I spent ...
4
votes
1answer
379 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 ...
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 ...
2
votes
3answers
250 views

How important it is to learn different proofs

As one studies mathematics, how important it is to find various proofs? I mean that if one has to prove for example that conditions (i), (ii), and (iii) are equivalent then is it enough to learn to ...
9
votes
3answers
728 views

How to deal with the temporary nature of my knowledge?

I'm a self-learner trying to learn Math while enrolled in a wrong major (Humanities). I have gone through the many amazing questions and answers here (& elsewhere, including Prof. Tao's blogs) ...
6
votes
3answers
582 views

The Importance Of Good Teachers and Guidance In the Academics

I'm a first year student for a math degree. I'm very curious on how good students overcome their bad teachers in the journey of learning and grasping the courses material fully, all in the pressure of ...
5
votes
2answers
703 views

Math for a high school junior?

I don't find the math taught at my school too challenging so out of personal interest I teach myself other fields of math. I was wondering if you could recommend some areas with a bit more complexity? ...
2
votes
2answers
570 views

Can SRS technique help math learners? [closed]

I have used SRS for learning stuff in other subjects like History and Language in the past (Using Anki). It seems like a good deal since I get punched with something I was about to forget at the point ...
10
votes
1answer
715 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 ...
3
votes
1answer
1k views

Learning Math On my own

I'm a physics major and I'm pretty sure that I'm interested in theoretical physics research. However, I haven't been able to take math courses in a systematic way (as a math major would) due to ...
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 ...
7
votes
2answers
3k views

Some basic practical applications of Calculus

I am currently studying Calculus on my own for fun. I enjoy different components of math and how they can be used to solve so many problems. Many people, however, think I am crazy because I am ...
4
votes
1answer
462 views

Learning approach of simultaneously enhance creation and imagination skills instead of 'follow' approach

I am a math-major bachelor student. And I want to get some advice about the approach I'm trying now for learning maths, not for efficiency, but for depth and fully-mastered. Firstly, I want to know ...
16
votes
5answers
10k views

Which calculus text should I use for self-study?

I am 36 years old, and have forgotten a lot of math from high school, of which I only took up to Algebra 2. However I am teaching myself mathematics and am now, as an adult, completely fascinated ...
10
votes
4answers
4k 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 ...
10
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 ...
2
votes
2answers
3k views

How to simplfiy $ \cos^{2}(\theta) \sin(\theta) $ to terms of $\sin$ or $\cos$ only?

Is it possible to simplify $$ \cos^{2}(\theta) \sin(\theta) $$ to terms of only $\sin$ or $\cos$? I need to simplify this to take the integral.
3
votes
1answer
961 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 ...
56
votes
4answers
7k 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 ...
2
votes
2answers
1k views

Generalized eigenvalue solver online

For demonstrative purposes, I am trying to find an online solver where alumni can input data of two matrices A and B, then the system outputs the first eigenvalues and eigenvectors in the generalized ...
6
votes
2answers
638 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 ...
9
votes
3answers
2k views

The most common theorems taught in Abstract Algebra

I am self learning abstract algebra. I want to know which theorems are a must to understand. Now these are limits I have to deal with (please consider when answering): I have limited ...