Questions tagged [self-learning]

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

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How to study for a mathematics undergraduate entrance examination?

TL;DR: Tell me which topics should i study the most, based on this three tests: Mathematics (A): 2020 2019 2018 This question may sound a bit weird, since the natural answer would be "study ...
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3 votes
2 answers
199 views

How to understand the book and the material to the deepest possible level?

I'm a first year mathematics major and I have a problem with my learning process. In my university, I only have books and questions that the university published, so I have to learn the most of the ...
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0 votes
1 answer
118 views

Abstract math, examples and understanding or visualising

After reading some papers about special kinds of algebras and rings like Gorenstein rings, Dickson algebras, Cayley-Dickson construction, i want to ask do examples of general abstract objects in math ...
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  • 137
0 votes
0 answers
73 views

Problem solving approach to learning and psychology

I try to have a problem solving approach to learning math. What i mean by this is if someone sets some questions or problems regarding the material i am reading how should i answer or what questions ...
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  • 137
4 votes
2 answers
187 views

How do you study subjects you're not that interested in

I'm an undergraduate who doesn't find analysis particularly interesting, but I'm taking a calculus on manifolds course next semester, so I'm reviewing measure and integration theory since my grasp on ...
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  • 141
1 vote
1 answer
161 views

Math outside of undergraduate studies and proofs

I read sometimes mathematical works of others outside my undergraduate studies. I think i can not follow the understanding of the proofs of theorems sometimes. What should i do? Should i read other ...
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  • 137
1 vote
1 answer
145 views

Best books for mathematical statistics self-study?

I'm hoping to start a masters in mathematics in the fall, and am hoping to find a good book on mathematical statistics to study so that I'll be able to take graduate level mathematical statistics once ...
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5 votes
4 answers
1k views

How long would it take someone to master the topics in the book "Book of Proof" by Hammack and similar?

If someone never had any experience with mathematical proofs and had only classes like Calc I-III (which he passed, without paying any attention to the proofs present in the textbooks), how long would ...
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  • 53
3 votes
0 answers
176 views

Doctorate and examples of difficult solved problems

Okay. My questions are: How do some people do doctorates in mathematics and spend so much time like three to six years trying to answer one or two open problems? How do they have the patience, ...
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  • 137
2 votes
1 answer
355 views

Solving math problems and learning

Should i solve math problems by writing the answers to papers or notebooks with pencils or should i try solving them in my head at undergraduate studies at university? Also, sometimes after learning ...
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  • 137
2 votes
0 answers
95 views

How to make progress as an independent student?

In recent times, I have been studying mathematics (topics related to mathematical logic, more specifically) independently and I feel a great deal of passion about it. However, although I have made ...
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  • 121
12 votes
6 answers
5k views

Dealing with disagreeable students and not compromising

I act as a tutor sometimes for students who are self-studying undergraduate-level math. Most of the students have already earned an undergraduate degree in something and some of the students are PhDs ...
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  • 123
-3 votes
1 answer
74 views

Abstract math and making proofs

What is abstract math about? I think we can not visualise probably what we read. Or can we? I am talking about the theorems, definitions and proofs in areas of math like Riemannian geometry, ...
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  • 137
1 vote
1 answer
124 views

Analysis of math and its elements

Can anything in math ultimately be analysed into symbols, equations, formulas, with as exeption perhaps the Euclidean geometry we know with triangles,straight lines etc? Can also proofs, definitions ...
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  • 137
5 votes
5 answers
2k views

Is Calculus Made Easy by Silvanus P. Thompson a good book for first-time calculus learners?

Specifically the one updated by Martin Gardner. I'm not studying as part of a high school or college course (I, in the near future, will though) just as a personal project.
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0 votes
3 answers
186 views

Highly intuitive yet comprehensive and easily readable (student friendly) book on linear algebra which do not focus much on applications, just basics

I came to know about Gilbert Strang's two books, "Introduction to Linear Algebra" and "Linear Algebra and its Applications". The first is the one used as the text in the 18.06 ...
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4 votes
2 answers
185 views

Study multiple subjects at the same time or deep dive into one?

