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0answers
35 views

Is it important to study plane algebraic curves before read Fulton's book

I'm studying Fulton's algebraic curves book and I would like to know how important study plane algebraic geometry before read Fulton's book. Example of books on this subject: Algebraic Curves - ...
0
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2answers
74 views

What are the differences between mathematics courses taken by engineering majors and by math majors? [closed]

I am curious to know what are the differences between mathematics taken by engineering students and by math majors. Let's say in terms of the approach, depth and in the topics covered. And even within ...
3
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2answers
61 views

Is calling a linear-equation a linear-function, misnomer or completely wrong?

From my college life, I remember many professors used to call a linear-equation a linear-function, however: A standard definition of linear function (or linear map) is: $$f(x+y)=f(x)+f(y),$$ ...
2
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1answer
96 views

Why is the powerset axiom more acceptable than the axiom of choice?

The key step in Zermelo's proof of the well ordering theorem is to use $\text{AC}$ to simultaneously choose the next elelment for all possible partial chains in prospective well orderings, but that ...
6
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2answers
57 views

Geometric interpretation of complex path integral

Let's say that we want to make sense of integrating a function $f: \mathbb{C}\rightarrow\mathbb{C}$ over some path $\gamma$. I can imagine two reasonable ways of doing it. First, there's the way ...
2
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0answers
64 views

Tool for converting maths writing to $\LaTeX$ [migrated]

I have a dream. I want my maths writing to magically be made into a .tex file so that I can edit it. I want to write my papers, my exams, my lecture notes, ...
3
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2answers
268 views

Degrees of separation between famous mathematicians

I was recently doing some reading on Wikipedia, and I noticed that if you go far enough though Isaac Newton's notable students' students' students. . . (and so on), eventually one was Augustus De ...
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0answers
45 views

Intuitive explanation for $\zeta (2)=\frac{\pi^2}{6}$ [duplicate]

Using $f(x)=x^2$ Fourier' series, the proof for $\zeta (2)=\frac{\pi^2}{6}$ is pretty straight forward. I'm wondering if there is a more intuitive explanation for the equality, one that a layman could ...
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1answer
53 views

The art of solving exercise problems [closed]

I do not know whether this question appears to be off topic or not. But I really want to know, how to be well versed in solving exercise problems prescribed at the end of each section. I understand ...
26
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7answers
2k views

Mathematical literature to lose yourself in

H.M. Edwards in the preface to his book on the Riemann Zeta Function, summarises his philosophy on learning Mathematics: ...I have tried to say to students of mathematics that they should read the ...
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0answers
67 views

Is there a name to this equation: $(y - a|x|^b)^2 + (cx)^2 = d$?

While doing a survey of the various equations that generate the universal love symbol, a heart curve, I find that many fit into this parametrised form: $$(y - a|x|^b)^2 + (cx)^2 = d $$ Where   ...
3
votes
1answer
58 views

How does research in math differ from research in statistics?

I'm at a crossroads where I'm considering switching my major from electrical engineering to math, because quite frankly, I'm just not getting enough math to satisfy my passion from engineering. While ...
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5answers
293 views

I need help finding a rigorous Pre-calculus textbook

I dislike modern textbooks; their cookie-cutter approach and appearance, over reliance on breaking things down into little boxes, the general spoon-feeding they engender and most of all the poor ...
10
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1answer
225 views

How inequalities are made

I've been solving a lot of math contest inequality problems last few days and sometimes when I solve the problem I can easily ''see'' the idea behind it's creation (for an example, one clever ...
0
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2answers
29 views

Splitting a matrix $A \in \mathbb{M}^{n \times n}(\mathbb{C})$by solving $Av = \lambda C v$ for some chosen $C$

If we know a matrix $A \in \mathbb{M}^{n \times n}(\mathbb{C})$ and solve $Av = \lambda v$ where we try to find $\lambda,v$, we can rewrite $A$ in a nice way. What if we choose a matrix $C$ and we ...
3
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0answers
75 views

What's so special about binomial coefficients that someone decided to organize them in a triangle?

