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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1
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0answers
51 views

How to become fluent at reading math formulas? [on hold]

As part of my studies, oftentimes I need to read research publications which contain mathematical formulas. Whenever I have to do that, I feel discouraged. Somehow I can not comprehend the ...
-1
votes
1answer
35 views

How can i best learn advanced calculus over two months? [closed]

I am currently a second semester physics student at a german University and have set the goal of learning a lot of advanced calculus over the semester break for myself. I am motivated to do this, ...
81
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9answers
26k views

Learning mathematics as if an absolute beginner? [closed]

I dread mathematics, and I believe it's because I have come to associate mathematics with the experience of terrible teachers. All of my math teachers have been grumpy, but one in particular was the ...
10
votes
3answers
271 views

How exactly does Mathematics help me becoming more intelligent (at least, in high school)? [closed]

[Please reditect me to a different site/sub-site/pretty-much-any-relevent-place if I've posted the question in the wrong forum, please do not downvote before attempting to redirect me to the adequate ...
-1
votes
0answers
31 views

How to study for open book exams?

I hope it's ok to ask about exams here? If not please tell me. This year was the first time I had open book exams, varying from three to six hours long. The six hour ones go fine because I have time ...
0
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0answers
70 views

What's the point of studying differential geometry? [duplicate]

I've been taking a graduate differential geometry course this semester, and since the beginning I have wondered why one should try to learn that subject. It doesn't mean I don't like it, because I ...
6
votes
6answers
173 views

How to explain to a school kid that on a sphere the shortest path between 2 points is given by a great circle?

I will be teaching some "topology" to high school students. I was wondering how to explain to such a school student that on a sphere the shortest path between 2 points is given by a great circle? ...
54
votes
6answers
3k views

Am I too young to learn more advanced math and get a teacher?

I am still 15 years old, but I am very interested in pure math. I have been teaching myself though books, from the internet and from others for the past year or so. I haven't mastered all the topics ...
2
votes
2answers
64 views

How to access the world's specialised knowledge? [closed]

This is a question that relates to almost all domains, I just happen to be passionate about maths. In my early teens, I used to believe that the path through all stages of standard education would ...
0
votes
0answers
22 views

Is there a broad map, guide or list of all or most of math's fields? [duplicate]

Has someone ever garthered all the different fields in maths (single variable function analisis, multivariable analisis, complex number analisis, number theory, graphs, succesions, etc) and made a (...
34
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8answers
7k views

How can I learn to “read maths” at a University level?

When I look at math, it's like my mind goes fuzzy. The only way to describe it is in terms of what I can relate it to. You know how when you read, you see the letters and words, but your brain picks ...
7
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0answers
64 views

A List of Standard or “Cliche” Homeomorphisms [duplicate]

Learning topology has been hard. I just cannot see how some people can come up with complex functions that link one space to another, in a homeomorphic sense. The explanations are always "Well if you ...
3
votes
2answers
54 views

learning linear algebra [duplicate]

So I'm a college student that has taken 3 semesters of calc/diff eq/linear algebra and I think linear algebra has been by far my favorite course so far and I would love to know more in the subject, ...
2
votes
2answers
356 views

Dynamic Geometry Software for Straight-edge and Compass Constructions

Geogebra is a very good dynamic geometry software. It has so many default tools, e.g. parallel line, angle bisector, tangent to the circle, inscribed and circumscribed circles, etc. But I want the ...
68
votes
8answers
14k views

Learning Lambda Calculus

What are some good online/free resources (tutorials, guides, exercises, and the like) for learning Lambda Calculus? Specifically, I am interested in the following areas: Untyped lambda calculus ...
19
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6answers
7k views

Is memorization a good skill to learn or master mathematics?

I sometimes spend inordinate amounts of time memorizing math articles or theorems/proofs or formulas. My question is "am I wasting time?" and will 'active thinking' or 'working out problems' be faster ...
1
vote
3answers
4k views

James R. Munkres' TOPOLOGY, 2nd edition: How to check my work?