I want to learn probability theory and discrete math. However, I also need to brush up on computational calculus and linear algebra. Would you recommend only studying one subject at a more intense ...
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2 votes
1 answer
167 views

An intuitive (non rigorous) text book on graph theory which is student friendly with vivid illustrations

Background Hello, I am an undergraduate in CS. I would like to study Graph Theory on my own (self-study) for a competitive examination (named GATE). It is an examination for undergraduates and as such,...
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1 vote
2 answers
228 views

Should I do all the proof practice problems in How to Prove It, an intro to proofs book?

Like the title says. I am self studying intro to proofs(How to prove it by velleman) so I can start an introduction to analysis. I am wondering if I should complete all the exercises in the textbook(...
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1 vote
0 answers
68 views

Is there any video lecture series on (UG level) graph theory (might not be specific on any books) but the video/content quality is like that of MIT?

Previously I had asked a question about something similar, but more constrained. But now I ask something more general. I just got hold of the Linear Algebra by Prof Gilbert of MIT and they are just ...
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5 votes
0 answers
224 views

Self study curriculum for a working professional who is enthusiastic about mathematics

I had some mathematics education during my high school and Electrical Engineering studies, but I never used any of them during my career as a software professional. Now I am again coming across Linear ...
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  • 151
5 votes
2 answers
373 views

How to reduce tilting when going over drills?

Tilt originated as a poker term for a state of mental or emotional confusion or frustration in which a player adopts a less than optimal strategy, usually resulting in the player becoming over-...
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5 votes
1 answer
263 views

Is there any video lecture series on Graph Theory which uses "Introduction to Graph Theory" by Douglas West? as the text

I am interested in learning graph theory, and from many resources I came to know that Douglas West's Introduction to Graph Theory is a good textbook. But since I am doing self-study, it is at times ...
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3 votes
1 answer
146 views

Self-study: how much should we try to figure out material on our own before studying from a textbook?

We can spend a lot of time thinking of material which we have basics for without ever studying the original ideas from a textbook, for example, once one has finished regular derivatives, it is pretty ...
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1 vote
1 answer
181 views

Mnemonics to correlate the definition of "asymmetric relation" and "antisymmetric relation" with the terms [closed]

The definitions from Kenneth Rosen textbook are as : A relation $R$ on a set $A$ such that for all $a,b ∈ A$ ,if $(a,b) ∈ R$ and $(b,a) ∈ R$,then $a=b$ is called antisymmetric. A relation $R$ on a ...
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7 votes
4 answers
485 views

Statistics, for the mathematically rigorous

I don't know where I can find a rigorous statistics course or textbook. The closest thing I can think of is measure-theoretic probability theory, but I wouldn't really call that "statistics"....
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3 votes
2 answers
289 views

Looking for a rigorous middle school self-study math course

My son is in 5th grade (US) and since he is doing remote learning, we have been doing a lot of topics in pre-algebra just using worksheets. I'd like to start him on a formal middle school curriculum, ...
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  • 363
1 vote
1 answer
120 views

Questions relating to inclusion-exclusion principle [closed]

Today I came across the inclusion-exclusion principle for the first time. I believe I have understood it, however when I tried solving some questions on it, I got severely stuck. I couldn't solve any ...
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  • 113
2 votes
2 answers
185 views

What should be the bare minimum wrong answer threshold when self studying a math text?

I'm currently self studying a Linear Algebra text book due to the fact that I forgot the vast majority of it since I took the course 10 years ago. My general strategy is to take every single example, ...
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  • 23
1 vote
2 answers
183 views

Where can I find a good course on tensor calculus not focused on applications and physics?

Where can I find a good course on tensor/ricci calculus not focused on applications and physics? I've been running into lots of tensor-theoretic stuff in differential geometry, so I don't know if ...
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3 votes
1 answer
183 views

Learning strategies for high volume/pace learning?

Background: I am a graduate student in a mid-tier U.S. university, and I am struggling. I feel like I during my undergrad, I haven't aquired the neccesary skills to keep up with the high volume/pace ...
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7 votes
3 answers
893 views

How to structure undergraduate level private lessons?

I'm on a semester break and thankfully I was recently provided with an opportunity to hire any private teacher I like to learn even more math while on break. However, I don't really know how to ...
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1 vote
0 answers
170 views

Would the SMSG textbooks provide adequate extracurricular study?