I know that binomial coefficients are related to figurate numbers (which were studied by Greeks a loooong time ago, because of its connections to geometry). I also understand how the Pascal's triangle ...
2
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0answers
48 views

What is combinatorial probability a special case of?

Once I complained to one of my undergrad math professors that I was hopelessly lost when it came to combinatorics and combinatorial probability problems. He remarked, half-jokingly, that combinatorics ...
2
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3answers
110 views

Chess and mathematics

I have to choose a research-like project to follow the next year. Because I'm a chess enthusiast, I was thinking of trying to tackle an (open) problem related to chess, and relevant to mathematics. ...
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0answers
65 views

The steps to becoming a Pure Mathematician

I'm a college freshmen intending to major in Mathematics. I started college with not so great grades in my calculus courses. However, I realized that to get the grades I just have to practice. I ...
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3answers
145 views

Is Adobe Acrobat's icon a special function?

It looks like a function in polar coordinates. Is it a special function ?
2
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3answers
84 views

“Practical” Claim about Hypothesis Testing of Bernoulli Distribution Parameter

First, let me state the original problem (in my own wording): Describe the decision procedure for testing the hypothesis about the parameter $p$ (success rate) of a Bernoulli distribution. The ...
5
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5answers
265 views

Examples of advancement in mathematics due to war

It's not a lie that, in most sciences, some of their advancement comes from war. A couple examples would be the Haber process in chemistry and none other than the Manhattan Project in both physics and ...
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8answers
2k views

Problems that become easier in a more general form.

When solving a problem, we often look at some special cases first, and then try to work our way up to the general case. It would be interesting to see some counterexamples to this mental process, ...
3
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0answers
50 views

Undergraduate Schools for the Mathematically Inclined

I'm a rising senior and working on generating a list of colleges to apply to, but it seems to me that (with few notable exceptions) my two main criteria are mutually exclusive. Are there any schools ...
3
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2answers
54 views

Any suggestion on how to justify true/false question in linear algebra exams?

I have hard time bringing words on paper when it comes to true false justification of linear algebra problems. My technique is to use counter example for false and use book theorems for true ones. ...
2
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0answers
36 views

Equillibrium between Programming and Math Skills? [closed]

So I enjoy recreationally doing math and programming and am now at a stage where I will be pursuing them in University but I have found myself in a bit of a bind. My programming ability seems to lag ...
0
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1answer
59 views

Dealing with questions with unknown answers

The vast majority of textbook exercises are worded essentially in the format: This assertion is (true/false). Prove this or find a counterexample. This, of course, is not how mathematics is ...
2
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1answer
109 views

Too Many Books - Not Enough Time

I am currently a high school student trying to get as far ahead in mathematics as I can. In doing so, I accumulated a good 10 physical math books, and a library of online resources including 2 or 3 ...
3
votes
1answer
73 views

What are the big issues in modern graph theory?

This is inspired by the similar question on modern set theory. I've read through the open problems in graph theory on Wikipedia's list of unsolved problems in mathematics, but what I'm looking for is ...
2
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1answer
121 views

Are there any “obviously” true propositions in number theory?

After all efforts spent on wrong proofs of famous number theory conjectures and theorems like Goldbach's or Fermat's last theorem, could one find some simple statements (might be correct ones) whose ...
1
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1answer
18 views

I have been offered year 2 entry for a maths degree but am not sure I want to take it -would love some advice

I am about to start an undergraduate maths degree (MMaths) and am extremely excited about studying maths . I applied for the normal first year entry and was offered an unconditional mid January ...
40
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6answers
4k views

What should an amateur do with a proof of an open problem?

