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0
votes
1answer
81 views

Gerd Faltings Interview

I wanted to read about Gerd Falting's journey as a mathematician . I was searching for a link having his interview but unable to find any . Can anyone here suggest any link for Gerd Falting's ...
3
votes
1answer
86 views

Examples of how to apply algebraic number theory

I am reading about algebraic number theory mainly following milne's notes. But currently I really wonder how such theory can help solve problems of number theory. One example I know is we can use ...
1
vote
0answers
46 views

``angle" between two group elements

For the group $\mathbb{Z}^n$, we may embed them in $\mathbb{R}^n$ and then it is clear that for any two elements in $\mathbb{Z}^n$, we may treat them as vectors and hence the notion of ``angle" ...
0
votes
1answer
62 views

Soft question: Can one learn Fourier Analysis without a working knowledge of Integration Theory

As the title indicated, I am wondering if one (probably as an undergraduate math major) can learn much of Fourier Analysis, without taking a course in integration theory. I am taking a very light ...
1
vote
0answers
60 views

Why is the decimal number system so popular?

This probably isn't a great question, but I was just wondering that why is the decimal number system used around everywhere( not talking about machine languages). My first thought was that it appears ...
7
votes
2answers
75 views

The role of the Zariski topology in algebraic geometry

I am having trouble understading the relevance of the Zariski topology being a topology. Every time I see the proof that sets of the form $V(I)=\{p\in\mathbb{A}^n\mid f(p)=0 \ \forall f\in I\}$ ...
4
votes
0answers
35 views

(Soft Question) Formal name for something one is taking the limit of

When you are taking integral you have an integrand. When you are taking a sum you have a summand. Is there an analog of this for limits? How should one refer to $f(x)$ in the expression ...
0
votes
2answers
108 views

Ideas for a Talk [closed]

I'm trying to think of a suitable topic for a math talk. I'll have 15 minutes to present, and the audience is math grad students of all different specialties. My talk should be accessible to any ...
4
votes
2answers
87 views

Differentiation and integration

Which came first : Differentiation or Integration? If one of them was developed to solve certain types of problems, was the other developed for backward compatibility, or was it an independent ...
3
votes
1answer
60 views

Texts on the History of Linear Algebra

I thought I hated math at first, but linear algebra really changed my outlook on mathematics. What I really didn't like was calculus, which is fine, there are plenty of folks who would love to focus ...
5
votes
2answers
99 views

Is there an advantage to using polish notation in terms of human readability?

Lately I've been reading a lot of questions and answers related to logic and I have found some of them in the style of this one. As I'm not a fan of using Polish notation, I honestly just skip them. ...
11
votes
3answers
138 views

How does one interpret statements like: “The traveling salesman problem is NP-complete?”

The world abounds with statements like: The traveling salesman problem is NP-complete. But when I follow try to follow the Internet's links "down the rabbit hole," I don't get a truly sensible ...
1
vote
3answers
50 views

If $ax^2+bx+c \leq p(x) \leq lx^2+mx+n$ , show that the degree of $p(x)$ is $2$.

If $a,l\neq0$ , $ax^2+bx+c \leq p(x) \leq lx^2+mx+n$ , show that the degree of $p(x)$ is $2$. How can we exactly say (how to prove) that $p(x)$ is a quadratic ? What methods can be used to ...
0
votes
0answers
42 views

Self-study note taking from a formula heavy math textbook

Having graduated, and trying to decide what I want to do for graduate school I decided I want to read a math textbook. The textbook in question is "An introduction to Analysis of Financial Data with ...
0
votes
0answers
44 views

inquiry about differential geometry texts.

i am very interested in diff geometry as a math undergraduate student and want to study the diff geometry in the graduate school. so what would be a good book for the advanced diff geometry to get ...
6
votes
4answers
117 views

Could we “invent” a number $h$ such that $h = {{1}\over{0}}$, similarly to the way we “invented” $i=\sqrt{-1}$? [duplicate]

$\sqrt{-1}$ was completely undefined in the world before complex numbers. So we came up with $i$. $1\over0$ is completely undefined in today's world; is there a reason we haven't come up with a new ...
0
votes
1answer
25 views

the main measure

I'm looking for the following notion in english if exists, called in french "la mesure principale" ( the main measure ) Let $\theta$ be an angle in standard position the main measure for $\theta$ ...
1
vote
2answers
30 views

