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0
votes
2answers
54 views

Is 1 rad important?

Of course radians generally come in ratios of π. So is 1 rad important/useful/special? Or, for that matter, is any integer radian measure important? Besides being approximately 57°, I can't seem to ...
8
votes
3answers
634 views

Does writing a bachelor thesis make sense?

I am a math student in my fourth semester. At my university, it is common to write a bachelor-thesis in the end of the bachelor program in almost all subjects while in the math undergraduate program ...
1
vote
1answer
57 views

How to study analytic number theory?

Should i study many books at the same time? Or should i go one by one? I started with Apostol's book... But for example if i don't understand a proof, i check another book for a different proof of the ...
3
votes
3answers
60 views

Analysis on manifolds after course on Lebesgue integration

I am an junior currently taking a course on measure theory and Lebesgue integration using Royden's text. Before this, I took a standard intro to analysis course covering the first seven chapters of ...
8
votes
3answers
162 views

$1^3 + \dotsb + n^3 = (1 + \dotsb + n)^2$: reason? [duplicate]

We have $$ 1^3 + \dotsb + n^3 = (1 + \dotsb + n)^2 $$ as we can establish by induction. But why does this hold? Can we connect it to something else?
20
votes
3answers
638 views

Totally lost and frustrated [closed]

I love maths. Rather I think I love maths. I am not sure. Whenever I study maths, I like it but there are times that i get really frustrated and stop studying it. I am preparing for an entrance exam ...
0
votes
1answer
49 views

Working towards Abel's proof of unsolvability of quintics

I am currently doing a course in Abstract Algebra. I have been told that while some of the basic theory is laid down, we will not get as far as actually proving the unsolvability of quintics. ...
0
votes
0answers
62 views

Copying and Pasting $\LaTeX$ [closed]

Is there any way to copy and paste $\LaTeX$ directly out of someone's question into the answer or comments? This would save a lot of time answering certain questions it seems like... Also, can this ...
0
votes
0answers
21 views

Translation of Théorie des distributions?

Does anyone know why there is no English translation of Laurent Schwartz's Théorie des distributions? Also, is it then worth attempting a translation?
0
votes
1answer
32 views

Changing the subject of formula to calculate data transfer speed

I am looking into buying a fast card reader, and concluded that to transfer $8 GB$ of data $(8\cdot 1024 MB)$ to my computer at a data transfer speed of $130 MB/s$ would take me $1.024$ minutes. ...
0
votes
2answers
70 views

Which do you prefer sine or cosine? [closed]

A soft question. Which do you prefer between sine function or cosine function? While I feel the sine funciton more clear and comfortable, but I prefer cosine, since $\Re{e^{ix}} = \cos{x}$, The ...
57
votes
14answers
5k views

A good way to retain mathematical understanding?

What is a good way to remember math concepts/definitions and commit them to long term memory? Background: In my current situation, I'm at an undergraduate institution where I have to take a lot of ...
3
votes
3answers
58 views

How to tell if algebraic set is a variety?

I've been reading some basic classical algebraic geometry, and some authors choose to define the more general algebraic sets as the locus of points in affine/projective space satisfying a finite ...
5
votes
1answer
65 views

What's the trick to re-focusing on your math studies?

If you check my history on MSE, you'll see that I was very active about 1/2 a year ago. Right now I'm working and socializing a lot, which is important, but I also have spare time to devote to my ...
3
votes
1answer
79 views

Examples of the Mathematical Red Herring principle

I read the Mathematical Red Herring principle the other day on SE and wondered what some other good examples of this are? Also anyone know who came up with this term? The mathematical red herring ...
3
votes
1answer
72 views

Where to begin my Math journey

I apologize if this is not the correct forum for this, but I felt it appropriate. I want to start getting into more mathematics and learning all I can to step up my programming career. I know plenty ...
2
votes
5answers
298 views

What area of Abstract Algebra do you find most interesting? [closed]

For my Abstract Algebra class, we will be doing small presentations (2 class periods) covering some topic in Abstract Algebra. Thus far, I have studied groups, rings, fields, modules, tensor ...
7
votes
1answer
91 views

why is that most of the books in mathematics don't include answers?

