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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21
votes
7answers
6k views

How to study for analysis?

I am currently a first year undergraduate majoring in mathematics. I'm taking an introductory analysis course and find it very hard compared to other math couses. I know that the topics covered in the ...
2
votes
2answers
930 views

Difference between Logarithms of different bases

Every time i see a logarithmic function and if it so happens that i'am required to take the derivative or the integral of that particular function i get stumped and i tend to avoid that problem. What ...
24
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 ...
4
votes
1answer
1k views

Self-study: part 2

So I'm thinking of doing the following course progression: Baby Rudin Finite dimensional vector spaces Halmos Abstract Algebra Herstein Big Rudin (Real and complex analysis). Is this a good ...
6
votes
3answers
940 views

Rigor in Mathematics

Since starting my undergrad studies (in Maths -- !) I have struggled to grasp the concept of "rigor". My "proofs" tend to have the right framework but somehow they are said to "lack rigor", this has ...
3
votes
1answer
553 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 ...
5
votes
5answers
1k views

How might I refresh high school level mathematics and extend upon it much further?

I did well at Mathematics at school (top 0.1% in the country, approximately), however I stopped studying it when I was 16. Since then I've studied a couple of highly specific mathematics modules in ...
2
votes
2answers
585 views

Getting up to speed enough to tackle mathematics and logic applied in programming?

I'm a games programmer with an interest in the following areas: Calculus Matrices Graph theory Probability theory Combinatorics Statistics More linguistic related fields of logic such as natural ...
38
votes
13answers
3k views

Is there a good “bridge” between high school math and the more advanced topics?

I love math and would like to know more of it. However, whenever I try to pick up a book on what I consider to be "advanced" mathematical topics, I often have a hard time understanding some of the ...
2
votes
3answers
356 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?
36
votes
5answers
1k views

Book/tutorial recommendations: acquiring math-oriented reading proficiency in German

I'm interested in others' suggestions/recommendations for resources to help me acquire reading proficiency (of current math literature, as well as classic math texts) in German. I realize that ...
4
votes
5answers
447 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 ...
17
votes
4answers
1k views

Grasping mathematics

First, I'm not trying to make this sound like a "poor-me" story. I understand fully that every decision I've made leading to this is my fault. I am genuinely looking for advice. So, I am a high ...
2
votes
1answer
3k views

Start learning A-Level further maths

I want to start learning what I need to know for A-Level further maths to take some of the "weight" off of year 12 and 13. What topics should I begin learning and what key ideas do I need to grasp and ...
10
votes
5answers
773 views

Should I study algebra more?

My background is about third-year mathematics major, including linear algebra and abstract algebra. I'm now studying Atiyah's commutative algebra, but it lacks some concrete, easy examples and it's ...
0
votes
1answer
400 views

suggest a textbook on calculus [duplicate]

Possible Duplicate: What are the recommended textbooks for introductory calculus? Hi, i am a software engg. and math was never my favourite. I somehow dragged thru the math i had to do in ...
47
votes
9answers
7k views

How to effectively study math?

Maybe this is too general for here, but I am having a lot of difficulty studying math. Just got out of the military and I guess I am not use to this yet but when I run into a problem I have trouble ...
14
votes
1answer
2k views

Which is better strategy to learn and read books, traditionally one by one OR re-read carefully on perfect books

(Just focus on how to learn and master the stuff pretty well, not involve the aspect of courses or exam) Because recently I always feel that the time and energy are pretty limited, I want to try ...
66
votes
3answers
2k views

Is there a definitive guide to speaking mathematics?

Is there a definitive guide to speaking mathematics to avoid ambiguity? I'm writing a program to generate text for a variety of mathematical expressions and would like to code it so that it adheres ...
29
votes
3answers
4k views

Math Major: How to read textbooks in better style or method ? And how to select best books?

I'm a bachelor student of Math major. The question is about the better way to select and read maths text- or non-text- books, without considering the course and exam. (Because we follow the lecture ...
2
votes
4answers
679 views

How i can learn mathematics these days?

i am currently have no idea where i can learn mathematics online. whenever i am in schools my math goes too bad but now i want to learn mathematics online. any idea where i can get education for ...
19
votes
5answers
4k views

What's better strategy to handle tons of formulas, definitions?

I'm freshman, bachelor of Math major. When I read and learn the textbook, there're lots of formulas, laws, definitions and so forth. But what is the better way to handle it ? I mean, is it necessary ...
1
vote
4answers
758 views

I haven't studied math in 12 years and need help wrapping my mind back around it

I was never fabulous at Algebra and have always studied the arts. However, now I have to take Math 30 pure 12 years after I finished my last required high school math class. If anyone has thoughts on ...
6
votes
2answers
554 views

Does anyone know of any good ways to get good at algebra without as much“grind” as doing hundreds of questions a night

I'm coming to a point in college where I can't avoid my math classes any longer. I need to get better at algebra so I don't flunk out of the class when I take it, however I've never been able to get ...
13
votes
2answers
3k views

When to give up on math? [closed]

How do I know when I should give up on math? I can't pass any of my math tests no matter much I study, I have tutors, attend office hours and I still can't do better than a D on any test. Most of the ...
6
votes
3answers
770 views

Mastering Math - Grade school- to College-level?

