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3
votes
1answer
94 views

Gain confidence in maths.

I am a maths student and I really want to stand out in maths, to be good at it because I like it. But the transition from high school's computation-based maths to uni's concept-based maths made me ...
0
votes
2answers
75 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 ...
12
votes
3answers
1k 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 ...
2
votes
1answer
142 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
368 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 ...
7
votes
3answers
606 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?
0
votes
1answer
78 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
1answer
358 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. ...
75
votes
15answers
7k 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
95 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
152 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 ...
4
votes
1answer
178 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 ...
4
votes
1answer
168 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 ...
3
votes
5answers
398 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 ...
8
votes
1answer
157 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
144 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
67 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 ...
6
votes
0answers
148 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
75 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
206 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 ...
13
votes
1answer
2k 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
70 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
147 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 $\sec(x)$ ...
2
votes
0answers
66 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 ...
5
votes
1answer
101 views

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
67 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 ...
99
votes
10answers
7k 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 ...
6
votes
1answer
166 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 ...
26
votes
6answers
3k 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 ...
89
votes
20answers
17k 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
2answers
72 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 )? $$l^2> 4πA$$
12
votes
3answers
219 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 ...
6
votes
1answer
68 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 ...
4
votes
1answer
74 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, ...
1
vote
2answers
40 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? ...
8
votes
4answers
230 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
84 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
207 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 ...
2
votes
1answer
65 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 ...
2
votes
2answers
196 views

Recommendation for Number Theory Textbook

. Greetings, every mathematicians! I'm a foreigner (meaning English is not my first language) and an undergraduate student. I'm currently studying linear algebra, set theory and have already studied ...
3
votes
0answers
79 views

Is this a field of study?

Is there a name for an equation that takes the following form? $$F(f(x),f^{-1}(x),x)=0$$ A nice example being $$f(x)-f^{-1}(x)=0$$ because the solutions of this equation are their own inverses. ...
9
votes
6answers
2k views

Should I do all the exercises in a textbook?

The problem sets that you usually get in a university course is a small fraction of the exercises in your textbook. Which raises a question: do you need to solve all the exercises from your textbook? ...
0
votes
1answer
27 views

How do i analyze this complex diagram?

I'm asking how to analyze diagrams like this : http://upload.wikimedia.org/wikipedia/commons/thumb/9/96/Complex_LogGamma.jpg/600px-Complex_LogGamma.jpg What do distinct colors here mean? What do the ...
5
votes
1answer
183 views

Struggling with Topology. Any advice?

I'm a Junior Mathematics major at a small Liberal Arts college. I'm currently taking first semester topology (Munkres text). I feel like I'm barely able to tread water in this course. I was able to ...
4
votes
4answers
107 views

Is there a shorter path to these results?

I'm a student of Physics, however I usually study mathematics on texts aimed at mathematicians to gain a deeper understanding. Currently I'm studying differential geometry on Spivak's book and one of ...
3
votes
1answer
153 views

Best proof of some theorems in calculus

I would like to choose (among the miriads of proofs) a well-structured, elegant, neat, clear proof of the first fundamental theorem of calculus; the second fundamental theorem of calculus; the mean ...
11
votes
3answers
386 views

Is calculation a part or just a result of Mathematics?

There is a question that came to my mind that I'd like to discuss here. I hope it is clear what I want to express since English is not my mother tongue. Since I have started studying mathematics and ...
3
votes
1answer
99 views

why calling these 'algebra' and 'ring' too?

In measure theory you have 'algebra's' and 'rings' as subsets of the powerset of the underlying set of the measurable space. If I am well informed then you speak of an algebra if it is closed under ...
3
votes
0answers
37 views

Examples of functions which grow faster than their computational complexity.

A good example of this would be the function $f$ defined as follows, $f(n) = (10^n-1)$. While in this form it's equation is exponential, it is easy to note that $$f(n) = 99...9 \,(n \text{ times}).$$ ...
2
votes
0answers
44 views

Replacing $q^2$ by $q$

I have a rather strange question. Suppose we are given a formal power series $$S(q^2) = \sum_{n = 0}^\infty a_n q^{2n}.$$ I wish to replace $q^2$ by $q$. This implies that $S(q) = \sum_{n = 0}^\infty ...