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2
votes
3answers
83 views

A useful math project for high school [closed]

I need a project that will be useful for anything or anybody and it must be related to maths. It can also be related to other subjects. The math project should also be able to complete in 2 weeks. ...
4
votes
1answer
72 views

How should we think about equations like $dy = 2x \cdot dx$ from the viewpoint of modern geometry?

We've just started learning about (smooth) manifolds at uni, and I'm kind of hoping this will finally help me get a handle on the dreaded Leibniz notation. Now I've read that expressions $dy$ like can ...
0
votes
1answer
26 views

needing general information (algebra)

I plan to study algebraic number theory (arithmetic and Galois theory) in order to start research in cryptography and coding theory and all the staff... Also, i would like to introduce myself to ...
1
vote
0answers
35 views

What are metric spaces examples of?

A metric space is a very strange kind of object. It is not simply a set with some operations that satisfy some operations, like a group. In the higher reaches of abstract algebra, an algebra is ...
2
votes
3answers
86 views

What is an Isomorphism: Linear algebra [duplicate]

this is a rather soft question to I will tag it as such. Basically what I am asking, is if anyone has a good explanation of what a homomorphism is and what an isomorphism is, and if possible ...
1
vote
2answers
20 views

Methods to quickly compute percentages

Yesterday, talking with a friend of mine, she asked me what is a quick (and – of course – correct) way to compute percentages, say $3.7 \%$ of $149$. Frankly, I was sort of dumbfounded, because I use ...
2
votes
4answers
53 views

motivating diagonalization of a matrix [duplicate]

I have to teach about diagonalization of a matrix to a first year undergrad student and I was wondering what would be a good way to motivate this concept. I would appreciate any suggestions. Thanks!
3
votes
4answers
125 views

Good way to convince a young kid that $0*0 = 0$?

My little brother (6 years old) asked me a question ("What is $0*0$?") and gave an answer to his own question which I found ridiculous so I refuted it but he still thinks he is right. He says that ...
1
vote
0answers
34 views

Why are free objects related to tensors important?

Let $R$ be a commutative ring and $M$ be an $R$-module. Then, we can construct the tensor algebra $T(M):=\oplus_{n\in \mathbb{N}} M^{\otimes n}$ which is likely a free object. That is, for any ...
4
votes
1answer
100 views

Quality of Videos Lectures and Lectures vs Textbooks

I am a student trying to learn different subjects by watching video lectures and reading on my own time. I was wondering if the lectures from ICTP and nptelhrd are a great use of my time. I tried ICTP ...
5
votes
3answers
197 views

Is there an area of study regarding why certain mathematical definitions are useful?

Often in my studies I'll come across an definition, which I understand, and but don't necessarily see why the particular definition was chosen to be studied. For example, the topological axioms ...
0
votes
2answers
60 views

Are the angles adjacent?

$\angle 1 $ and $\angle 2$ are adjacent . So are $\angle AOD$ and $\angle BOD$ also adjacent. ? I am confused. EDIT: Suppose the point $C$ is not in the diagram , then in this case are ...
3
votes
2answers
86 views

Reference Text that develops Linear Algebra with Knowledge of Abstract Algebra

Background: Due to some unfortunate sequencing, I have developed my abstract algebra skills before most of my linear algebra skills. I've worked through Topics in Algebra by Herstein and generally ...
2
votes
3answers
52 views

Open Source Software for Creating Mathematical Diagrams

I work as a software engineer at a company developing navigation systems. As I have a mathematical background I normally get assigned the more mathematical problems and I find myself regularly having ...
4
votes
2answers
52 views

Looking for at least one surjective ring homomorphism from $M_n(R)$ to $R$

Let $R$ be a ring , I am looking for a surjective ring homomporphism from $M_n(R)$ to $R$ . Please help . Thanks in advance .
0
votes
1answer
54 views

How to interpret a matrix operation?