I'm having difficulty with my math, fractions and up. I used to understand it all, but it's been so long since I've touched the book (I finished it a couple of months ago, picked it up to review ...
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 ...
1
vote
2answers
141 views

Cross product: problem with breakdown of vector to parallel + orthogonal components

Vector $\vec{a}$ can be broken down into its components $\vec{a}_\parallel$ and $\vec{a}_\perp$ relative to $\vec{e}$. $\vec{a}_\parallel = (\vec{a}\vec{e})\vec{e}$ and $\vec{a}_\perp = ...
2
votes
4answers
709 views

Calculus for beginners

What resources for "Calculus" do you recommend for beginners; they should describe the topics in a way easy to understand?
29
votes
13answers
12k views

Formerly good at math, but after 12 years I've lost most of my skills. Now I need them once again. Any advice to grow them back?

I love math, and I used to be very good at it. The correct answers came fast and intuitively. I never studied, and redid the demonstration live for the tests (sometimes inventing new ones). I was the ...
77
votes
8answers
22k views

Learning mathematics as if an absolute beginner?

I dread mathematics, and I believe it's because I have come to associate mathematics with the experience of terrible teachers. All of my math teachers have been grumpy, but one in particular was the ...
11
votes
6answers
8k views

In what order should the following areas of mathematics be learned?

I am in a biological field (medicine) but I have genuine passion for mathematics. I want to learn it on my own , in my spare time. Mathematics , as I gather, is learned best when you have grasped ...
5
votes
3answers
305 views

Fundamental Math Theory Resources?

I became interested in how numbers actually work recently. I want a source that covers number theory. Explaining how and why numbers react the way they do. A friend recommended Mathematical Proofs: A ...
11
votes
7answers
12k views

Can I learn Calculus on the web, for free, using simple tutorials?

I'm a lazy type of person. I love experimenting with things before learning the theory. I like to practice, and learn from my mistakes. In 3-4 months I have a basic University exam on Calculus, and ...
8
votes
4answers
5k views

Where to learn the syntax of mathematics?

Since I started university, almost every exam I've had in mathematics have ended up as failed mostly due to my lack of using proper "syntax" on paper, written by hand. Where can I learn the standard ...
13
votes
3answers
2k views

What are the prerequisites for learning category theory?

Is category theory worth learning for the sake of learning it? Can it be used in applied mathematics/probability? I am currently perusing Categories for the Working Mathematician by Mac Lane.
9
votes
2answers
514 views

Automatizing computational skills

"It is a profoundly erroneous truism, repeated by copybooks and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise ...
10
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 ...
2
votes
2answers
360 views

Good SAT learning resources?

I'm looking to brush up on SAT math. (That's basic algebra, probability and trigonometry.) I'm interested in books and websites.
21
votes
7answers
2k views

Teaching mathematics in intuitive and thought provoking way

I'm a private tutor of High school & pre-engineering level mathematics. Obviously, only those people who have some trouble with maths take tuitions. Most of my students are actually good. I mean ...
26
votes
11answers
23k views

How to start with mathematics? [closed]

I fell in love with mathematics a bit too late when I've already taken decisions regarding my future, career-wise. Now I would like to learn math on my own but I'm a bit confused as where to start. My ...
8
votes
8answers
9k 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. ...
1
vote
3answers
480 views

Free introductory resources for learning algebra?

I have a non-mathematician friend who is interested in re-learning algebra. I am more than happy to help, but I am in no position to judge what is a good introductory text --- only to identify when a ...
2
votes
4answers
170 views

Is are there software package that can help one find a path between two mathematical statements?

Sometimes when I am reading a mathematical text I will be unable to decipher the steps necessary to translate one mathematical statement into the next. Usually I have to ask for help, but I was ...
1
vote
1answer
677 views

Learn Probability and Permutation and combination [closed]

I am very weak in solving problem related to probability and permutation and combination. Can you please guide me the good content by which I can understand it better. Thanks in advance.
8
votes
3answers
431 views

Books/Notes recommendation request: Multivalued functions/Riemann surfaces

I'm trying to read a document that applies Riemann-Roch left, right and center. I don't know this theorem or the theory it comes from so I need to build up a bit more background before I can tackle ...
51
votes
8answers
9k views

Learning Lambda Calculus

What are some good online/free resources (tutorials, guides, exercises, and the like) for learning Lambda Calculus? Specifically, I am interested in the following areas: Untyped lambda calculus ...
49
votes
19answers
4k views

Mathematical subjects you wish you learned earlier [closed]

I am learning geometric algebra, and it is incredible how much it helps me understand other branches of mathematics. I wish I had been exposed to it earlier. Additionally I feel the same way about ...