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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7
votes
1answer
184 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 ...
69
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
436 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
763 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?
52
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
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) ...
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
281 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 ...
39
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
369 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
246 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
696 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
567 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
690 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
529 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
685 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
451 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 ...
15
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 ...
9
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 ...
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 ...
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
922 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 ...
54
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 ...
0
votes
2answers
953 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
609 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 ...
12
votes
2answers
798 views

Is Mathematics graduation important for a Computer Scientist?

I know this might be a personal problem, but I often find some friends in the same problem as me so I think this might be helpful to them after all. I am going to graduate in Computer Science in ...
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 ...
11
votes
3answers
5k 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 ...
1
vote
1answer
70 views

Resource to improve ability to interpret and understand formulas and algorithms

I wasn't sure whether this belonged here or on StackOverflow but here goes: I've been doing a lot of research into algorithms recently and I've found that my inability to properly interpret and ...
37
votes
2answers
817 views

How do I find partners for study?

I want to find partners to study some post-graduate topics together online (because I'm pretty much out of steam as far as self-study goes, and I have problems finding a decent grad school). Are there ...
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 ...
26
votes
3answers
1k views

When to skip sections of a book when self-studying?

When you're taking a mathematics class, you usually know exactly what sections of a book you need to know, and you can focus your time on these important sections. However, when studying by myself, ...
5
votes
3answers
728 views

How can I find videos of mathematics at graduate level, especially on linear algebraic groups

I am studying mathematics by myself, and I find it very helpful to watch online course videos. There are many such videos on undergraduate courses, such as elementary calculus, abstract algebra, ...
16
votes
3answers
1k views

Learning math-oriented French

I'd like to read several papers which I find interesting, but they are all in French. I have no problem with taking a traditional French class or learning it via some other method. However, I realize ...
19
votes
5answers
6k views

Is memorization a good skill to learn or master mathematics?

I sometimes spend inordinate amounts of time memorizing math articles or theorems/proofs or formulas. My question is "am I wasting time?" and will 'active thinking' or 'working out problems' be faster ...
2
votes
1answer
117 views

weakly locally one-to-one?

Is there any standard name for this concept that is weaker than local one-to-one-ness? In some open neighborhood of $x_0$ there is no point $x\ne x_0$ such that $f(x)=f(x_0)$. Or, if you like: In ...
8
votes
2answers
715 views

How much rigour in proofs?

Just a quick pointer: you could probably get away with skipping to the last 2 paragraphs, as the rest covers my motivation for answering this question. Over this coming holidays I'm hoping to spend a ...
10
votes
3answers
772 views

A Concrete Approach to Category Theory

Is there a way to learn Category Theory without learning so many concepts of which you have never seen examples?
34
votes
6answers
1k views

Attitude towards exercises in mathematics

I'm doing self study on a couple of topics in mathematics, such as real analysis, abstract algebra, and linear algebra. From time to time, there are always a couple of exercises which I found too ...
8
votes
2answers
230 views

The role of writing in understanding concepts

I am an engineer student from Norway who is not that fascinated with "engineering maths", so I am trying to work through Spivak's Calculus book on my own. I know that there is no "how to" manual for ...
31
votes
8answers
6k views

How can I learn to “read maths” at a University level?

When I look at math, it's like my mind goes fuzzy. The only way to describe it is in terms of what I can relate it to. You know how when you read, you see the letters and words, but your brain picks ...
3
votes
4answers
378 views

Getting Help in Abstract Math Classes

This semester I am taking abstract algebra, and I am finding the homework to be much more difficult than calculus or linear algebra. The book my class uses is Fraleigh's Abstract Algebra. Although I ...
18
votes
1answer
2k views

Can an older person become an expert in math? [closed]

Is learning math like learning a language, in that there's a certain cutoff age (pretty young) that you need to start learning by, otherwise you'll never be fluent? Is the novice older brain ...
12
votes
2answers
5k views

How to improve mathematics for Programming Contests?

You might close this question or vote "-1" for this but I just can't stop myself from asking this question from the experts of mathematics which solves thousands of problem related to mathematics and ...