Suppose we have a 3-term vector $v_1 = [1, 2, 3]$, and another 3-term vector $v_2 = [16, 20, 22]$. Now suppose we find a 3 x 3 matrix $$M = \begin{pmatrix} -2 & 3 & 7 \\ 9 & -2 & 6 \\ ...
0
votes
0answers
59 views

Number of non-isomorphic groups of order $n$

$G$ is a group of order $n=p_1p_2....p_k$ then how to find the number of non-isomorphic groups of order $n$ where $p_i's$ are distinct primes I can find the number of number of non-isomorphic ...
1
vote
0answers
40 views

Visualization of theorem relationships

A few minutes ago a thought for a website/program crossed my mind and now I somehow hope that such a thing already exists. I thought of: A set of theorems linked by arrows telling the viewer/reader ...
2
votes
1answer
41 views

Suggestions to solve for $A$ in the equation $e^{-\frac{(A-B)^{2}}{D}}=C$

This seems almost silly to ask but I am stuck with it. I have the following equation \begin{equation}\tag{*} e^{-\frac{(A-B)^{2}}{D}}=C \end{equation} I know $A,B \in \mathbb{R}, ...
0
votes
3answers
36 views

Cross products and determinants in $\mathbb{R}^3$

I know that the absolute value of determinant of three vectors in $\mathbb{R}^3$ is the volume of the parallelepiped determined by the three vectors. The volume can be computed by basic calculation ...
1
vote
1answer
29 views

Soft Question-Will P/NP Grade Option matter a lot?

Currently I enroll in Second Course in Abstract Algebra. I don't think I perform well (Two Mid-Terms show that I am in the 50% percentile range which will probably lead me to a B/B+). So I am ...
2
votes
1answer
51 views

Does the ternary dot product have any geometric significance?

Given vectors $x,y,z \in \mathbb{R}^n$, define that their ternary dot product $x \cdot y \cdot z$ is the following real number: $$\sum_{i=1}^n x_i y_i z_i$$ Recall that the usual (binary) dot ...
0
votes
0answers
32 views

It is possible to show that given a statement, to show that is true instead of giving a proof, by showing that a proof is constructable?

I was thinking that we make proofs to show that there is a least one chain of reasoning that starts on p and ends on q. But in math, we dont always have to show something to argue that exist. Is ...
3
votes
1answer
32 views

Fundamental Ideas involved in Non-Existence of Minimum in (0,1] [closed]

The fact that there is no minimum in the interval $(0,1]$ is one of the first ideas introduced in an introductory analysis course. Its proof is simple enough: for all $\epsilon$ in $(0,1]$, ...
2
votes
1answer
54 views

Is it possible to provide a proof of some unsolved result using elementary methods? Is there no merit to this?

Is it possible to provide a proof of some unsolved result using elementary methods? I get the feeling it would be looked down upon and/or not taken seriously. Why is this? Is there no merit to ...
0
votes
1answer
14 views

regression question

Is the total sum of squares for multiple regression the same as the total sum of squares for anova? Is anova a test for bivariate correlation or multiple regression?
1
vote
1answer
22 views

Why there is a less care of symmetricity of bimodules over a commutative ring?

Let $R$ be a commutative ring. Then, we say $M$ is an $R$-module instead of left $R$-module or right $R$-module or $(R,R)$-bimodule. I'm curious why this convention is acceptable in general. Let's ...
0
votes
1answer
54 views

Question about graduate textbook and class.

I am a senior in mathematics, and I have had Advanced Cal I, but currently go to a no name school (there were only three people in the class). I have also taken Advanced Cal II as an independent ...
1
vote
0answers
68 views

Can we say anything about the relationship between these functors?

I am working with a category $\mathcal{C}$ and two functors $F:\mathcal{C}\rightarrow \mathbb{R}$-$\mathbf{Vect}$ and $G:\mathcal{C}^{\operatorname{op}}\rightarrow \mathbb{R}$-$\mathbf{Vect}$ where ...
3
votes
0answers
32 views

Idempotents and symmetries of Zn

[Soft question out of curiosity] While reading about idempotents of a ring, I used $\mathbb Z_n$ as a convenient example. In visualizing the ring's structure, I was intrigued by strange symmetries ...
1
vote
0answers
61 views

Undergraduate research in logic and/or algebra

I am currently an undergraduate in my junior year and am planning to do a yearlong project next year (essentially a yearlong undergraduate thesis). I am interested generally in algebra and logic, and ...
3
votes
2answers
60 views

Which optimization problem to use when I want to explain the concept of optimization to a layman?