Context: I'm a Grade 11 IBDP student and very fond of math. Assuming that I get the spare time to self-study material alongside the syllabus, I wish to spend it constructively (the only step I've ...
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  • 111
9 votes
2 answers
572 views

Fear of notation and hazily-appeared writing in Mathematics

I am looking for literature related to fear of notation in mathematics. It is even heard that the font size and font type make a reader reluctant to study mathematical literature, often lecture notes,...
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5 votes
2 answers
216 views

Introductory book or other resource on $p$-adic numbers/number theory/analysis

I am having problems understanding $p$-adic numbers/$p$-adic number theory/$p$-adic analysis. I have tried some notes on the internet, but these notes were not helpful. Can anyone suggest a book, ...
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21 votes
8 answers
6k views

How do I learn advanced mathematics without forgetting?

I am pursuing mathematics through distance education and I find that it takes me a long time to understand the concepts (e.g. sigma fields, measure theory, connected topological spaces, etc.). After I ...
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1 vote
2 answers
191 views

What are the resources to learn prerequisite knowledge to latter High school and undergrad prep textbooks?

I use textbook study and am planning on studying Spivak's Calculus, Mathematics It's Content, Methods, and Meaning, How to Prove it by Velleman, etc. However, I'm worried I lack the prerequisite ...
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1 vote
2 answers
265 views

Future way of learning mathematics (towards graduate level)

Recently, there is an idea sparkling out from my mind due to the COVID-19 outbreak. In the past, we typically attend a course, complete homework and assignment, then finish the semester with a final ...
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  • 119
3 votes
1 answer
130 views

Refreshing math knowledge

How do I refresh advanced math I learned at a graduate level? I once was able to do the full solution of a particle in a parabolic well and other advanced math, however 20 years later I'm struggling ...
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  • 141
6 votes
3 answers
1k views

Looking for a HIERARCHY of math subjects

If you were to "map" mathematics onto a tree structure where the top is "Mathematics", and then below it the different branches, then sub-branches, etc. What do you suggest is a good structure, for ...
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4 votes
1 answer
332 views

Is there a 'statistics theory' course plan for practitioners?

My job is starting to have me delve into categories that require things like regression analyses on data sets, essentially I'm being introduced to "Data Science" type material. Coming from a ...
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  • 363
5 votes
3 answers
199 views

Can you ace one branch of math, while bumbling another branch? [closed]

This r/math post spurred this question. To concretize the meaning of "ace", assume success means earning professorial tenure at a Top 100 world university. your liked stronger branch doesn't exactly ...
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20 votes
5 answers
3k views

What does it take to find a good math book for self study?

I'm 20 and I never learned math properly in my highschool. I found my interest in math last year and I've been searching for books since then. I tried Khan academy but I have difficulty paying ...
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6 votes
4 answers
2k views

What will my academic path look like after testing out of high school math classes?

I am currently a 15-year-old in the 9th grade, and I am studying to test out all of my high school math classes, which is something I didn't realize I could do in the 8th grade and would have if I had....
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6 votes
2 answers
777 views

Textbooks for an independent study in point-set topology

I am planning to sign up for an undergraduate "course" in point-set topology next semester. It is really an "independent study" in that this course will not have any lectures. It will just have two ...
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-1 votes
1 answer
113 views

How to start tackling a 200 page big script? [closed]

I am really not sure how to tackle a 200 page huge script with a lot of information about the topic linear algebra. Writing down the definitions would not make sense in my opinion, because if I want ...
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3 votes
1 answer
114 views

Mental/"Paper and Pencil" Arithmetic

Recently, I was watching this video and I began thinking about how much my arithmetic skills have declined in recent years due to over reliance of calculators in upper year (high school) math courses. ...
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3 votes
4 answers
308 views

Best resources for probability/statistics textbooks

I'm looking for a good textbook introduction to probability/statistics that a first/second year undergrad math student could use! I'd like a book that emphasizes theory over procedure. I'd prefer an ...
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  • 496
12 votes
5 answers
919 views

About the effectiveness of self-studying maths (compared with other subjects)

An important feature of mathematics is that it is relatively easy (compare to many other subjects) to know whether or not one's understanding is correct. There are plenty of ways to check: one can ...
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  • 1,575
2 votes
0 answers
109 views

Is There Book on Collection of Theorems? [closed]

For example, there is a book titled "Synopsis of Elementary Results in Pure and Applied Mathematics: Containing Propositions, Formulae, And Methods Of Analysis, With Abridged Demonstrations" (...
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