Questions tagged [self-learning]

Questions about how someone learns on their his or her own, outside of traditional classroom environments.

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35
votes
5answers
2k views

Effects of early study of advanced books

Context: There was recently a question on Math.SE: Inferior to Other Younger and Brighter Kids which starts as follows: I'm a high school student (Junior/Grade 11) and I'm currently studying ...
22
votes
4answers
2k views

Lesson plan to self-teach real analysis to student with comp-sci background

For my background, I'm a software engineer currently studying for his master's degree in information security. But when that's all done, I plan on going back to mathematics to keep me busy. But with ...
17
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4answers
575 views

Inquiry about my note-taking skill

I am a rising college junior in US with a major in mathematics. I recently noticed a problem in my note-taking skill in the mathematics, both from the textbooks and lectures. When I was a ...
17
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3answers
6k views

Learning Mathematics with the aid of spaced repetition systems

I am currently self-studying, so I learn using a textbook which I work through in a linear fashion. As I am introduced to new concepts I ask myself questions and I attempt to answer these questions ...
16
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2answers
920 views

Why do most of the books in mathematics not include answers?

I am currently going through the Topics in Algebra by I.N. Herstein. The problems are pretty good, but there are no answers. The same is the case with Mathematical Analysis by Rudin. Why is this? ...
16
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5answers
408 views

How do you revise?

I'm not too sure if this is the right place for my question, but I couldn't think of anywhere more suited. I am a first year university Math student, I am currently revising for six end of year ...
15
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3answers
1k views

Are there technique to help with poor recall?

Let's be clear from the start - I'm NOT a maths educator. I have a reasonable aptitude for maths: I've passed my high-school level exams in the subject, taken a life science degree and gone on to ...
15
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4answers
523 views

How to learn math from textbooks in the right way?

I am a freshman studying math. Everytime I learn Mathematics, I do it the slow-way. I tend to read the definitions until I make sense of what is written in the texts. I can spend a whole day trying ...
15
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2answers
486 views

Why are hand waving arguments made in textbooks of undergraduate analysis and how should readers deal with them?

Having read several undergraduate textbooks in complex analysis (Stein-Shakarchi, Gameline, etc.), I find that some "hand-waving" arguments are frequently used. An example (the proof of the Cauchy ...
15
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3answers
681 views

Is it natural for self-learners to forget most proofs of the theorems they learn?

When I read a theorem and read its proof and fully understand it, am I supposed to know the proof even after a long time or is it natural to forget the it? I ask this question as I'm a self learner ...
14
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9answers
13k views

Is it too late for me to start learning mathematics?

I am 26 now. I left study after completing school. Now I am thinking of doing a Bachelor's degree in mathematics. I purchased a basic Calculus book and I found it interesting. So I took some advice ...
14
votes
4answers
331 views

Without a constraint of time, is self-study with math textbooks better than college courses?

This question is about mathematics only. My forethought is that courses are usually based on textbooks, but they have less content than the textbooks. There are less problem sets, and chapters are ...
14
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1answer
889 views

Proving theorems on one's own: how long should one persist?

I've recently started learning linear algebra on my own. I always try to prove the theorems I encounter by myself, without looking at the book (only to check if my proof is correct), because I found ...
13
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4answers
583 views

How does a student learn to 'dig behind the scenes' or 'feel' math like a Fields Medallist?

Source 1: Siobhan Roberts, Mathematical Beauty: A Q&A with Fields Medalist Michael Atiyah, Quanta Magazine, 2016/3/9. Is there one big question that has always guided you? I always want ...
13
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2answers
957 views

How to effectively internalize math?

Terrence Tao commented of internalizing [here: https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/ ] "It is true that some mathematicians can be vastly more ...
12
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8answers
2k views

What things should one know in order to enjoy their undergraduate degree?

From looking at undergraduate mathematics programmes it's quite apparent that mathematics degrees are demanding, one could even say the work load is gruelling. However I'm certain that there are ...
11
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3answers
291 views

How to write a book for someone who learns math alone?