I am looking some problem, which would be: Easy to understand Hard to solve intuitively Touch our everyday lives I am doing research in optimization using evolutionary computation. When people ...
6
votes
1answer
91 views

An equivalence of categories which looks like Voevodsky's Univalence Axiom

Let $\mathcal{C}$ be a category. Consider the full subcategory $\mathrm{Isom}(\mathcal{C})$ of $\mathrm{Mor}(\mathcal{C})$ whose objects are isomorphisms $A \xrightarrow{\cong} B$. It has a full ...
1
vote
0answers
47 views

Munkres' Analysis on Manifolds and Differential Geometry

Will Munkres' Analysis on Manifolds prepare me for a text like John Lee's Introduction to Topological Manifolds and his Introduction to Smooth Manifolds text? Would one be able to successfully tackle ...
2
votes
2answers
46 views

Structure theorems for modules over 'good' rings

Structure theorem for finitely-generated modules over PID is well-known fact. But is there similar theorems for modules(maybe finitely-generated) over noetherian or artin or some other 'good' rings? I ...
0
votes
0answers
20 views

How Leibniz invented the Binary System?

Do you know which reasoning and observations made Leibniz invent the Binary system ? Some say that he was inspired by Chinese mathematicians do we have any record of how he came with this idea ?
3
votes
1answer
65 views

What is the role of fixed point theorems in modern mathematics?

About Fixed Point Theorems, Wikipedia says: Results of this kind are amongst the most generally useful in mathematics. This seems an accurate statement: indeed, there are many journals ...
-1
votes
1answer
59 views

Basic Concepts of Mathematics by Elias Zakon

Has anyone studied the book "Basic Concepts of Mathematics" by Elias Zakon? (To whom) Can you recommend it? On what level of difficulty is it (like early undergraduate for example)?
2
votes
1answer
85 views

Projects for Topology?

I am in a Topology course in undergraduate. We are in Chapter 2 right now of Patty's Foundations of Topology. We are supposed to do a project outside the book but I'm not feeling creative right now. ...
0
votes
3answers
89 views

Best way to learn pure mathematics [closed]

I'm currently enrolled in an introductory real analysis course. While I enjoy the beauty of pure mathematics, there are 2 problems I face. 1) Constructing proofs 2) Attempting to understand a proof ...
3
votes
2answers
58 views

What are the uses of cross-theoretic identifications within mathematics?

I've been thinking about the identification of objects from different mathematical theories. For example, when you do set theoretic constructions of the natural numbers and identify, e.g., 0 with the ...
2
votes
2answers
63 views

A break in symmetry between Algebraic number fields over Q and otherwise

Most of the theorems in algebraic number theory seem to generalize to arbitrary base fields apart from $\mathbb{Q}$ apart from one. The characteristic of the residue field is equal to positive prime ...
1
vote
0answers
17 views

On the existence of certain Weierstrass-type Extreme Value Theorems

It is well-known that Weierstrass Extreme Value Theorem can be generalized to lower and upper semi-continuous functions. Are there any other generalizations of this important result; and more in ...
4
votes
2answers
102 views

Does randomness exist? [closed]

I've been plagued with this question for a few years now and wanted to know what others think. Does true randomness really exist? In mathematics, a random process is based on the concept of random ...
1
vote
0answers
21 views

What is the state of art of the question that pi has every secuence on it´s decimal expansion? [duplicate]

I have heard that if pi have all disctinct sequence on it´s decimal expansion, then all the books that are not written can be found there and it is one of the most romantic stories i have ever heard ...
1
vote
0answers
71 views

P = NP, NP example problems in our daily life

For a little presentation for school, i want to try to explain the P=NP? Problem. I'm searching for examples for daily life NP-problems. (example: is making the weather forecast a NP problem?) And if ...
0
votes
0answers
39 views

Is there a name for an object with both position and velocity?

I know of "position vectors" and "velocity vectors". I'm looking for the name of an object which contains both a position vector and velocity vector, if such a name exists?
4
votes
1answer
73 views

Maths Discoveries thanks to Computer Science

Which discoveries have been made in mathematics thanks to computer science ? For example fractals have been discovered thanks to computers (correct me if im wrong) do you know any similar discoveries ...
3
votes
0answers
104 views

Are there human integrators? [closed]

Are there human "integrators", "differentiators", or "analysts"? I've heard of and seen people capable of performing seemingly complex arithmetic calculations mentally. Often this involves memorizing ...
1
vote
0answers
21 views

Usage: Holomorphic Functions

This isn't a math question, but rather a question is word usage in mathematics. Why do people say " $f$ is an isomorphism," or "$f$ is a diffeomorphism," but in complex analysis, we say that "$f$ is ...