33
votes
Is it too late for me to start learning mathematics?
Certainly someone your age (or even much older) can learn Calculus, even get a degree in mathematics. And get a good job afterward.
That "young man's game' quote refers to doing mathematical ...
- 7,369
20
votes
Accepted
Is Linear Algebra Done Right too much for a beginner?
Unguided self-study of mathematics is difficult, and harder for someone with little experience at it. It is normal to take time to advance. One should think in terms of months not hours. A typical one ...
- 5,728
20
votes
Accepted
Dealing with disagreeable students and not compromising
It sounds like your students are not getting what they wanted from your tutelage; since they are not getting a formal credential from their work with you, their likeliest motivation is that they think ...
- 1,404
19
votes
Why are hand waving arguments made in textbooks of undergraduate analysis and how should readers deal with them?
A proof is meant to convince a reader of the truth of some statement. When a mathematician is communicating an argument to another mathematician, you only include the level of rigor that you need so ...
- 24.4k
18
votes
Lack of intuition, retention while self studying
Perhaps you should seek texts that emphasize the high-level viewpoint that you are missing in the details of the more advanced texts. Three examples:
(1) Bressoud, David M. A radical approach to ...
- 29.5k
16
votes
How to learn math from textbooks in the right way?
I tend not to answer the questions that I have no professional knowledge about or the questions that are too general to be answered here. But, your question reminded me of my own undergraduate years ...
- 4,428
16
votes
Accepted
Why are proofs written in flowery language incomprehensible?
To answer the question in the title, I would say that one problem with no-symbols reasonings is that one need to use a lot of pronouns. Problem is, pronouns usually leave too much ambiguity. At some ...
- 9,079
16
votes
How do I learn advanced mathematics without forgetting?
For context, I have a lot of experience self-learning mathematics. I spent a summer learning additional algebra, point-set topology, linear algebra, and analysis (to extend my undergraduate degree) ...
- 3,996
16
votes
Dealing with disagreeable students and not compromising
I think the real issue here is that you thought you were essentially doing undergraduate tutoring, and you weren't. You were doing adult education, and that is not the same thing.
When someone is in ...
- 261
16
votes
Walter Warwick Sawyer: How has reading his works changed your learning or teaching?
No, I was never inspired by him because I had never heard of him before you mentioned it.
Note: My answer is for the original version of the question. Since then, the question has been edited so my ...
- 10.8k
16
votes
Accepted
Should I really just "shut up and calculate"? On learning at a good pace without sacrificing rigour
I looked at some of your posts on MSE before answering. Well, I wouldn't say that you are a "Jack of trades" yet, but you are certainly way above what one would expect from somebody 2 years ...
- 3,599
13
votes
Accepted
What is abstraction and generalization ?
By abstraction, we mean that we step back from concrete objects to consider a number of objects with identical properties simultaneously.
For instance, consider the following three objects:
The set ...
- 1,776
12
votes
Accepted
Is it possible to improve logical thinking and problem solving abilities?
First of all I want to laud you on your knowledge of programming. You know a lot more than I did when I was your age. I tried to learn Italian after watching The Godfather but lost interest after a ...
- 378
12
votes
Lack of intuition, retention while self studying
You need to pick pedagogically appropriate texts. Not the Rudin ballbusters. Pick ones that have explanations and were written for students with occasional imperfections in their previous knowledge. ...
- 325
11
votes
Accepted
How long would it take someone to master the topics in the book "Book of Proof" by Hammack and similar?
This is a text for an "introduction to proofs" course.
It might not be well-known outside mathematical circles, because mathematics educators don't like to advertise this fact, but, outside ...
- 2,484
10
votes
How does a student learn to 'dig behind the scenes' or 'feel' math like a Fields Medallist?
In addition to other insightful answers/comments/remarks, apart from the issue of "degree" and "what kind of genius", I think a large part of the problem is exactly that mathematics is mostly ...
- 14.2k
10
votes
Is it too late for me to start learning mathematics?
For sure you are not too old. If you are really interested and if you are motivated to work hard, then you can have a shot. Maybe you try some of the exercises in the book to get an impression, how ...
- 201
10
votes
Electronic devices to replace pencil and paper
Taking a break from a convoluted computation...
To me the key limiting factor is space. I can spread out several sheets over the table and have various bits and pieces directly visible. I cannot do ...
quid♦
- 7,652
10
votes
What will my academic path look like after testing out of high school math classes?
So you dual enroll at the community college while you're in high school, and you finish up in two more years. While you're at it, consider some computer science courses. Also, physics is a lovely ...
- 20.1k
10
votes
Accepted
The Interleaving Effect: How widely is this used?
In an answer to question 2, a few references I am familiar with are brought up at https://www.learningscientists.org/blog/2016/8/11-1. I was made aware of interleaving through this website. I will ...
- 3,996
9
votes
How to effectively internalize math?
This is an excellent question. Some good advice on this can be found in the writing of Bill Thurston, some of which I have posted in an answer to this question on Math Overflow.
The opening of the ...
- 6,133
9
votes
How does a student learn to 'dig behind the scenes' or 'feel' math like a Fields Medallist?
This question makes me think of the James Gleick quote on two kinds of genius:
"There are two kinds of geniuses: the 'ordinary' and the 'magicians'. An ordinary genius is a fellow whom you and I ...
- 1,346
9
votes
Is it too late for me to start learning mathematics?
No, it is not too late.
Not even close.
I failed at my first attempt at college, went back at 28, initially only part-time, and eventually ended up with bachelors degrees in math, physics, and CS. ...
- 221
9
votes
Self-study: how much should we try to figure out material on our own before studying from a textbook?
My advice (IN GENERAL) is to follow the book VERY explicitly and closely. You still should be doing lots of active things, not just "reading". But use the book as a scaffold. In self ...
- 121
9
votes
How long would it take someone to master the topics in the book "Book of Proof" by Hammack and similar?
(I had tried to add a clarifying comment to @AlexanderWoo's good answer, but it was mysteriously deleted.)
My point was, and is, that it is not constructive to think of "proofs" as a thing ...
- 14.2k
9
votes
How can I internalize solutions/proofs to theorems and exercises?
The main intuition behind the proof is that you are trying to obtain an equality of the form $\sqrt{x} = r'$, with $r' \in \mathbb{Q}$, because we known how to disprove that one.
The intuition behind ...
- 407
Only top scored, non community-wiki answers of a minimum length are eligible