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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9
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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
809 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
233 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 ...
12
votes
5answers
6k 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
72 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
831 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 ...
16
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
810 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
2k 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
6answers
7k 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
734 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
795 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 ...
34
votes
8answers
7k 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
382 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 ...
15
votes
2answers
5k views

How to improve mathematics for Programming Contests?

You might close this question or downvote it, but I can't stop myself from asking the experts of mathematics who solve thousands of math problems. I'm a C++/C programmer who wants to improve his ...
8
votes
2answers
721 views

What is required to learn about algebraic geometry?

I want to learn about classical algebraic geometry. So what are subjects that are required to start learning about it? (Some preknowledge of algebra, commutative algebra?)
43
votes
7answers
12k views

I can't do math? [closed]

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 ...
6
votes
2answers
602 views

Self-Teaching: Is Geometry the Nexus of all Mathematics?

Necessary prologue: I'd really like to become more fluent in the language of mathematics. I don't have a schedule that permits me taking a class and any on-line tutors that I find seem relatively ...
28
votes
7answers
10k 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
1k 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 ...
26
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 ...
68
votes
20answers
49k views

Good book for self study of a First Course in Real Analysis

Does anyone have a recommendation for a book to use for the self study of real analysis? Several years ago when I completed about half a semester of Real Analysis I, the instructor used "Introduction ...
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
1k 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 ...
5
votes
1answer
2k views

Can I go through Hartshorne without knowing much analysis?

I know intro abstract algebra and some real analysis. Is this enough to study algebraic geometry from the book of Hartshorne?
3
votes
1answer
582 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 ...
3
votes
1answer
614 views

Making theorems into flashcards?

I am studying real analysis and trying to convert some of the rather wordy theorems into flashcards. Some of the theorems have names and so it's easy to make a flashcard that just asks that I state ...
6
votes
5answers
1k views

Materials for self-study (problems and answers)

I'm hoping to self-study Geometry, Algebra, Calculus, Vector Calculus, Linear Algebra, Probability and Statistics, and other intermediate maths. I've found the best way for me to learn is to work on ...
2
votes
2answers
683 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 ...
42
votes
13answers
5k 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
374 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?
14
votes
2answers
1k views

Math Notes and Knowledge Organization Methodology

I, like many of you I suspect, take copious notes when reading and working through math exercises/theorems/constructions. I have stacks and stacks of notes ranging from one day old to several years. ...
37
votes
5answers
2k 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
589 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 ...
47
votes
5answers
12k views

(Theoretical) Multivariable Calculus Textbooks [duplicate]

(Note that I have used bold text frequently simply to highlight the key points of my question for those who do not have the time to read through it thoroughly (it is not very long, however); I hope ...
4
votes
2answers
382 views

Study program for algebra for an math-phobic person

I have a female friend (Mid 20's) who wants to get an associates degree, who has an absolute phobia of math, and algebra in particular. I'm trying to find a good program that can help her to study ...
18
votes
4answers
3k views

Can I use Ravi Vakil's way of learning for elementary subjects?

I mean you can't learn math in a linear order. Can I just read a paper first on a subject I haven't studied and just work backwards? For example, I have never studied combinatorics but I sort of have ...
18
votes
4answers
2k 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
4k 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 ...
79
votes
6answers
7k views

Strategies for Effective Self-Study

I have a long-term goal of acquiring graduate-level knowledge in Analysis, Algebra and Geometry/Topology. Once that is achieved, I am interested in applying this knowledge to both pure and applied ...
10
votes
5answers
856 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
414 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 ...
14
votes
4answers
719 views

Recommended Math knowledge for programming

I wasn't sure if this is a math or programming question so I suppose I flipped a coin. I'm just learning programming thanks to my IT Support degree and was just wondering what the minimum recommended ...
55
votes
9answers
9k 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 ...