I am currently going through the " Topics in Algebra" By I. N. Herstein. The problems are pretty good. But there are no answers on the back. Same is the case with "Mathematical Analysis" by Rudin. I ...
5
votes
1answer
99 views

What happens if your manuscript is accepted as a filler?

I just got a responce from a journal of the MAA that my manuscript is accepted as a filler. The email says : "The Editorial Board likes your submission and has asked me to move it to the ...
0
votes
2answers
44 views

assuming the conclusion

A natural deduction proof goes from premmisses to conclusion, and under normal circumstances you will not assume the conclusion. Sometimes you may assume the negation of the conclusion and do some ...
5
votes
0answers
88 views

Help needed with Masters' Thesis

My brother is at the very end of his Masters Program at a well-known University (Math, of course, hence my inclusion of this question on this site) and he is totally done with course work, but is ...
0
votes
0answers
27 views

Apportionment of Credit for a Proof

I have a soft question about the apportionment of credit for a proof. The question was motivated by reading about computer-assisted proofs such as the 1976 proof by Appel and Wolfgang of the four ...
0
votes
0answers
39 views

Do All Structures have a lower dimensional analogy?

So, I was doing a double integration and a I realized, we may have $\mathrm{d}x$ for a 2D integration, $\mathrm{d}x\mathrm{d}y$ for a 3-Dimensional Problem, and presumably ...
5
votes
0answers
96 views

What is the best Mathematical Insight you have had? - PLEASE MOVE TO META [closed]

I've used this site a lot but am new to the actual forum. Basically, I am wondering if we could collect a list of mathematical insights / explanations / neat proofs etc. that people on this forum have ...
5
votes
1answer
158 views

Did Albert Einstein contribute to math?

Many great scientists have made important contributations to many related fields. Gauss, Euler and Newton each made many contributions to both math and physic. One of the great scientists of last ...
2
votes
1answer
43 views

The motivation behind axiomatisation

Axiomatisation in the context of rings I am in the middle of an elementary pure mathematics unit and have just started looking at the concept of rings. In lectures, we have divided up rings into ...
2
votes
1answer
70 views

Definition of the $\sec$ function

I am a postgraduate student of mathematics from Slovenia (central Europe) with quite some experience in mathematics. While answering questions on this site, I often encounter the function $\sec(x)$ ...
3
votes
0answers
48 views

What's going on in Ito calculus?

I've been studying Ito calculus a lot recently, and there's a lot of introductory material on it but nothing too dense. Everything I've seen about it has been mainly for financial engineers. What ...
4
votes
1answer
55 views
+50

Character Tables of $D_{4}$ and $Q_{8}$

Is there an intuitive reason that the Quaternion group and the Dihedral group on four vertices have the same character table? Does this indicate something special about the two groups? Or is it more ...
1
vote
1answer
35 views

Suggestion for independent study of mathematical logic

Hello I'm looking for advice on mathematical logic books that are good for self-study. I would really like a text that has some if not all of the answers to exercises so I can check my progress as I ...
75
votes
9answers
6k views

Are mathematical articles on Wikipedia reliable?

I know that Wikipedia gets a bad rap, and it seems like some teachers of mine have nothing better to do in class than harp on about the Great Academic Pastime of calling Wikipedia untrustworthy, but ...
0
votes
0answers
26 views

Your impressions of Mattuck's *Introduction to Analysis*

Has anyone here spent much time with the Mattuck book Introduction to Analysis? What are your impressions of it? A quick browsing showed me that I liked the organization of the material, but the ...
2
votes
0answers
54 views

Is an undergraduate in engineering sufficient preparation for a masters in mathematics?

I'm a high school student who is considering doing an undergraduate in engineering. However my the long term plan is to pursue math at a higher level. I want to do engineering at undergrad because I ...
24
votes
5answers
2k views

Tell me problems that can trick you

I am looking for problems that can easily lead the solver down the wrong path. For example take a circle and pick $N$, where $N>1$, points along its circumference and draw all the straight lines ...
74
votes
19answers
12k views

Visually deceptive “proofs” which are mathematically wrong

Related: Visually stunning math concepts which are easy to explain Beside the wonderful examples above, there should also be counterexamples, where visually intuitive demonstrations are actually ...
3
votes
0answers
44 views

How does one create “good” math problems?

