Questions tagged [self-learning]

The process of studying mathematics without formal instruction. Don't use this tag just because you were self-studying when you came across the mathematical question you're asking; it is only for when the fact that you're self-studying is what your question is about.

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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 through books to find [the best source]". It…
Alex Youcis
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On "familiarity" (or How to avoid "going down the Math Rabbit Hole"?)

Anyone trying to learn mathematics on his/her own has had the experience of "going down the Math Rabbit Hole." For example, suppose you come across the novel term vector space, and want to learn more about it. You look up various definitions, and…
kjo
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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 time. In most areas, there's a "cut off age" to be…
Thomas Nesbitt
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How do you revise material that you already half-know, without getting bored and demotivated?

Mathematics inevitably involves a lot of self-teaching; if you're just planning to sit there and wait for the lecturer to introduce you to important ideas, you probably need to find yourself another career. So, like a lot people here, I try to…
goblin GONE
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What's the point in being a "skeptical" learner

I have a big problem: When I read any mathematical text I'm very skeptical. I feel the need to check every detail of proofs and I ask myself very dumb questions like the following: "is the map well defined?", "is the definition independent from the…
Dubious
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Why is learning modern algebraic geometry 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 strong point of modern algebraic geometry. I'm reading…
Dubious
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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 advisability of participating, the career…
Potato
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A good way to retain mathematical understanding?

What is a good way to remember math concepts/definitions and commit them to long term memory? Background: In my current situation, I'm at an undergraduate institution where I have to take a lot of core classes and easy math classes because there are…
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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, however, the self written syllabus was not self study…
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Does notation ever become "easier"?

I'm in my first semester of college going for a math major and it's pretty great. I'm doing well, however, there seems to be huge gap between how difficult /complex an idea is and how convoluted it is presented. Let me make an example: In Analysis…
Jonathan
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Self-studying real analysis — Tao or Rudin?

The reference requests for analysis books have become so numerous as to blot out any usefulness they could conceivably have had. So here comes another one. Recently I've began to learn real analysis via Rudin. I would do all the exercises, and if I…
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A path to truly understanding probability and statistics

I'm embarrassed to say that I have a PhD and hold an asst professorship, but get tripped up when reading statistics research. I am in a field of Business that is similar to IO Psychology or Social Psych. I spend too much time reading applied stats…
user27634
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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 studies -- sequence two of Calculus -- but what I'm…
user24383
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Why can't you pick socks using coin flips?

I'm teaching myself axiomatic set theory and I'm having some trouble getting my head around the axiom of choice. I (think I) understand what the axiom says, but I don't get why it is so 'contentious', which probably means I haven't yet digested it…
MGA
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Difference between continuity and uniform continuity

I understand the geometric differences between continuity and uniform continuity, but I don't quite see how the differences between those two are apparent from their definitions. For example, my book defines continuity as: Definition 4.3.1. A…
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