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.

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2answers
57 views

How to study Advanced Level mathematics?

I have heard some people say that A levels maths is difficult. I have yet to choose a subject for A levels, but I would like to try Mathematics. I would like to know if there is any way to learn A ...
0
votes
4answers
258 views

Recommended math background for game theory

I recently got interested in some game theory applications to poker. I want to try some of them out programmatically, but a lot of the math is a bit confusing. I learn math on my own fairly quick and ...
11
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4answers
472 views

The best balance in studying Mathematics? [closed]

I'm a student studying Mathematics at a university level. I've completed Single Variable Calculus, Differential Equations, Multivariable Caculus, Real/Complex Analysis, and Linear Algebra and I've ...
181
votes
7answers
9k views

Best Sets of Lecture Notes and Articles

Let me start by apologizing if there is another thread on math.se that subsumes this. I was updating my answer to the question here during which I made the claim that "I spend a lot of time sifting ...
2
votes
1answer
41 views

Can we see natural deduction rules as functions or even as formal grammars?

Is there a way of seeing natural deduction rules as functions or even as formal grammars, maybe context-free grammars or Lambek grammars? It seems quite "easy" to see the rules as functions which take ...
17
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1answer
2k views

Can an older person become an expert in math?

Is learning math like learning a language, in that there's a certain cutoff age (pretty young) that you need to start learning by, otherwise you'll never be fluent? Is the novice older brain ...
2
votes
2answers
49 views

How to retrieve the expression of $a^3+b^3+c^3$ in terms of symmetric polynomials?

I recently had to find without any resources the expression of $a^3+b^3+c^3$ in terms of $a+b+c$, $ab+ac+bc$ and $abc$. Although it's easy to see that $a^2+b^2+c^2=(a+b+c)^2-2(ab+ac+bc)$, I couldn't ...
0
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0answers
103 views

Where can I get detailed and comprehensive notes of a functional analysis course taught using the book by Erwin Kreyszig?

Where on the Internet can I find detailed and comprehensive lecture notes of an elementary functional analysis course taught using the book Introductory Functional Analysis with Applications by Erwin ...
6
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4answers
8k views

Math Textbooks for High School

I'm a high school student who is trying to figure out a complete course of self study for each year of high school. Is there a way to self learn grades of math without devoting too much time? For ...
2
votes
2answers
146 views

Why is math so difficult for me? [closed]

I'm an aspiring software engineer and currenly in college for computer science. For some reason, no matter what I try, math is so unbearably difficult and indecipherable until I design a program for ...
0
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0answers
70 views

Linear Algebra Book like Calculus Made Easy

Now, I know that there are a tons of reference requests for Linear Algebra books but mine is very specific: what is a nice, short, concise, simple, to the point book that gets at the heart of Linear ...
7
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2answers
150 views

Attemping Qualifying Exam Problems — and failing

My question is concerning learning strategy. I can solve the majority of the exercises in a typical graduate mathematics textbook like, say, Dummit/Foote's Abstract Algebra. To supplement my education ...
2
votes
3answers
94 views

How do I figure out my math aspirations? [closed]

I am really confused. Here's my present situation: I'm 18. I am about to start a computer science degree this August--going there only coz my parents want me to. I know most teachers for undergrads ...
2
votes
1answer
58 views

How should I learn the Mathematical Proofs?

S.E advisers, What is the most efficient way to learn the basic proof methodologies, which are essential for studying the mathematical analysis and number theory? I am very interested in studying ...
11
votes
7answers
11k views

Can I learn Calculus on the web, for free, using simple tutorials?

I'm a lazy type of person. I love experimenting with things before learning the theory. I like to practice, and learn from my mistakes. In 3-4 months I have a basic University exam on Calculus, and ...
14
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3answers
492 views

Why don't I understand “What is mathematics?” by Richard Courant [closed]

I am 14 years old and can do A level maths happily. However, I want to further my knowledge of mathematics to pave my way for more discrete maths and harder analysis etc. So I decided to pickup "What ...
0
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1answer
70 views

Severe problems with math undestanding

Recently (although still in high school) I've been at university, more precisely at information science engineering as apprenticeship. I want to become an operating system programmer but I severely ...
8
votes
3answers
426 views

Books/Notes recommendation request: Multivalued functions/Riemann surfaces

I'm trying to read a document that applies Riemann-Roch left, right and center. I don't know this theorem or the theory it comes from so I need to build up a bit more background before I can tackle ...
2
votes
1answer
41 views

The Monty Hall problem - convincing a skeptic

I have lost count of the number of times that I have been debating the solution of the Monty Hall problem with someone. Recently I had a long conversation with a colleague, who didn't seem to buy ...
2
votes
1answer
61 views

Explaining intersections to a 6th grader

$A=\{1,2,3,4,5\}$ $B=\emptyset$ How to explain to a learner from 6th grade the result for $A \cap B$ ? For a 6th grade student, it could be difficult to understand why the result is $\emptyset$. ...
0
votes
1answer
24 views

graph theory, economics and learning prerequisites

I'm a undergraduate student of economics and I"d like to know which classes I have to take to get in in graph theory with the purpose to apply it to economic theory. Undergraduate math is sufficient ...
66
votes
9answers
3k views

How to make notes when learning a new topic [closed]

At the moment I'm trying to teach myself Riemannian geometry by reading some books. I take notes by hand but I find that I forget it all and worse, either lose the sheets of paper or don't want to ...
10
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0answers
138 views

Is it a good approach to heavily depend on visualization to learn math?