As lifelong students of mathematics, we find problem-solving to be absolutely essential to enhance our understanding of the subject. Teaching others what we know serves to reinforce our existing ...
3
votes
2answers
59 views

What is the most elementary but still correct according to the most rigorous standard proof of the isoperimetric inequality?

Can you write the most elementary proof of the isoperimetric inequality (but still correct according to the most rigorous standard )? $$l^2> 4πA$$
9
votes
3answers
112 views

How to recognize adjointness?

Reading math has gradually expanded my understanding of the word "symmetry", so that now I can recognize symmetries that I would have not noticed before, and without having them pointed out to me. I ...
0
votes
1answer
32 views

Examples of journals dedicated to the popularization of Mathematics?

I don't need a big list, I'd just like to have some examples of the most relevant journals that are dedicated to the popularization of Mathematics. Thanks in advance!
5
votes
1answer
54 views

Simple Grammar Question

Perhaps this question fits on an English Language wiki, but it is more likely a question that mathematicians would know the answer to. I know that all uses of the words "Theorem" and "Lemma" should ...
0
votes
0answers
13 views

Is there a good introductory complex-analysis text in general setting, namely Riemann sphere?

I have studied first 1~3 chapters of some complex analysis texts (Ahlfors, Conway, Silverman) Well, i specially like Ahlfors in many ways but this text doesn't seem to develop a theory in a general ...
4
votes
1answer
50 views

Are there numbers that if proven rational (or irrational) will have important consequences to mathematics?

We see all the time conjectures and proofs that specific (real) numbers are (more often than not) irrational. I'm wondering that apart from the mathematical curiosity motivating such proof attempts, ...
0
votes
2answers
33 views

does the p-adic shows the other end side of numbers? i.e, from right to left? [closed]

Reading this scientopia link i pondered whether p-adic shows the numbers from the other side (right to left from infinity's side)? For example the last digits the last digits of $\sqrt 2$ in 10-adics? ...
7
votes
4answers
180 views

“important” math concepts to pass on to next generation of creatures at some cataclysm [closed]

This may be somewhat silly to ask, but I couldn't resist the temptation. The idiosyncratic physicist Richard Feynman was once asked If, in some cataclysm, all of scientific knowledge were to be ...
2
votes
2answers
47 views

Relationship between mathematics and music

I have a strong mathematical background and I am interested in the relationship between mathematics and music. I have found some introductory material on the web. Do you know any good books that will ...
1
vote
2answers
22 views

Given a congruence equation ax = b (mod n), how can I prove this GCD?

I am given the equation $ax = b (mod$ $n)$ and that $d = (a,n)$. Suppose that $x_o$ is a solution to the equation. I need to prove that d is the greatest common divisor of not only a and n, but b as ...
0
votes
4answers
39 views

What modular arithmetic theorem is being ignored here?

Suppose $4x\equiv 6 \pmod {18} $ Then $2x\equiv 3 \pmod 9$ Then $6x\equiv 9 \pmod 9$ Then $6x\equiv 0 \pmod 9$ Then $x\equiv 0 \pmod 9$ Then $x=9k$ vs. Suppose $4x\equiv 6 \pmod {18}$ Then ...
1
vote
2answers
79 views

Number Theory and Cryptography

I am a math tutor at a community college, and I stopped in to ask one of the professors a question about crypto and he lent me a graduate level book on for a full year course in the title of this ...
1
vote
2answers
27 views

Can someone help me solve this system of congruences?

I'm a little new to congruences but I think I have it right. I started with the following congruences: $19x \equiv 5 \pmod{2}$ $19x \equiv 5 \pmod{3}$ $19x \equiv 5 \pmod{5}$ $19x \equiv 5 ...
1
vote
1answer
25 views

Why use Gauss and mean curvature to characterize a surface's deviation from being “flat” at one point?

We know for a 2-dimensional surface there are two orthogonal principal directions at every point, where the principal curvatures $\kappa_1$ and $\kappa_2$ are the two ends of the curvature spectrum ...