I'm thinking of general rules on how to write mathematics books to people that teach themselves, and are quite alone with only the single aid of the printed book (no YouTube, no software, and so on). ...
11
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2answers
299 views

How to stay interested in less-tangible math

I've graduated high school and I am joining college soon. The problem with me is that I'm not finding less tangible math interesting at all. Some people find abstract math to be very beautiful, and I'...
11
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2answers
188 views

The Use of Sound in Mathematics

I asked this question on Mathematics Stack Exchange first. It was well-received, but put on hold as off-topic. This site seems more appropriate. Here it is verbatim. I'm not sure that this question ...
10
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4answers
1k views

Mathematical concepts and techniques that **pay off the most**? [closed]

There is a smart way of learning, and it consists in first finding out what are the most valuable pieces of knowledge to acquire. The ones that will give you the highest value for your investment in ...
10
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5answers
1k views

I wanna learn math! [closed]

I'm a 25 years old guy and I wanna learn math. I haven't had a good relationship with them until now. My background is that I know how to add, subtract and multiply. In theory I also know how to ...
10
votes
4answers
8k views

Is it possible to improve logical thinking and problem solving abilities?

I'm from Italy and I'm 13 years old. I'm good in Math and I'm good in languages (I know Italian, English and Russian and I think I'm good at them). I'm a programmer and I know HTML, CSS, JS and Python....
9
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4answers
246 views

Is it better to study in groups or by yourself?

As the title says, do you learn math faster by working on problems in groups, where you can discuss your solutions or by doing it all by yourself? I can't see any advantage of working in groups ...
9
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3answers
3k views

What is abstraction and generalization ?

Mathematicians does something when they mean by doing "abstraction" or "generalization". I can't exactly decipher what they mean, but I suppose i. Abstraction is of finding patterns from some objects(...
9
votes
4answers
452 views

How can I implement the principles of deliberate practise in my mathematical studies?

I have been reading a lot of books about deliberate practise recently like Angela Duckworth's "Grit", "Talent is Overrated" - Colvin and "Peak" - Ericsson and Pool. I want to apply these principles. ...
9
votes
1answer
209 views

How can I improve my concept map?

I've decided to create a concept map of a chapter I covered in a textbook, it's about basic set notation. What I want is suggestions on how to improve the presentation of the map. It seems quite ...
8
votes
5answers
741 views

Electronic devices to replace pencil and paper

My question is similar to this one: https://math.stackexchange.com/questions/1833459/math-without-pencil-and-paper Except I'm not physically disabled. Pencil and paper have been used for centuries to ...
8
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4answers
512 views

I'm a self learner, what are some ways that I can compensate for the lack of a study group?

I am teaching myself mathematics, and I don't really know anyone who is interested in mathematics. I find that the hardest part about teaching myself is that I am lacking the social aspect of being in ...
8
votes
2answers
301 views

Learning Math like Euclid

I'm posting this here as it's off-topic for the Math stack exchange, and I'm hoping there will be some educators here that can point me in the right direction. I enjoyed watching the YouTube series ...
8
votes
3answers
1k views

Self-study Linear Algebra textbook for Machine Learning and Statistics

I am looking for a good linear/matrix algebra textbook, suitable for self-study, that covers topics relevant to statistics and machine learning. I have access to ...
8
votes
1answer
228 views

How to study for university level math olympiads and competitions?

I participated in some high-school-level math competitions, but I never invested much of my time in them at that time, something that I regret immensely. Now that I am an engineering grad student, I ...
8
votes
1answer
126 views

What specifically should I include to my self study notes?

I am a high school student who will be entering college in one and a half year (It is so long though). For me, Mathematics primarily means Number Theory. My interest in Number Theory always motivates ...
7
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5answers
3k views

Is Linear Algebra Done Right too much for a beginner?

