Questions tagged [learning]

Questions about the process of learning mathematics, both inside and outside a formal environment, including learning strategies, recommendations for learning particular subjects, and studying habits.

68 questions with no upvoted or accepted answers
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122 views

Strategy for self-studying after M.S.

For someone who has finished their M.S. degree in pure mathematics, what is a good way to keep learning mathematics within your specialization? Would you suggest reading research articles from ...
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642 views

How important is the “prestige” of your university for undergraduate mathematics?

I go to a university in Canada. It's not really considered a top university (it is one of the best universities in the province but is ranked really low nationally). I study mathematics here and didn'...
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1k views

Analysis or (abstract) algebra first?

Which one would you recommend? I only know calculus and linear algebra when it comes to university-level mathematics. Is one required to understand the other?
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309 views

Recommendation Request: Easiest Exercise Book for Algebraic Topology

There probably is no exactly comparable book for algebraic topology, but I really like Algebraic Geometry - A Problem Solving Approach for beginning/elementary algebraic geometry. I have substantial ...
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2k views

How to Read Michael Artin's Algebra

I am currently reading Algebra by Michael Artin (for self study). I'm finding the book pretty interesting, but I'm still not sure how I should study the book. For example, should I try to prove every ...
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133 views

Monads, monoidal categories

I'm interested in learning about monads and their relations to algebraic structures (as a generalization of universal algebra, if I understand well -correct me if not) . In the process of learning ...
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115 views

How to select good exercises?

I'm studying on Rudin "Principles of of Mathematical Analysis" which I begin to find as a good and complete reference. I wonder how many exercises shall I do at the end of each chapter ? In case of ...
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229 views

Where to start?

I want to learn Mathematics but I don't know where to start. Sometimes I really get frustrated as I am a Software Engineering graduate (currently working) and I feel like I don't know anything about ...
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21 views

Ansatz for Merton's Problem

I've been reading about the Merton Portfolio problem and how you can use the HJB equation to solve it where $0 = (∂_t + rx∂_x) h(t, x) − \frac{λ^2}{2} \frac{(∂_xh(t, x))^2}{∂_{xx}h(t, x)}$ with ...
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1answer
153 views

(Soft question) How to study for a proof-based math class?

I'm an undergrad at a top US university and I'm currently taking an Introduction to Analysis class. I really really enjoy this class and it's actually getting me more interested in math in general. I ...
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155 views

Is it too late to aim for postgraduate maths?

I don't know where to ask but I decided to give this part of the community a shot. Anyway I am currently studying an IT related degree but lately I have started to found a love on maths. Sadly I ...
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497 views

How to learn problem solving strategy for Measure Theory?

I have taken both graduate level Algebra and Measure theory courses but found the latter much more difficult for me. I have put a lot effort on learning it by reading a few reference books and ...
3
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1answer
808 views

Quality of Videos Lectures and Lectures vs Textbooks

I am a student trying to learn different subjects by watching video lectures and reading on my own time. I was wondering if the lectures from ICTP and nptelhrd are a great use of my time. I tried ICTP ...
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93 views

How to approach real analaysis

I'm just starting first year in university in Europe and here there there is no Calculus, instead you jump right into Analysis. The trouble is, for some time I self-studied through US style books and ...
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59 views

No Free Lunch in statistics

I was wondering if the No Free Lunch (NFL) theorem applies to even the estimation problem. Suppose there are $N$ points in the input. We are trying to estimate the mean value say weights associated ...
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77 views

What is the meaning of subsampling level in machine learning/statistics?

I am reading a paper but nowhere it is defined but the term is being used a lot. The paper is - Less is More : Nystrom Computational Regularization -Rudi,Camariano, Rosasco Link : ...
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1answer
196 views

Can the action-value function be “expanded”?

I know the basic language of probability, but not fluent in it, and the text books on reinforcement learning usually assumes one is fluent in it, so they don't define everything rigorously, here is my ...
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117 views

Should I jump directly to “differential geometry”?

I am a (now) math major who has taken a standard undergraduate course in engineering multivariable calculus. I say "engineering" since the course was directed at engineers, and mainly focused on ...
2
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1answer
163 views

Undergrad looking for study material/advice for applied mathematics.

I am an undergraduate math student (junior) who is looking to get a masters degree in Applied Math. I like pure math, but I want to use my education to get a great-paying job. Here are a few questions ...
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903 views

Solutions for “What is Mathematics?” by Richard Courant

I am currently reading through Courant's "What is Mathematics?" Most of the time I am not taking the exercises too seriously, given that I am reading this for pleasure, and that often my solutions are ...
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199 views

Sample complexity of coin bias problem

I am reading a paper involving learning in Multi-armed bandit case (its okay if you don't know what that is. Just trying to give context here.) To give sample complexity lower bound, they reduce their ...
2
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1answer
123 views

Learning from Alternative Sources

I have a very general question about people's experiences with learning math. I can think of a couple of times where I had the following situation. I was seeking to learning about topic A. However, ...
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1answer
142 views

Learning concepts in mathematics

Apologies for the soft question, but I was wondering whether it is a good idea, in mathematics, to learn/study things simply for the sake of studying it. A very good example comes from category theory....
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107 views

Can any one recommend a way to “quickly” learn a subject?

I would love to read a well written book on a subject - provided that I have the time. But sometimes we do not need to become experts on a particular field but still need the basics. For example, a ...
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347 views

Vector spaces - Multiplying by $-1$ yields inverse element of vector addition.