Looking for websites to brush up on algebra skills needed for calculus

I've enrolled in an 8 week online Calculus 1 class, we're currently in week 2 and while I understand the calculus concepts (average rate of change, limits) I'm having a hard time on my homework due to ...
1
vote
1answer
19 views

Term for using a number as an exponent (complementing “raise to the power of …”)

If we have an equation we want to solve such as $\sqrt{x} = 3$, we can say something such as square both sides or "raise both sides to the power of 2", to arrive at $x = 9$. So $3 \rightarrow 3^2$ ...
5
votes
2answers
73 views

Probability: mathematically what does it mean to say “let $X$ be a random variable WITH a cdf/pdf”

I don't quite understand what people mean by let "$X$ be a random variable WITH a cdf/pdf". For example, there is a question that says: "Let X be a random variable with the 3-parameter Weibull pdf and ...
3
votes
0answers
44 views

Failing to recognize the importance of compactness, connectedness, and other topological notions in Real Analysis [closed]

I'm currently taking a course in Real Analysis that uses Principles of Mathematical Analysis by Rudin, and having a somewhat difficult time on tests. I always read that notions like compactness, ...
62
votes
7answers
5k views

Is linear algebra more “fully understood” than other maths disciplines?

In a recent question, it was discussed how LA is a foundation to other branches of mathematics, be they pure or applied. One answer argued that linear problems are fully understood, and hence a ...
0
votes
0answers
35 views

Strange type of matrix equivalence, $\bf P=Q$. What applications or properties can it have?

Stemming from this question when actually searching for matrix similarities, having found this matrix equivalence: $$\bf A = PBP$$ That is neither transpose nor inversion on either of the $\bf P$s. ...
4
votes
2answers
57 views

Etymology of transpose of morphisms in an adjunction

Let $F: \mathbf{C} \to \mathbf{D}$ be left adjoint to $G : \mathbf{D} \to \mathbf{C}$, witnessed by the family of bijections between hom-sets, natural in objects $X, Y$: ...
2
votes
2answers
90 views

What is the simplest mathematical object? [closed]

What is the simplest mathematical object? I am talking about mathematics in the most abstract way possible, and not as some concrete axiomatic theory (e.g. foundational ones, like ZFC). After a lot ...
-1
votes
2answers
184 views

How to study for hard math proofs?

Most of the content is new to me and there are a lot of theorems and proofs that I am learning; not that I need to know all of them but I enjoy to learn more. Some of the concepts (like open sets) or ...
5
votes
2answers
180 views

Ugly solutions to easily stated problems [closed]

I recently saw a very hideous closed form for a quartic equation here: Does a closed form solution exist for $x$? For fun, I'm wondering about surprisingly ugly solutions/ complicated machinery ...
2
votes
1answer
32 views

Interesting sequence of all the natural numbers [closed]

What are some sequences that contain all of the natural numbers that come up naturally in mathematics? (Obviously, there are an infinite number of sequences of all the natural numbers ($2^{\aleph_0}$ ...
3
votes
0answers
92 views

Intersection of Algebraic Geometry and Algebraic Topology

What mathematical areas lie at the intersection of algebraic geometry and algebraic topology? I'm aware of certain ones such as derived algebraic geometry and motivic homotopy theory, which all ...
0
votes
0answers
29 views

Error Correcting Code and Graph Theory

I am currently in an introductory graph theory class, and we are supposed to give a short presentation by the end of the semester. Recently, I've learned (a very small amount) about error correcting ...
4
votes
1answer
73 views

Approaching a seemingly intractable problem

This is a soft question that questions how to be efficient in approaching a problem that seems intractable to solve. In particular in abstract algebra, I feel that certain proofs are 'magic'. When ...
3
votes
1answer
63 views

Are there any instances of significant progress deriving from mathematical 'silliness'? [closed]

Last night I thought I'd be silly finding the eigenvalues of a $2\times2$ matrix $A$ with real components. Instead of calculating $\det(A-\lambda I)=0$ I tried to compute the determinant by ...
1
vote
2answers
71 views

Earth population growth rate is exponential or logarithmic?

