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.

learn more… | top users | synonyms

11
votes
3answers
3k 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
64 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 ...
11
votes
3answers
2k 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 ...
2
votes
1answer
106 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 ...
9
votes
3answers
635 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?
2
votes
4answers
300 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 ...
3
votes
0answers
389 views

How does learning math affect other skills? [closed]

I have found two things since I started immersing myself in math: 1) I have a much better sense of direction. Not in absolute direction (i.e. whether I'm facing West), but in generating a mental map ...
17
votes
1answer
1k views

Can an older person become an expert in math?

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 ...
36
votes
7answers
6k views

I can't do math?

So after failing another math test today I have realized that I can't do math on my own. For whatever reason when I get to a test I just can't do math without extra resources. I think this is because ...
12
votes
6answers
2k 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
700 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 ...
15
votes
0answers
848 views

Efficient ways to read and learn a new topic

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 ...
6
votes
3answers
769 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 ...
1
vote
2answers
464 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 ...
35
votes
13answers
2k 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
342 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?
-3
votes
1answer
903 views

How to engage extremely proficient math kid who hates math? [closed]

Well hate is probably too strong, maybe "doesn't enjoy" is a better description. I have a 5 year old son who generally doesn't like math, though he is extraordinarily talented. I'm looking for books ...
23
votes
4answers
985 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 ...
3
votes
5answers
271 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 ...
0
votes
0answers
59 views

Survey of balanced languages/grammars etc

Is there any good survey of nested/balanced/parenthesed/bracketed/XML/Dyck/Floyd languages/grammars and their applications? If no, can you please list all relevant keywords to allow gathering all ...
16
votes
4answers
946 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
2k 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
672 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
367 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 ...
41
votes
9answers
5k 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 ...
11
votes
0answers
1k 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 ...
59
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 ...
25
votes
3answers
3k 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
659 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 ...
17
votes
5answers
2k 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
478 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 ...
5
votes
2answers
507 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 ...
11
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
643 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 ...
18
votes
2answers
2k views

How to think deeply in mathematics way?

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
131 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 = ...
1
vote
3answers
622 views

Calculus for beginners

What are resources for Calculus you recommend for beginners such that it describes the topics easily? Thanks.
28
votes
13answers
10k 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 ...
5
votes
3answers
286 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
6answers
9k 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
4k 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 ...
10
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
416 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
325 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
6answers
1k 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 ...
23
votes
11answers
12k views

How to start with mathematics?

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
6k 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. ...
4
votes
0answers
183 views

physics/mathematic simulations [closed]

Related to this question: http://math.stackexchange.com/questions/2626/modelling-forces-acting-on-a-sail I would like to create a simulation of the forces. I have done this before with cars: ...
1
vote
3answers
453 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 ...