Questions tagged [self-learning]

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

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3
votes
3answers
169 views

What kind of problem do you learn most from (hard problems or easy problems)?

I am curious if you guys learn more from Hard problems, or do you learn more from easy problems. I heard that you learn a lot more from doing harder problems, because you have to learn all of the ...
7
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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 ...
3
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1answer
122 views

Is there a rigrous and relatively complete book/lecture notes for selfstudying several variable calculus?

I would like to study university level mathematics on my own. I found rigorous books on single variable calculus and topology and learned those. But what would one recommend for several variable ...
3
votes
1answer
193 views

I want to learn how things function and continue my life work of learning

I am 37 years old and I have a mild learning difficulty. I never went to a special school, but yes, I got some help and I never got held back. I left my grades on borderline. I always loved to learn ...
5
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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 ...
4
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4answers
333 views

Best Way to Learn Trigonometry

What are the best resources to learn trigometry? I recently decided to pursue a BS in mathematics at uni. I used to fail all my math classes with D's or F's until I started teaching myself, and so far ...
14
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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 ...
2
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3answers
133 views

Self-Study of Calculus Two [closed]

I just finished self study of Calculus One and I am looking to begin Calculus Two. Is there a free platform that can help me with this?
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'...
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 ...
2
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5answers
494 views

Can I succeed in university math, if I loathe physics?

I hope never to study physics. Can I still ace undergraduate and PhD math? Or ought I major in something else? Background I finish high school in 2019, and I'm mulling majoring in math/statistics. ...
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 ...
15
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3answers
679 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 ...
-2
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1answer
138 views

Could students be taught the concept of rational numbers the same way as in the Formal construction section of the Wikipedia article rational number?

Link to article cited in title, Wikipedia rational number. According to this answer, some students 14-18 are still struggling to understand fractions. Maybe some students know how to perform the ...
3
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2answers
196 views

Selected Exercise for Linear Algebra Done Right Edition 3 [closed]

I am self learning the book Linear Algebra Done Right. I tried to complete all exercises in each chapter. I am currently at Chapter 3 and found that it is not feasible to complete all of the exercises....
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 ...
22
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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 ...
14
votes
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 ...
15
votes
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 ...
3
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0answers
157 views

According to Nathan Jacobson, what is Intermediate Algebra and Advanced Algebra?

Nathan Jacobson's Basic Algebra I, II covers many topics in Algebra that is probably even beyond many pure mathematics full professor's scope of knowledge, unless the professor is specialised in ...
35
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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 ...
8
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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 ...
1
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1answer
128 views

When self teaching, should I learn set theory before continuing ap calculus?

I am studying ap calculus now, before I move onto differential equations etc., but the thing I am unsure of is, should I learn set theory before continuing on my ap calculus sections?
0
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2answers
105 views

Returning Student for STEM - Brush-Up Resources? [closed]

All, I am hoping to wade into an Electrical Engineering or Mechanical Engineering degree, but I have been out of college for almost 10 years. My last major exposure to math was good grades in ...
4
votes
1answer
237 views

How to become really interested in math [closed]

I'm a high school senior. What can I do to be really interested in mathematics ? I know some of my batch-mates (from meeting them at several math Olympiads) are like insanely good at math (know lots ...
7
votes
1answer
685 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 ...
3
votes
2answers
377 views

Why are proofs written in flowery language incomprehensible?

Let's take an example in Wu-Ki Tung, Group theory in physics: Theorem 3.4: Irreducible representations of any abelian group must be of dimension one. Proof: Let $U(G)$ be an irreducible ...
6
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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
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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 ...
3
votes
1answer
116 views

How can students self-learn creativity in math that “demand more than just deduction”? [closed]

From: Philip Johnson-Laird BA PhD Psychology (UCL), Stuart Professor of Psychology Emeritus at Princeton. (Author isn't a logician.) How We Reason (1st edn 2008). p. 112.   You might ...
15
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4answers
521 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 ...
-2
votes
3answers
319 views

Why's math more complicated to understand than philosophy? [closed]

Why's math more abstruse, perplexing than philosophy? This feels true, as intelligent laypeople can understand unsolved philosophy problems and competing possible solutions, but can't understand or ...
4
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5answers
671 views

Reading Your Algebra Book

An algebra book requires a different type of reading than a novel or a short story. Every sentence in a math book is full of information and logically linked to the surrounding sentences. You should ...
0
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1answer
104 views

Good Combination for Self Study for a Mathematical Novice

Hi There I am new to Mathematics Educators so please bear with me if my question is not up to mark? I am interested in mathematics and have gotten comfortable with basic proofs with Daniel J Velleman'...
2
votes
1answer
193 views

Ordered checklist for learning Mathematics for Data Science

I want to understand and teach Mathematics for Data Science. I know for Data Science I need to understand: Probability Statistics Linear Algebra Calculus But I want a quick refresh of everything ...
2
votes
1answer
224 views

Learning High School Geometry in Ten Days

I would like to attempt this, as I want to place out of geometry next year. It is imperative that I do it now. How should I go about doing this? I have a copy of Elementary Geometry for College ...
2
votes
1answer
110 views

books to teach K-12 math/science via real-world approach?

I volunteered abroad in rural Ethiopia and a village in a remote mountainous area of China. I plan to return to both places and teach for as long as I can make it work. I want to focus on STEM, but ...
13
votes
4answers
582 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 ...
2
votes
0answers
105 views

Strategies for learning proofs

What are the best methods for learning proofs? I'm tasked with learning two dozen proofs about the properties of continuous functions and real numbers in a week well enough to be able to present them. ...
7
votes
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 ...
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
5answers
736 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 ...
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 ...
9
votes
4answers
245 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 ...
11
votes
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). ...
9
votes
4answers
447 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. ...
16
votes
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? ...
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 ...
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 ...
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 ...