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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 ...
Gerald Edgar's user avatar
  • 7,607
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 ...
Dan Fox's user avatar
  • 5,869
20 votes
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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 ...
Steve's user avatar
  • 1,604
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 ...
Steven Gubkin's user avatar
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 ...
Joseph O'Rourke's user avatar
17 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 ...
Amir Asghari's user avatar
  • 4,438
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 ...
Benoît Kloeckner's user avatar
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) ...
Opal E's user avatar
  • 4,043
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 ...
tbrookside's user avatar
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 ...
JRN's user avatar
  • 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 ...
fedja's user avatar
  • 3,869
13 votes
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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 ...
Andrew's user avatar
  • 1,786
13 votes
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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 ...
Saikat's user avatar
  • 398
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. ...
guest's user avatar
  • 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 ...
Alexander Woo's user avatar
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 ...
paul garrett's user avatar
  • 14.7k
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 ...
epsilon's user avatar
  • 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's user avatar
  • 7,712
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 ...
Sue VanHattum's user avatar
  • 20.8k
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 ...
Opal E's user avatar
  • 4,043
10 votes

Why don't these 'solve in 2 sec' tricks work?

I think the mistake here is using videos to learn skills. I suggest you obtain a text which suits you, sit down on a hard chair (not a comfortable arm chair), at a table, with a pen and a piece of ...
mdewey's user avatar
  • 311
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 ...
Jon Bannon's user avatar
  • 6,173
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 ...
Syntax Junkie's user avatar
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. ...
ShadSterling's user avatar
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 ...
guest's user avatar
  • 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 ...
paul garrett's user avatar
  • 14.7k

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