I am a third year undergraduate and I am a beginner on these "real mathematics" (no pun intended). Before contacting the "real math", my math level should be considered to be "good", although I was ...
0
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0answers
18 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 ...
0
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1answer
69 views

Math without notation

Are there any researchers that try to develop learning materials to teach the core mathematics knowledge without using notation (and instead just plain English -- preferably without images)?
2
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0answers
66 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 ...
12
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4answers
2k views

Is it necessary for one to understand analysis?

Is it necessary for one to understand analysis in order to pursue a career in mathematics? Basically, I am very weak at analysis. But the problem is that most of the topics listed in the syllabus ...
2
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1answer
46 views

Matrix multiplication memorisation

So I'm writing an exam about matrices in a few weeks time, and I'd like to know if anybody has any tips about multiplying matrices.
0
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1answer
62 views

Requirements for learning and understanding trigonometry?

Im reaching a point in programing where I need to create basic shapes which I simply cant since my math skills are very bad. After finding out that the skills required are trigonometry I read a few ...
1
vote
2answers
47 views

Representative Pedagogical Examples of Groups, Real Functions, Modules, etc.

In the preface of Munkres's Topology, he writes, Fortunately, one does not need too many counterexamples for a first course; there is a fairly short list that will suffice for most purposes. Let ...
8
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2answers
159 views

Learning modern differential geometry before curves and surfaces

What might one miss by learning modern differential geometry without first learning about curves and surfaces? I'm currently reading this book on differential geometry which starts with manifolds and ...
8
votes
1answer
170 views

Importance of Exercises in Mathematics for Self-Studying

I am a high school student wanting to major in Mathematics in the future. I started to like Mathematics recently, starting a year ago and I watched some interesting math videos on YouTube for fun (ex: ...
5
votes
1answer
106 views

Being a good listener in math [closed]

I'm reasonably good at learning from textbooks, but I often find that when people explain mathematical ideas to me in person I don't understand what they are saying. I sense that there is actually a ...
11
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1answer
117 views

How to stay productive while you are studying math? [closed]

Not sure that this question is a good fit for this site, but I will try. When I am working through a chapter of a mathematical book first two hours are normally very productive (easily remember ...
4
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0answers
115 views

How can I retain the mathematics that I've supposedly learnt?

So my question simply is "What is the best method to make sure you retain what you have learnt?" Okay so I've tried learning mathematics up to where I should be at in the past. Every time though I ...
75
votes
9answers
7k views

Math and mental fatigue

Just a soft-question that has been bugging me for a long time: How does one deal with mental fatigue when studying math? I am interested in Mathematics, but when studying say Galois Theory and ...
2
votes
1answer
82 views

Mathematics Learning Process: Plan of Attack [closed]

I have been intrested in a lot of topics concerning Mathematics for the past few months: I ordered some textbooks from Germany which cover essential Algebra and Geometry, and they are excellent. ...
4
votes
1answer
137 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 ...
2
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2answers
117 views

Is there a math website to study math from a mathematician point of view (ie proof oriented?)

I´m a student of the University of Puebla, Mexico, and I think that we lack of exigence there so I want to study math on internet to improve my education. I have already looked sites like edX, but I ...
14
votes
0answers
378 views

IMO programs of different nations?

We in Albania have a good team in the IMO, and this year I will probably be part of it. Since Albania does not have a public training programme, I have to consult the training programmes of other ...
1
vote
1answer
116 views

In balancing effort and advancement in what concerns learning

What's new besides showing modern advancements in modern mathematics as well as eloquently written notes also contains some good advice to young people like me in this room (career advice:!). in ...
9
votes
4answers
808 views

Forgotten old results break my motivation

I'll begin graduate school next year and I am very impatient to learn new things such as theories, ways of thinking and so on (I enjoyed reading about category theory on my own and I find Galois ...
9
votes
1answer
149 views

How to listen math lectures?

Many times, the lectures goes beyond the head and not easy to follow, (at least with me),mainly in the workshop/conferences, though the audience are eager to learn something from it. Also, most of ...
13
votes
13answers
4k views

How to explain the formula for the sum of a geometric series without calculus?

How to explain to a middle-school student the notion of a geometric series without any calculus (i.e. limits)? For example I want to convince my student that $$1 + \frac{1}{4} + \frac{1}{4^2} + ...
2
votes
0answers
73 views

What is the best way to master my algebra skills without taking an algebra class?

I was in advanced math my entire life. I got through all the math I needed for my original degree. 8 years later here I am changing degrees and I need more math. I just took calculus I and I passed ...
4
votes
4answers
1k views

Why is “All horses have the same color” considered a false proof by induction? [duplicate]

Upon reading of All horses have the same color "paradox", I began to wonder a couple of things. First of all, to me the inductive step seems flawed. Just because I have $n$ white horses, does not ...
3
votes
0answers
40 views

Advice on methods to capture lecture board and add notes [closed]

I am looking for a method to save the lecture materials, and examples without hand copying from the boards during the lectures. Unfortunately some courses don't have the material available, and ...
1
vote
2answers
88 views

Memorising lots of maths theorems/lemmas

In a few weeks I'll have my summer exams in a Senior Freshman Mathematics course. Two of my modules have a huge number of theorems, lemmas and definitions - over 200 definitions and 250 proofs by my ...
26
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11answers
22k views

How to start with mathematics? [closed]

I fell in love with mathematics a bit too late when I've already taken decisions regarding my future, career-wise. Now I would like to learn math on my own but I'm a bit confused as where to start. My ...
0
votes
1answer
81 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 ...