Questions tagged [self-learning]
Questions about how someone learns on their his or her own, outside of traditional classroom environments.
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0answers
94 views
I’m considering buying Art of Problem Solving. For those who read it, what’s your review of it? [closed]
As you know, Art of Problem Solving includes 11 books that comes with their solutions and they are PreAlgebra, Introduction to Algebra, Introduction to Counting and Probability, Introduction to ...
7
votes
1answer
179 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
287 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 ...
5
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0answers
127 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
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1answer
106 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 ...
4
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1answer
129 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 ...
2
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4answers
368 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. ...
-1
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3answers
278 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 ...
0
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1answer
92 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
155 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
204 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
99 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 ...
2
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0answers
89 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
142 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 ...
13
votes
1answer
285 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 ...
11
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3answers
259 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 ...
8
votes
2answers
242 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
499 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
116 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 ...
6
votes
2answers
228 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 ...
0
votes
1answer
77 views
How to explain inverse modulo? [closed]
Do you know a (simple) inverse modulo calculator somewhere on the Internet?
How to explain simply inverse modulo? (when the concept of modulo is already a bit known)
How to explain someone how to ...
9
votes
4answers
223 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 ...
4
votes
1answer
211 views
how to prove my 6th grade son knows algebra 1?
My son is taking pre-algebra in 6th grade. He mastered algebra 1 in detail more than what school can teach. How to prove to school that he mastered Algebra 1? He wants to start Algebra 2 in 7th grade. ...
1
vote
2answers
113 views
Complex numbers [closed]
I would like to learn the subject 'complex numbers'. My goal is to study this on my own. Are there any good tips, books, sites to study this?
8
votes
1answer
121 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 ...
13
votes
9answers
7k 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 ...
12
votes
4answers
495 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 ...
5
votes
2answers
142 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 ...
16
votes
4answers
438 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 ...
5
votes
2answers
116 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 ...
4
votes
5answers
628 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 ...
5
votes
0answers
181 views
How Can I Mitigate My Learning Disabilities And Improve My Abstract-Reasoning Abilities?
I am seeking advice for understanding how I can improve my abstract reasoning abilities. More specifically, I would like to understand how I can revise my reasoning abilities in mental areas such as ...
3
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1answer
168 views
Relearning Mathematics
During K12 I had problems understanding maths because in most cases I could not understand how it would be useful or what its applications are. I passed K12 maths mostly by memorizing the process to ...
9
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4answers
6k 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
votes
4answers
302 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.
...
4
votes
0answers
67 views
Accepted mathematical training methods?
I recently read the book "Peak: Secrets from the New Science of Expertise" by Karl Anders Ericsson and Robert Pool. Ericsson is a respected researcher in the field of expertise formation, this is why ...
7
votes
2answers
183 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
4answers
500 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 ...
9
votes
3answers
1k 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(...
4
votes
2answers
125 views
suggestion for probability and stats text to suit my learning style.
I am of a mature aged learner and want to learn probability and statistics at a senior high school (k12) and undergraduate level for my own general understanding. I have discovered in the past that I ...
9
votes
4answers
859 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 ...
13
votes
2answers
720 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 ...
10
votes
3answers
284 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). ...
4
votes
2answers
209 views
If you do not 'read A to Z', then how can you discover the idea? [closed]
The following is from an article in The New Yorker on Y. Zhang and his proof on gaps between primes:
Rutgers University Professor [Henryk] Iwaniec and his friend, John Friedlander, a professor at ...
1
vote
1answer
75 views
Moving lines in schematic diagrams
I am self-teaching myself precalculus.My biggest sticking point is to move lines within a diagram, especially, functions in the coordinated plane. For instance, doing horizontal and vertical shifts of ...
6
votes
2answers
303 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 ...
5
votes
2answers
101 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 ...
9
votes
1answer
196 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 ...
4
votes
0answers
409 views
How to prepare for Putnam Competition? [closed]
I am a rising college junior with major in the mathematics. I recently got interested to the contest mathematics through working with few Putnam problems in the real analysis and linear algebra, and ...
16
votes
4answers
433 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 ...