I'm trying to learn, or revise, some topology from James R. Munkres' TOPOLOGY, 2nd edition. I'm working alone; that is, I'm self-learning. It is quite fun. But the problem is how do I check if I've ...
1
vote
2answers
36 views

how to know when a particular proof is appropriate for the given problem?

The main trouble I am currently having in math is knowing when the use cases are appropriate in a proof. I see many videos where they seem to choose a strategy like proof by contrapositive or proof by ...
2
votes
1answer
106 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 ...
15
votes
2answers
5k views

How to improve mathematics for Programming Contests?

You might close this question or downvote it, but I can't stop myself from asking the experts of mathematics who solve thousands of math problems. I'm a C++/C programmer who wants to improve his ...
0
votes
0answers
31 views

Coordinates of vector in new Basis

Find coordinates of vector $$\vec{u} $$in Basis $$ V={ (x−4y, x+y, 3x+y, x+y): x,y ∊ R} , \vec{u} =(−2, 6, 9, 2) $$ How can I do this? I found only examples for basis with explicit vectors.
25
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4answers
2k views

What are the dangers of visual exposition of mathematics?

I've heard several times (such as this one) that it's dangerous to learn/prove/teach mathematics through images. I've also read somewhere that showing mathematics through images helps one's intuition ...
5
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0answers
94 views

How can I learn Math intuitively? [closed]

I am currently a Junior in High School. I am in an Intermediate Algebra class, but my teacher does not always explain things in a way I can understand. I like to learn Math intuitively, but my teacher ...
4
votes
1answer
2k views

Vector spaces - Multiplying by zero scalar yields zero vector

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 related axioms. ...
1
vote
1answer
45 views

where to find good examples of combinatorics (online resources only please)?

one of the most beautiful/hard things in the study of combinatorics is the fact that is not just about memorizing 4 or 5 formulae but developing a whole reasoning ability. Such thing can only be ...
2
votes
2answers
79 views

How should I start solving a calculus problem? [closed]

There are so many books teaching how to take derivative and integration of a function. I think I'm good enough (enough for me lol) in those parts, my problem is that I can't start solving a question ...
12
votes
5answers
6k views

Why is it that when proving trig identities, one must work both sides independently?

Suppose that you have to prove the trig identity: $$\frac{\sin\theta - \sin^3\theta}{\cos^2\theta}=\sin\theta$$ I have always been told that I should manipulate the left and right sides of the ...
68
votes
20answers
49k views

Good book for self study of a First Course in Real Analysis

Does anyone have a recommendation for a book to use for the self study of real analysis? Several years ago when I completed about half a semester of Real Analysis I, the instructor used "Introduction ...
0
votes
1answer
16 views

Use of the Bezout Theorem in the Proof of Field Extension

Let $p$ be a prime number. Let $F$={0,1,...,p-1}. += addition mod p .= multiplication mod p The only nontrivial thing to check is the existence ...
0
votes
1answer
65 views

Understanding Proof that $\mathbb{Q} \left( \sqrt {2}\right)$ is a field. [duplicate]

Prop. $\mathbb{Q} \left( \sqrt {2}\right)$ under usual properties, i.e., $\mathbb{Q} \left( \sqrt {2}\right)$ is a field. Proof. (Step of multiplicative inverse of $\mathbb{Q} \left( \sqrt {2}\right)$...
0
votes
1answer
21 views

Understanding of example of subspacee

Let F be a field. Then, { (a,b) $\in$ F: $\alpha$a+$\beta$b=0} is a subspace of FxF for any $\alpha$, $\beta$ $\in$ F. My question is that can be FxF is a subspace of f? If not, why?
72
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3answers
3k views

Is there a definitive guide to speaking mathematics?