Assuming that somebody is not an employee of a university, just a math amateur, and makes a proper proof of some well known open math problem, what should he do with it? Publish on the internet for ...
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0answers
11 views

A name for the number system used in versioning software

Software often uses a numbering system where one "digit" increments independently of the others. For instance, the next version of Software 2.9 might be Software 3.0 or Software 2.10 or Software ...
12
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2answers
285 views

Why are people more interested in the Riemann hypothesis than Goldbach's conjecture? [closed]

One of my friends, a math professor, told me almost every one of his colleagues (in the math department) had attempted to prove the Riemann hypothesis at some point in their life (maybe secretly). ...
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0answers
12 views

Phrases for uniform boundedness and uniform convergence

I have some doubts about using prepositions. I. Let $f_a : \mathbb{R} \to \mathbb{R}$, $f : \mathbb{R} \to \mathbb{R}$. Assume that $f_a (x)$ converges uniformly to $ f (x)$, $x \in [0;1]$, as $a ...
0
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0answers
35 views

How do you look for classic/normative/standard books about an established branch of mathematics?

If you want to immerse yourself in a branch of mathematics (e.g. linear algebra and linear optimisation) which is new to you, then you often look for standard books which you can rely on. You could ...
0
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2answers
49 views

An ABC soft question about epsilon-delta argument

Someone told me that some textbooks present epsilon-delta argument somewhat misleadingly. For example, consider the simplest one: the convergence of the sequence $(1/n)_{1}^{\infty}$ to $0$. These ...
3
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0answers
51 views

Etiquette for proper usage of Greek letters and other notation

I've progressed to the "output" point in my mathematics career and have run into a slightly embarrassing problem while writing a paper. Clearly, certain Greek letters are suitable for some situations ...
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0answers
22 views

Usage of the phrase “constant parameter”

In general, constants are globally fixed, while parameters are a bit more free. But suppose I wish to use the word "constant" as an adjective to emphasize that a parameter is fixed w.r.t. other ...
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3answers
149 views

Is tutor essential for success in mathematics? [closed]

Everyone in my Pre-Calc - Calc I class is failing, except the kids who go tutor. They get top percentile ranks in the class. Should I drop maths all together so I don't have to invest in a tutor? I ...
3
votes
0answers
61 views

Is it too late to start studying maths? [closed]

I am 24 years old and I am just beginning to study undergraduate level maths. I have a bachelors and masters in mechanical engineering. Is it too late for me to start studying maths now? I plan to do ...
8
votes
0answers
90 views

Is Category Theory geometric?

In "From a Geometrical Point of View" (http://www.amazon.com/gp/aw/d/1402093837?pc_redir=1407132421&robot_redir=1) Marquis states that category theory is thoroughly geometric. Could someone ...
0
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0answers
43 views

Can a Computer Algebra System 'experiment' with expressions?

I have recently been reading about software for symbolic manipulation, and I can see its use as a tool for performing large calculations that would be unfeasible otherwise. Given that these systems ...
5
votes
4answers
197 views

What sequence should I study these topics in?

I will shortly list a series of topics that amount to what is essentially the first two years of an undergraduate degree. I'd like to know what is considered best order in which to study these ...
1
vote
0answers
71 views

Why nobel prize is not for mathematicians [closed]

I have heard from many people that nobel prize is not given to mthematicians.Waht is the reason behind this?I also heard that a women rejected the nobel because of some famous mathematician.Is this ...
6
votes
1answer
171 views

How much mathematics should a student of mathematical logic know?

I would like to know what areas of mathematic are directly related to mathematical logic, besides the usual courses on model theory, proof theory and computability. If you suggest only one book on ...
6
votes
7answers
756 views

A question regarding irrational lengths in reality

I have a square stone slab 1 metre by metre, by the Pythagorean identity the diagonal from one corner to another is given as $\sqrt 2$. However $\sqrt 2$ is an irrational number, could someone ...
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4answers
88 views

What functions are most useful after the ones learned in high school?

I have learnt how to use trig functions, hyperbolic trig functions, exponentials and logs and simple things like polynomials, ellipses, hyperbolas and rational functions but lately when doing calculus ...
3
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0answers
63 views

In what order should I study?

I would like to study the basic fundamentals of mathematics from the beginning and move on from there as my understanding of the subject is lacking. In what order should I study? Arithmetic ...
2
votes
1answer
129 views

Math enthusiast wants to learn math

I'm an english major with a vivid interest in mathematics,I've read and enjoyed What Is Mathematics? by Courant and Robbins (does this count as some background?),and I've decided to begin a serious ...