All Questions
495 questions
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What is the geometric meaning of the third derivative of a function at a point? [closed]
What is the geometric meaning of the third derivative of a function at a point?
This question is now asked on the sister site: https://math.stackexchange.com/questions/14841/what-is-the-meaning-of-...
- 61
2
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0
answers
1k
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Good sources for linear algebra for convex optimization and graph analysis?
What are some good sources for linear algebra for convex optimization and graph analysis?
In Particular, is Gilbert Strang's MIT course suitable, or some other online course? I prefer online courses (...
- 2,383
2
votes
0
answers
526
views
How much of math could be taught without using mathematical notation? [closed]
Given that mathematics is not about number, and that it is not even about the cryptic notation used to describe mathematical problems, how much of mathematics could be taught without reference to ...
1
vote
1
answer
378
views
Why is $n_{n^2-1}$ the smallest graph that clearly shows the structure of multiplication by $n$?
Initially, I wanted to ask this question as a puzzle.
Consider a regular $m$-gon. Let $0$ be the lower corner and count the corners clockwise.
Let $n_m$ be the multiplication-by-$n$-graph of $...
- 9,720
1
vote
1
answer
489
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Book on analysis and algebra at the undergraduate level [closed]
I am writing this post because I would like to know what are your references concerning math book showing the interplay between analysis and algebra at an undergraduate-advanced undergraduate level.
...
1
vote
2
answers
825
views
Simple yet interesting applications of Calculus or Linear Algebra to Economics [closed]
This is essentially a vast generalization of my previous question: Examples of separable ordinary differential equations in economics
I'm giving a talk to college-level math teachers on some ...
1
vote
2
answers
1k
views
An "Elementary" Math Question Generalized (Ring Theory Perhaps)
The following question is posed in the book "The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics"
"Prove that if integers a_1, ..., a_n are all distinct, then the ...
- 1,801
1
vote
1
answer
387
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proof without words for logarithms [closed]
Does anyone know of any PROOF WITHOUT WORDS for logarithmic functions?
The only one I've seen in calculus based and I need one for high school math kids in MATH 1,2,3.
Any suggestions would be ...
1
vote
1
answer
117
views
Resources on blended teaching and flipped classroom in undergraduate mathematics education [closed]
I'd like to learn about the implementation of "blended teaching" in general and "flipped classroom" in particular for the teaching of undergraduate mathematics. Can anyone ...
- 141
1
vote
1
answer
116
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Expectation of changing the gift choice [closed]
Suppose we are given two boxes, with one of gift valued $n$ dollars and the other one valued twice as much. We can pick a box, and after open it we have the choice of switching to another box. Shall ...
- 19
1
vote
1
answer
181
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Distance between two distribution of image
I am looking for a common distance method to compare two distribution (ex: histogram of image). Please suggest to me some common method to do it. I found some method ex: Bhattacharyya distance , K-L ...
- 119
1
vote
1
answer
7k
views
Websites hosting free math ebooks. [duplicate]
Possible Duplicates:
Free, high quality mathematical writing online?
Most helpful math resources on the web
A lot has been said about different kinds of math resources here in MO.
To mention a ...
1
vote
0
answers
106
views
The proposition associated with a set
Given a set $U$ and a set $A \subseteq U$, is there an accepted symbol for the proposition $p$ over the universe $U$ such that for each $x \in U$, $p(x)$ is the assertion that $x \in A$? (The symbol $...
- 19.7k
1
vote
0
answers
109
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Problems Correction of "Algebra, Topology, Differential Calculus, and Optimization Theory For Computer Science and Machine Learning "' [closed]
Where I can find the problems correction of this book " Algebra, Topology, Differential Calculus, and Optimization Theory For Computer Science and Machine Learning "
- 11
1
vote
0
answers
155
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Introducing generating functions to engineer audience?
What is a good way of summarizing when "generating function" approach is useful to an audience of practitioners?
I'm giving a talk on training neural networks (see Velikanov, Kuznedelev, and ...
- 2,252
1
vote
0
answers
190
views
what belongs in a first university-level geometry course? [closed]
I know this is not really a research question, but I would like to ask it of research mathematicians, to see if there is a consensus. In a recent discussion on this topic, someone suggested that if ...
- 99
1
vote
0
answers
167
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A taxonomy of proof methods [closed]
I am looking for a taxonomy of proof methods in mathematics.
For basic proof methods I would think of proof by contradiction, mathematical induction, structural induction (yes I am a computer ...
- 289
1
vote
0
answers
322
views
Online courses for mathematics [closed]
I'm sorry if I'm posting this in the wrong forum. My background is in biology and medicine. I am looking to re-learn undergraduate-level mathematics, in particular discrete mathematics, calculus, and ...
- 19
1
vote
0
answers
134
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What benefits of math can be conveyed to mid/high schoolers? [closed]
I'm teaching mathematical proof writing to a few of math teachers (in the US) this summer. In the beginning of class, I send a survey asking them why they are here. Most of them are here for getting ...
