Skip to main content

Questions tagged [self-learning]

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

Filter by
Sorted by
Tagged with
0 votes
0 answers
53 views

Wanting explore mathematics [closed]

Hi everyone I am student. Since few months I am using discord to improve my mathematics understanding. It helps a lot so I am here to ask I know there are many good discord servers but I don't why I ...
2 votes
2 answers
1k views

Is Morris Kline's 'Calculus: An Intuitive and Physical Approach' a Good Book to Learn Calculus From?

Would I have to read a standard textbook in addition — i.e. Stewart, etc. — or would Kline's Calculus: an Intuitive and Physical Approach be sufficient? My interest is in applications: dynamical ...
41 votes
6 answers
3k 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 ...
4 votes
4 answers
495 views

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

I am a med student and left maths in 10th class. Log and antilog and calculus etc are taught in 11th and 12th. Every time I have any exam that includes usage of these topics I go to Youtube and search ...
2 votes
1 answer
213 views

How to grade a flipped class to improve participation and attendance

A flipped service course for me is an arrangement where videos are online and on-campus class time is used for problem solving by students. I usually have a homework due date the day after the ...
5 votes
2 answers
447 views

Overcoming Dyslexia and Building Intuition

I am 25 and have been studying mathematics on my own for several years, but I am still between the middle and high school levels. My main weakness is my dyslexia. I sometimes forget words or confuse ...
-4 votes
1 answer
107 views

Condense a logistic function around its midpoint [closed]

I have a function $$ f(x) = {1 \over 1 + e^{-k(x-0.5)}} $$ that plots a logistic curve that is symmetric around the point $0.5 / 0.5$. $k$ defines the steepness of the curve. I would now like to add ...
5 votes
2 answers
503 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 ...
3 votes
3 answers
256 views

Relearning math after long COVID using AoPS or developmental math textbooks?

This is a little bit of a niche topic. I've dealt with a pretty bad dose of long COVID that has caused some serious gaps in my mathematics (basically causing terrible arithmetic skills and a really ...
8 votes
5 answers
2k views

Should I really just "shut up and calculate"? On learning at a good pace without sacrificing rigour

This question is about getting realistic expectations for how a university student actually does and should learn maths. I'm becoming increasingly suspicious that my approach is detrimental, but I don'...
11 votes
4 answers
624 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'...
15 votes
2 answers
1k 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, Gamelin, etc.), I find that some "hand-waving" arguments are frequently used. An example (the proof of the ...
-1 votes
1 answer
240 views

Learning, exams, math degree

I have only passed the one fourth of my courses so far, which means like one year of the maths undergraduate studies. I live in a different place from where the university i study at is and try to ...
2 votes
1 answer
187 views

Rediscovering euqation of line [closed]

I am studying (self learner) linear equations/equation of line and my idea is to discover the equations myself rather than try and understand ready-made equations available in text books. I am using X-...
-2 votes
1 answer
124 views

On doing scientific research [closed]

What I want to ask is: can I use the results of others when doing scientific research, whether it is math, physics or other science, without trying to prove them myself or try to verify them? For ...
4 votes
1 answer
94 views

Research Into Self-Learning at Undergraduate Level and Above

My motivation for this question is personal. I'm a software engineer and I study mathematical logic as a hobby. Subjectively, it feels like I make the most progress after asking a question on the Math ...
7 votes
3 answers
766 views

How can I internalize solutions/proofs to theorems and exercises?

In particular, my question is about abstract mathematics such as group theory, analysis, topology, etc. where most textbooks are filled with exercises which require proof, and how to go about ...
9 votes
3 answers
344 views

How do you know when a textbook is too difficult for you?

Not sure if this is more appropriate for here or for Math.SE, but here goes: How does one who is self-studying mathematics determine if a textbook is too hard for you? Math is hard in general, but ...
5 votes
4 answers
528 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, ...
11 votes
4 answers
494 views

For students who don't have instant recall with basic arithmetic, should I be stubborn about training them to have instant recall before moving on?

I'm a maths tutor, and my students/tutees are aged $11 - 18.$ Obviously I have limited time with students, usually one hour per week. Moreover, if parents don't see improvement over a year or two they ...
9 votes
1 answer
368 views

The Interleaving Effect: How widely is this used?

I came across the idea of mixed up practice in Benedict Carey's book, How We Learn, in a chapter on the benefits of interleaving, particularly for learning Maths. For instance, in "blocked ...
0 votes
1 answer
122 views

Problem solving and independent scientific research [closed]

Is analogy a way to solve problems when doing research in math and physics? Is it very important?How important is it? Could i do independent scientific research on some open problems perhaps having ...
9 votes
6 answers
1k 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"....
3 votes
3 answers
859 views

Walter Warwick Sawyer: How has reading his works changed your learning or teaching? [closed]

I recently worked my way through Walter Warwick Sawyer's book, Mathematician's Delight, which has opened my eyes to Maths. I used to fear maths, feeling I was incapable. Sawyer (among other authors) ...
3 votes
2 answers
172 views

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 ...
3 votes
2 answers
291 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 ...
7 votes
1 answer
285 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 ...
5 votes
4 answers
2k 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 ...
0 votes
1 answer
225 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 ...
0 votes
0 answers
97 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 ...
4 votes
2 answers
224 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 ...
1 vote
1 answer
205 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 ...
1 vote
1 answer
551 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 ...
2 votes
1 answer
370 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 ...
2 votes
0 answers
99 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 ...
6 votes
3 answers
199 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 ...
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 ...
-3 votes
1 answer
89 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, ...
1 vote
1 answer
128 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 ...
5 votes
5 answers
3k 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.
4 votes
1 answer
359 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 ...
0 votes
3 answers
306 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 ...
6 votes
2 answers
972 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 ...
4 votes
2 answers
630 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 ...
21 votes
8 answers
7k 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 ...
5 votes
0 answers
354 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 ...
1 vote
1 answer
230 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,...
6 votes
4 answers
564 views

Source material to study number theory?

I don't know if this is the correct site to ask this question, but I felt it was off-topic on the Mathematics forum. I really like Number Theory and would like study some on my own. Which books should ...
12 votes
5 answers
1k 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 ...
1 vote
2 answers
433 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(...