Is there a definitive guide to speaking mathematics to avoid ambiguity? I'm writing a program to generate text for a variety of mathematical expressions and would like to code it so that it adheres ...
1
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3answers
41 views

Understanding Defiinition of Vector Space

Let $F$ be a field. A vector space over $F$ is a set $V$ together with $+$,$\cdot$ satisfiyng: $$+: V \times V \rightarrow V$$ $$\cdot: F \times V \rightarrow V$$ with usual properties. My ...
0
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0answers
50 views

How do I memorize mathematical proofs?

I first started wanting to know about the derivation of theorems because certain ones help you memorize the theorems better. But as I take harder math classes, it turns out better for me to use ...
1
vote
2answers
83 views

Should non mathematicians learn mathematics “just in time” or ahead of time? [closed]

I am wondering how someone that is not exclusively interested in mathematics (but nevertheless aims to become a decent applied mathematician), but for example, a theoretical computer scientist, should ...
0
votes
2answers
42 views

Understanding a problem

Note that these from linear algebra notes. İt was defined fields, showed $\mathbb{Q}$ is a field. Then, below-mentioned qustion was proved. Yet, I didn't ask what happened. Can you explain? What ...
16
votes
1answer
246 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 ...
2
votes
2answers
115 views

Diagnosing essential Classical Mathematical Analysis I knowledge needed for II

I need to take Classical Mathematical Analysis II (Chapters 7-10: Sequences & Series of Functions, Special Functions (Exp/Log/Fourier/Gamma), Functions of Several Variables, Integration of ...
68
votes
11answers
8k views

How do people who study intensely abstract mathematics “imagine” or understand the concepts they are studying or being taught? [closed]

This question is probably to the actual people who study such mathematics, rather than any "third-party". I haven't studied any such mathematics, but I can imagine that some (probably most of it) of ...
11
votes
4answers
686 views

How can I explain topology to my grandmother?

I was recently look at a post on tex.stackexchange about explaining $\LaTeX$ to the OP's grandmother. I was wondering, could the same thing be done for topology? Except in this case the "grandmother" ...
9
votes
6answers
11k 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 ...
13
votes
2answers
21k views

Tips for an adult to learn math — from the beginning. [closed]

First let me start with I am an adult and I can't do simple maths. I some how got through all of my math courses in University (after several attempts) but I honestly couldn't tell you how... I ...
4
votes
1answer
75 views

What is the significance of “Homomorphism”?

Certainly Homomorphism is a prerequisite to establish an “Isomorphism”(Bijection), but what does a Homomorphism tell independently when it is established between two sets? Homomorphism relates ...
1
vote
2answers
137 views

Should I continue trying to solve Spivak or pick up a lighter book?

Some background: I have no mathematical maturity. Last year I completed my schooling and the only time I picked up a math/science book was when exams were due, needless to say I haven't actually given ...
1
vote
1answer
97 views

Scratch paper alternatives? [closed]

How do you practice complicated calculation when the problem is displayed on your computer screen? Do you always have pieces of paper on the side, or do you have a Wacom tablet connected to your ...
56
votes
4answers
7k views

Do you prove all theorems whilst studying?

When you come across a new theorem, do you always try to prove it first before reading the proof within the text? I'm a CS undergrad with a bit of an interest in maths. I've not gone very far in my ...
1
vote
2answers
143 views

How much group theory is required before undertaking an introductory course on Galois Theory?

How much knowledge of group theory is needed in order to begin Galois Theory? Which topics are most relevant?
19
votes
3answers
1k views

Working habits in mathematics [closed]

Short version of my question: What are good and motivating working habits for a mathematician? N.B. There are similar questions to mine: see this (how to read maths) or this (efficient study) or this ...
5
votes
3answers
452 views

How to determine if I'm talented enough to study math? [closed]

After getting Bachelor's degree from Computer Science I changed my field to Applied Mathematics. The previous degree was mostly programming-oriented, so I know quite a lot about software engineering, ...
5
votes
2answers
420 views

Numerical analysis, differential equations, complex analysis for statistics

I am a student of the Statistics Department. And now I can choose a subject from such list: numerical mathematics (analysis), differential equations, complex analysis, real analysis. Can you please ...