Please rate and comment. I want to improve; constructive criticism is highly appreciated. Please take style into account as well. The following proof is based on vector space related axioms. Axiom ...
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0answers
174 views

How to model a real-world graphical structure into a mathematical formulation?

I am trying to learn how to model programming problems in a mathematical way. I am a software engineer, but have recently been running into road blocks where I can't solve some problems very ...
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1answer
62 views

Are there online-platforms where to find people for joint learning and discussions?

After quite some time in academia I ended up in a nice company but the math to use is not really demanding. Hence I am still reading and working a bit on some university level math. It's roughly at a ...
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1answer
228 views

Does math have to be learned linearly?

I am asking because often times one doesn't know where to start in math. "Just learn what you need" is very vague and unspecific ... for example, assume I'm a beginner at Algebra and was considering 3-...
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15 views

What are the minimum prerequisites to understand queueing theory?

I have limited mathematical ability, never did calculus and only a tiny bit of linear algebra. Most mathematical notation is lost on me. What are the minimum prerequisite topics that I can familiarize ...
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37 views

Was my skepsis justified?

The other day I got asked to answer a survey, in order to get to know, why people sometimes have problems learning limits. I got asked some, in my humble opinion, rather easy questions for a math ...
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1answer
102 views

How to approach calculus?

I've recently worked my way through high school math and am about to complete the linear algebra course (https://www.khanacademy.org/math/linear-algebra). I've done most of the stuff on the ...
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60 views

Different stages of learning Arithmetics?

Arithmetics is like the most basic part of Mathematics, but that too takes effort to learn. How would organize or call different stages of learning arithmetics, or can there be stages? Can it go ...
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38 views

Math formalisation of simple programming procedures

I would like to translate some simple programming operation in mathematical equation. I am very new to formalisation. I would like to describe these 2 sequences formally. I am not really sure how ...
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342 views

What is the difference between motivation and intuition of a theorem/result?

What is the difference between motivation and intuition of a theorem/result? Are they same or different in some way? Edit 1 To me intuition appears as the set of ideas (which may or may not contain ...
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205 views

Is propositional logic enough to study real analysis?

Is it necessary to study relational logic before starting real anylisis(from Bartle and Scherbert) or propositional logic enough? Also for topics like topology and differential geometry is ...
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1answer
228 views

Is the i-e principle for symmetric difference useful?

Let $E$ be a set and $A$ and $B$ two subsets. We may define the symmetric difference of $A$ and $B$ by setting : $$A\Delta B:=(A\cup B)\cap (A\cap B)^c $$ There are many interesting things about ...
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1answer
470 views

What are the prerequisites for learning abstract algebra?

Well, I want to learn abstract algebra. So, I get across this http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra. But I'm not sure whether I've understanding of prerequisites ...
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40 views

Is it more useful to study lots of methods/theorems or work with details?

Suppose one has to learn a new subject on book that contains hundreds of pages and hundreds of problems. Is it more useful to learn book by reading it and skipping those parts I don't understand and ...
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1answer
742 views

How to calculate number of triangles and points after dividing a triangle n times?

When having a triangle and dividing it n times, how to get the number of triangles and points? ...
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1answer
70 views

How can i learn when to use which multiplication rule: Probability

Hey guys im studying for a math exam and was wondering if anyone has some easy techniques to remember in what kind of scenario to use these equations. These are I believe called multiplication rules. ...
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0answers
111 views

How to deal with a lack of ability to apply ideas in math?

I am currently studying Theoretical Computer Science, but as a Computer Science student who does not have a formal background in mathematics, past A Level (High School), I find that the ideas I learn ...
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61 views

How do you look for classic/normative/standard books about an established branch of mathematics?

If you want to immerse yourself in a branch of mathematics (e.g. linear algebra and linear optimisation) which is new to you, then you often look for standard books which you can rely on. You could ...
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0answers
1k views

Another proof of uniqueness of identity element of addition of vector space

Please rate and comment. I want to improve; constructive criticism is highly appreciated. Please take style into account as well. The following proof is solely based on vector space axioms. Axiom ...
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0answers
70 views

Any quick mental mathematics techniques?

I recently came across a very easy way to find the squares of fairly large numbers ($1$-$100$, but could be extended indefinitely), by using a simple formula. It does require you to know the square ...
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66 views

Studies on how the wording employed on the explanation of mathematical concepts helps students to learn?

I remember that I had to learn division in my childhood, I could handle all the other mathematical concepts that were presented until then but division was a real pain to learn, somehow the idea of $n$...
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18 views

Looking for intuition for picking strategy on how many pages to flip

This question is going to sound more CS'y because that is my background. It also might be a bit vague but that is because I am not sure what the right thought process is in how to formulate it. I ...
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407 views

Programmer understanding academic writings on maths

I would like to know in which order I should learn different areas of maths so I can have a robust overview of all the theory in case I need something for a computer programming problem. So I've ...
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20 views

Is there a relationship between finger-counting technique, elevator ground floors and the index of the first cell of an array?

In the movie Inglourious Basterds the British spy outs himself simply by ordering a drink. (due to national differences in finger counting). The point being that some countries learn to count where ...
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27 views

Multi-arm bandit with multiple play

In the classic multi-arm bandit problem setting, we have $K$ arms, and need to pull only one arm in each iteration $t\in\{1,2,3,...,T\}$. Many algorithms that achieve a sub-linear regret have been ...
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75 views

Long derivative exercises: where to find them?

I am preparing for an exam. On the exam I will be asked to find the derivative of a long function, with a multiple chain rule. Such as: $$y = (\frac{3}{x} - 2^{{x}^3})^{6} + \frac{\ln \sin \frac{2x+1}{...