I have asked in Mathematics stackexchange, but I think asking here is more appropriate. I am self studying the book Linear Algebra Done Right by Axler. That's how I started using the great Stack ...
7
votes
2answers
241 views

Looking for a progression of learning to get back my math skills

I am an professional that has rarely used math over the last 20 years. Well, anything outside a spreadsheet and basic formulas. My son, who is quite bright, is now getting to an age where I am ...
7
votes
1answer
695 views

Curriculum for self taught Maths degree

Someone has made this template for a self taught CS degree. I am a CS grad and found it quite good. As I don't have much idea about a proper pathway to learn degree level mathematics in my own. Please ...
7
votes
5answers
207 views

About visual ways of teaching Math

There is a concept called 'Infographics' that uses lots of colourful diagrams and graphs and artwork to visually depict some set of concepts and tries to explain the ideas through pictures. I ...
7
votes
2answers
133 views

Summer Mathematics Workbooks for Elementary and Middle School

There is a wide variety of summer mathematics workbooks available for students in elementary and middle school (see here). With summer coming up, these books seem to be available everywhere. Thus my ...
7
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2answers
213 views

“Personalized System of Instruction” (PSI) vs. “Individually Prescribed Instruction” (IPI)

This question may be a bit overly-broad for MESE, but I am hoping to find some responses that can help to fill in my understanding of two similar forms of instruction that had their heyday in the ...
6
votes
2answers
279 views

How can I improve my problem solving/critical thinking skills and learn higher math?

I'm a rising sophomore in high school. So far, I've taken Algebra One, Two, and Geometry in school. I want to learn higher math such as precalculus/trigonometry, calculus, linear algebra, and more, so ...
6
votes
2answers
326 views

A Plan for a Treatise Study of the Classical Theory of PDEs

The Plan In the study of any special issue in mathematics, two things may be of importance, namely, subjects and order of them. I just wrote down a plan to study the theory of partial differential ...
6
votes
4answers
260 views

Fun resources and games for advanced elementary school math students?

My younger cousin (2nd grade USA) is advancing very quickly in his current math class. The school does not have much to support him in moving ahead in the material. What websites (preferably game or ...
6
votes
0answers
144 views

Learning math historically

What is meant by learning math historically (NOT learning math history only, but learning math with a historical development perspective)? I've seen some sources that to learn a math topic X, you need ...
5
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5answers
6k views

Is Applied Math easier than Pure Math? [closed]

Because I'm OK at Applied Math but failed Pure Math two times, I asked my instructors and a brilliant friend studying the undergraduate Math Tripos at the University of Cambridge for advice. They all ...
5
votes
2answers
104 views

What are the questions one should ask of oneself in trying to understand definitions and lemmas? [closed]

Definition (Finite series). Let $m,n$ be integers, and let $(a_i)_{i=m}^{n}$ be a finite sequence of real numbers, assigning a real nmber $a_i$ to each integer $i$ between $m$ and $n$ inclusive. Then ...
5
votes
2answers
118 views

Forming a Study Model for a Self-Study Beginner

I am very new to this platform so I may have misunderstood the intent of this site, or might seem a bit off, but please bear with me because I know what I want for certain. I always wanted to study ...
5
votes
2answers
128 views

Great Worked-out examples books for Mathematics

I'm studying Mathematics in the UK. Back in Italy, where I am from worked-out problems books are very popular in mathematics and they are always recommended or compulsory at university. Going through ...
5
votes
1answer
155 views

Are there any tips for studying an MSc Pure Mathematics online?

Course background I am planning on studying MSc Mathematics through the UK's Open University (distance learning). The course comprises of pure mathematics (number theory, complex analysis, coding ...
5
votes
2answers
473 views

Inquiry about My Self-Study Plan for Real Analysis (for my research and self-enrichment)

I am a college sophomore in US with a major in mathematics and an aspiring mathematician in the computation theory and cryptography. I recently got an undergraduate research in the computation theory, ...
5
votes
1answer
205 views

Self Teaching Theory for Olympiad. Need advice

(Cross-posted in MSE 1301476.) I want to start to do Olympiad type questions but have absolutely no knowledge on how to solve these apart from my school curriculum. I'm 16 but know maths up to the 18 ...
5
votes
2answers
156 views

Are there any math certificates/qualifications on high school maths that you can do after high school?

I hope this is a good place to ask the question. My issue is that I have finished high school a number of years ago, and although I did some (non-advanced) math courses then, I did not do an exam in ...