Questions about studying mathematics without formal instruction.
120
votes
27answers
7k views
Too old to start math
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 ...
62
votes
6answers
1k views
Best Sets of Lecture Notes and Articles
Let me start by apologizing if there is another thread on math.se that subsumes this.
I was updating my answer to the question here during which I made the claim that "I spend a lot of time sifting ...
60
votes
9answers
10k 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 ...
50
votes
21answers
4k views
Complete course of self-study
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 ...
40
votes
7answers
986 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 ...
39
votes
5answers
2k 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 ...
34
votes
6answers
981 views
Studying for the Putnam Exam
This is a question about studying for the Putnam examination (and, secondarily, other high-difficulty proof-based math competitions like the IMO). It is not about the history of the competition, the ...
32
votes
9answers
3k 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 ...
30
votes
6answers
3k views
How Do You Go About Learning Mathematics?
I really like mathematics, but I am not good at learning it. I find it takes me a long time to absorb new material by reading on my own and I haven't found a formula that works for me. I am hoping a ...
30
votes
3answers
2k 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 ...
29
votes
2answers
664 views
Are difficult exercises good for beginners?
I'm self-studying Rudin's Real and Complex Analysis. I've finished the first two chapters so far, and I don't have any major problems understanding the definitions and theorems. I can prove the ...
28
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 ...
25
votes
7answers
2k 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 ...
25
votes
1answer
428 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 ...
24
votes
13answers
8k 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 ...
24
votes
8answers
924 views
How to use math textbooks
I'm a higher schooler who was recently gifted a book by my teacher (Schaum's outline of advanced calculus) which is really awesome and I've started working my way through it.
I have run into a ...
23
votes
8answers
2k views
Math every mathematician should know [closed]
Sorry in advance if this question doesn't belong here. I know it walks the line of what kinds of questions should be asked, but I'm really interested in what the community here has to say on it. ...
23
votes
4answers
2k views
(Theoretical) Multivariable Calculus Textbooks
(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 ...
22
votes
8answers
744 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 ...
20
votes
3answers
617 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, ...
19
votes
3answers
1k views
Motivation and methods for self-study
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 ...
18
votes
3answers
709 views
I want to get good at math, any good book suggestions?
I have never been good at math. In my senior year I failed algebra 2 in the first semester because the teacher would refuse to show me how to solve problems saying that it's my fault for not paying ...
16
votes
7answers
2k 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 ...
16
votes
6answers
1k views
Self-Studying Abstract Algebra; Aye or Nay?
I am a high schooler with a deep interest in mathematics, which is why I have self-studied Linear Algebra and have begun my self-study in Differential Equations. As I am a man who likes to plan ahead, ...
16
votes
7answers
1k views
Game theory - self study
I want to self study game theory. Which math-related qualifications should I have? And can you recommend any books? Where do I have to begin?
15
votes
4answers
1k 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 ...
15
votes
8answers
5k 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 ...
15
votes
2answers
256 views
Do free online collaborative solution manuals exist?
I'm not a mathematician by training and a rarely come in contact with mathematicians. For this reason I find solution manuals to be incredibly useful - reading them allows me to see how experienced ...
14
votes
4answers
740 views
Number of subgroups of prime order
I've been doing some exercises from my introductory algebra text and came across a problem which I reduced to proving that:
The number of distinct subgroups of prime order $p$ of a finite group ...
14
votes
1answer
268 views
Why learning modern algebraic geometry is so complicated?
Many students - myself included - have a lot of problems in learning scheme theory. I don't think that the obstacle is the extreme abstraction of the subject, on the contrary, this is really the ...
13
votes
9answers
4k views
Good book for self study of 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 ...
13
votes
3answers
1k 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 ...
13
votes
6answers
591 views
Book on the Rigorous Foundations of Mathematics- Logic and Set Theory
I am asking for a book that develops the foundations of mathematics, up to the basic analysis (functions, real numbers etc.) in a very rigorous way, similar to Hilbert's program. Having read this ...
13
votes
1answer
374 views
Learning path to the proof of the Weil Conjectures and étale topology
Assume you are an algebraic geometry advanced student who has mastered Hartshorne's book supplemented on the arithmetic side by the introduction of Lorenzini - "An Invitation to Arithmetic Geometry" ...
12
votes
5answers
5k views
Good books for self-studying algebra?
I have a few weeks off from school soon, and I was hoping to self-study a bit of algebra. I don't think this question has been asked on here before, but does anyone have any suggestions for algebra ...
12
votes
3answers
2k 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 ...
12
votes
3answers
455 views
Careers in Math
I am a highschool freshman, and I really like to have goals for my life, one of the big ones is my career of choice. Previously, I have always wanted to be a programmer, and I have written a lot of ...
11
votes
9answers
460 views
Suggest an Antique Math Book worth reading?
I'm not a math wizard, but I recently started reading through a few math books to prepare myself for some upcoming classes and I'm starting to really get into it. Then I noticed a few antique math ...
11
votes
4answers
493 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 ...
11
votes
3answers
850 views
Learning schemes
Could someone suggest me how to learn some basic theory of schemes? I have two books from algebraic geometry, namely "Diophantine Geometry" from Hindry and Silverman and "Algebraic geometry and ...
11
votes
2answers
819 views
Baby Rudin: Advice
I am working through the first chapter of Principles of Mathematical Analysis and I am wondering how many of the twenty exercise problems I should do. I think the first ten are very to moderately ...
11
votes
2answers
350 views
Choice of $q$ in Baby Rudin's Example 1.1
First, my apologies if this has already been asked/answered. I wasn't able to find this question via search.
My question comes from Rudin's "Princicples of Mathematical Analysis," or "Baby Rudin," ...
11
votes
2answers
268 views
Math blogs, pros and cons for writers?
I regularly read blogs by three mathematicians, and occasionally run into others. Definitely they help me a lot studying mathematics.
But now I am more interested in the writers' perspective, and I ...
11
votes
2answers
200 views
Why don't i understand “what is mathematics?” by Richard Courant
I am 14 years old and can do A level maths happily. However, I want to further my knowledge of mathematics to pave my way for more discrete maths and harder analysis etc. so I decided to pickup "What ...
11
votes
2answers
331 views
Computation of $\operatorname{Tor}_1$ and $\operatorname{Ext}^1$
Can you please give some examples of computation of the derived functors $\operatorname{Tor}_1$ and $\operatorname{Ext}^1$ for some simple cases, say $R=\mathbb{Z}$ or $R=\mathbb{Z}[G]$ for some ...
11
votes
2answers
662 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. ...
11
votes
3answers
117 views
Transitioning to Elementary School teaching and need some advice on bolstering my math skills
I'm an English major trying to make the transition to Elementary School teaching. For as long as I can remember, I've been extremely math-anxious and I've only done the bare-minimum level of Math work ...
11
votes
4answers
607 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 ...
10
votes
5answers
5k views
Good abstract algebra books for self study
Last semester I picked up an algebra course at my university, which unfortunately was scheduled during my exams of my major (I'm a computer science major). So I had to self study the material, ...
10
votes
3answers
473 views
What is the prerequisite knowledge for learning Godel's incompleteness theorem
I am very interested in learning the incompleteness theorem and its proof.
But first I must know what things I need to learn first.
My current knowledge consists of basic high school education and the ...