How many points on a monotonically increasing curve is needed to determine if it is exponential or logarithmic? For example can we tell that in the most recent history population is increasing ...
4
votes
1answer
116 views

What is meant in the quotation of Terry Tao?

Terrence Tao commented of internalizing [here: https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/] "It is true that some mathematicians can be vastly more ...
1
vote
0answers
31 views

Symmetric Polynomials in Geometry

I'm interested in symmetric polynomials. Could you name some nice examples in Differential Geometry where they are clearly useful? I would also be interested in algebraic examples if connected with ...
0
votes
0answers
19 views

Condition on tightness of an inequality

How is generally the tightness of an inequality measured? Is the inequality tight when it is held with equality under certain conditions?
2
votes
0answers
57 views

Pocket Calculators- Obsolete? [closed]

I hope this fits into "software that mathematicians use" within the acceptable topics for this site. Are there still any instances where pocket calculators prove useful to professional mathematicians ...
6
votes
1answer
200 views

A book on advanced math for a “novice” mathematician, but “mature” thinker [closed]

I enjoy giving interesting problems to my peers who have not seen a lot of mathematics. It is a constant conversation I have with many friends who would interchange "mathematical thinking" with ...
4
votes
1answer
62 views

Studying Graduate Level Mathematics Outside Lecture Hours

I am not exactly sure if this should be posted on math.se or academia.se, but I think the question is more mathematical in nature. I am a first year graduate student in mathematics, and I would like ...
11
votes
5answers
626 views

Defining the Determinant

The concept of determinant is quite unmotivational topic to introduce. Textbooks use such an "strung out" introductions like axiomatic definition, Laplace expansion, Leibniz'a permutation formula or ...
54
votes
8answers
6k views

Is linear algebra laying the foundation for something important?

I'm majoring in mathematics and currently enrolled in Linear Algebra. It's very different, but I like it (I think). My question is this: What doors does this course open? (I saw a post about Linear ...
1
vote
3answers
80 views

Why do inequalities matter and what are they used for?

I am currently studying mathematical course at my college, and I cannot seem to grasp the concept of inequalities. What troubles me is that, like it's said, "triangle inequality matters because many ...
4
votes
2answers
78 views

Why is it so hard to translate some proves into machine-readable form?

I have just read a topic on mathoverflow about man vs. machine in mathematics. The topic was inspired by the recent victory of Alpha Go over the World Go Champion, Lee Sedol. It reminded me of an ...
2
votes
1answer
73 views

Necessity of Category Theory for understanding Algebraic Topology [duplicate]

I am studying Algebraic Topology and increasingly find that when I turn to the internet for help, the explanations and even definitions I need are given in terms of Category Theory (which I know ...
2
votes
1answer
50 views

Much used compass and straightedge constructions

I am a editor of wikipedia and would like to know which compass and straightedge constructions deserve a place in the list ...
2
votes
0answers
46 views

Can one cite REU papers written by students?

I am writing my Master thesis right now. Two arguments in the proofs are based on REU papers written by students. As those are not officially published but made available on the universities' websites ...
1
vote
1answer
62 views

Why should I expect the product of sum of four squares to be a sum of four squares? How did Euler come up with it?

Euler discovered the lovely identity shown here: https://en.wikipedia.org/wiki/Euler%27s_four-square_identity Is there a natural reason to assume a solution can be found? Any intuition? I saw that ...
0
votes
2answers
36 views

Dealing with computations that are tedious and time consuming

In attempting mathematics homework question one of the greatest redundancies I generally face is having to deal with long winded and tedious computations. For instance, in the field of Quantum ...
0
votes
0answers
42 views

What are some interesting results that could be derived if some conjectures were true/false?

I recently came up on Djikstra's idea of a fictional company called Mathematics.Inc which produced proofs as trade secrets which could then be used by customers.. For example, it produced the proof of ...
2
votes
2answers
47 views

What is wrong with my logic and derivatives?

Since the derivative of a function is analogous to a description on how fast the function grows, I thought that $\lim_{x\to\infty}\frac{f'(x)}{f(x)}=0$ for the following reason. Assume $f(x)$ is ...