# Tagged Questions

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.

69 views

Dear Math Stack Exchange advisers, I recently started to develop an OCD-like symptom about reading books in mathematics. Whenever I read previous pages and proceed to next, I always feel under a ...
158 views

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624 views

### Is it necessary to prove everything and solve every problem in the books? [closed]

I am an undergraduate really passionate about the mathematics and microbiology. I have few big problems in learning which I would like to seek your advice. Whenever I study mathematical books (...
55 views

### How to become fluent at reading math formulas? [closed]

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 ...
71 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 ...
176 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? ...
283 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 ...
65 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 ...
24 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 (...
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 ...
56 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, ...
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.
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### 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 ...
46 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 ...
82 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 ...
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 ...
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 $\mathbb{Q} \left( \sqrt {2}\right)$...
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### 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?
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### 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 ...
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### 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 ...
84 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 ...
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### 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 ...
116 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 ...
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### 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 ...
156 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 ...
104 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 ...
147 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?
482 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, ...
440 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 ...
588 views

### I like math, but can't keep up with the pace. [closed]

I'm a math major. I like math. I'm comfortable with it. I'm considering to do a PhD. The thing is I always fall behind. I can't keep up with the professor, can't turn in satisfactory homework in ...
134 views

### How do mathematicians come up with beautiful equations [closed]

In Linear regression for example, we can find weights as following: $\hat{\beta}=(X^{T}X)^{-1}X^{T}y$ how someone invented this? I mean how do they transform a problem to such an equation. And ...
160 views

### Effective Methods of Studying in different areas of Math

I apologize if this question isn't appropriate for this site, but I am looking for advice that I think other math students might be better able to give me. I am an undergraduate math major entering ...
68 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 ...
236 views

### Theoretical and applied math help - what and why? [closed]

(Edit: If you wish to skip the prologue, you may go straight to the questions in the last few paragraphs.) I'm not very far ahead at the moment (going to begin my undergraduate years after next ...
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### What can I do after calculus I besides calculus II? [closed]

I'm a high school senior that's just about finished studying calculus I. I probably can't take AP calculus BC, and I don't want to learn calculus II over the summer or during my spare time. I would ...
48 views

### Interpretation of a statement that I think I can prove by mathematical induction

I want to prove by mathematical induction the following statement: for any sequence (a_k) of non negative real numbers holds that: $$(1+a1)(1+a2)...(1+a_n) >= 1 + a_1 + a_2 + ... a_n$$ I think ...
758 views

### Write on my own my first mathematical induction proof

I am trying to understand how to write mathematical induction proofs. This is my first attempt. Prove that the sum of cubic positive integers is equal to the formula $$\frac{n^2 (n+1)^2}{4}.$$ I ...
106 views

### Learning how to prove by mathematical induction for the first time [duplicate]

So, I have to prove this by mathematical induction and I have never done it! $$\sum_{i=1}^n i^2 = n(n+1)(2n+1)/6$$ However, I have learnt better the theory behind this way to prove statements and ...
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### Natural proofs of theorems or exercises [closed]

Some mathematicians wants to hide their reasoning and proof process so that they appear smart. As most of the mathematics lovers I am not a genius and this is why I hate the magical proofs because ...
63 views

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 ...
1k views

### How do you resist thinking about you may not be able to go further in mathematics? [closed]

I believe that every mathematical "apprentice" more or less once found that some stuff that had been unclear somehow became clear; for example, some books might be unaccessible to you two years ago ...
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### New to Abstract Algebra, need guidance [closed]

I am new to Abstract Algebra. How should I begin learning it. On the face if it, it doesn't look easy to me.I have bought the book by Prof. Gallian. Is there any other book or any videos which I can ...
188 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 ...
111 views

### How to study Linear Algebra when lecturer moves too fast [closed]

Our Algebra and geometry class is moving so fast the lecturer does not have enough time to cover all material in class, and he is not very pedagogical at that. Trying to fill in gaps through reading ...
103 views

### What is the equivalent of musical ear training with regards to studying mathematics

When one aspires to be a professional musician, it is made clear that ear training is a very valuable skill that must be cultivated on a daily basis. The student is advised to put in the time and ...
115 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 ...
1k views

### Strategy for reading math books, is it better to prove the theorems yourself or just read them?

Context: I'm self-studying some mid to upper level undergraduate math subjects. For example, right now I'm reading Munkres' Topology book. Usually, the approach I use is to go through the book in ...
128 views

### If you don't read A to Z, then how can you discover the idea? [closed]

[Source:] Rutgers University Professor [Henryk] Iwaniec and his friend, John Friedlander, a professor at the University of Toronto, read with increasing attention. “In these cases, you don’t read A to ...