- 5,230
1
vote
0
answers
200
views
Studying the vast world of Number Theory [closed]
I'm a high school student, interested in mathematics, especially in number theory.
While preparing for the IMO test, and thinking about generalizations or the root of many olympiad problems led me to ...
- 141
1
vote
1
answer
249
views
Generalized Fourier integral and steepest descent path, saddle point near the endpoints
I am looking forward to solving the integration in the following equation with the assumption that $ka$ is very large
\begin{align}
H = 2jka\int_{-\pi/2}^{\pi/2}\cos{(\varphi-\phi)}e^{jka[\cos{\...
- 13
1
vote
0
answers
631
views
Arguments against Reductio ad Absurdum [closed]
Could Reductio ad Absurdum not be consireded a valid proof method? Are there any compelling arguments against it, or at it's favor?
I feel like I am assuming some metamathematical hypothesis about my ...
- 11
1
vote
0
answers
430
views
Professional skills advising for math jobs [closed]
Hi,
I am a postdoc at the University of Nottingham (UK) and I am beginning to apply for Assistant Professor positions in US.
I would like to receive a feedback on the material that I am sending (...
1
vote
1
answer
1k
views
Best examples of physics providing insight into math [duplicate]
Possible Duplicates:
Examples where physical heuristics led to incorrect answers?
Examples of using physical intuition to solve math problems
V. I. Arnold argues (http://pauli.uni-muenster.de/~...
0
votes
5
answers
2k
views
How to teach addition of negative numbers? [closed]
I have a friend with dyscalculia and was teaching her some some mathematics (namely, solving a linear equation, simplifying certain expressions, and what (affine linear) functions are).
She ...
- 648
0
votes
3
answers
1k
views
How to be a Great mathematician in prison/without a master? [closed]
Is it possible to be a great mathematician in our home with a laptop+poor internet+electronic books+some books+a little food +a little money or not? without having a constant job
without studying P.H....
0
votes
7
answers
3k
views
Good/Economical textbook for undergraduate intro to diff.eq. for engineers?
In the fall I will be teaching an intro to diff.eq.s course for undergrad engineers. The usual textbook is $150 with solution manual and it's not that great. There must be a cheaper alternative that's ...
0
votes
2
answers
852
views
Can one branch of mathematics be completely learned from the perspective of another branch of mathematics? [closed]
This arose from a discussion with a friend (people involved are two engineers) who argued that every result in mathematics should be transformable into another branch. For example, he argued that ...
0
votes
4
answers
400
views
Application for functions of the shape $r = f(\theta)$
A fairly ubiquitous object in elementary calculus is a function of the shape $r = f(\theta)$, where $r$ is the radius and $\theta$ the argument. Common examples include the cardiod and limacon, and of ...
- 26.9k
0
votes
2
answers
562
views
Lines on degree 2n-3 Fermat hypersufaces
It is well known that a generic hypersurface of degree $2n-3$ in $\mathbb CP^n$ has finite number of lines. I would like to ask a couple of questions about lines on Fermat hypersurfaces and their ...
- 14.3k
0
votes
1
answer
1k
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Best Practices for Learning Mathematics (especially in the classroom) [closed]
I am an undergraduate CS major with strong interests in applied math and theoretical computer science. In the past, I've done reasonably well grade-wise in all math-related (that is, pure math, ...
0
votes
1
answer
2k
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Dual of Zorn's Lemma? [closed]
It seems to me that the dual of Zorn's Lemma should be true: if $S$ is a non-empty partially ordered set and every chain of $S$ has a lower bound in $S$, then $S$ has at least one minimal element.
...
- 1
0
votes
1
answer
114
views
Name of a matrix with one column and row removed [closed]
I am looking for the exact name of a matrix where the i-th column and rows have been removed.
I cannot remember how it is called in linear algebra, does anyone got an idea?
Thanks!
- 111
0
votes
1
answer
2k
views
Everyday, real-life applications of mathematical concepts, and human intuition vs mathematical analysis [closed]
I'm working on an educational project about the applications of reasonably 'lofty', high-ish-level mathematical concepts in the real world. I've already scoured these links (1) (2) (3) after ...
0
votes
1
answer
860
views
Sierpinski Triangle and the Chaos Game
The chaos game is a way to construct (an approximation) of Sierpinski triangle. It's clear (using Thales' theorem!) that if we begin with a point on the sierpinski triangle, then we will never leave ...
- 87
0
votes
0
answers
303
views
Is Baire's theorem stronger than needed for functional analysis?
Many classic theorems in functional analysis involve using Baire's theorem to prove facts about topology that relate to maps between Banach spaces (or, more generally, F-spaces). The application ...
- 109
0
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0
answers
148
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About the theorem of Weierstrass?
Is $E=Vect\{1,x,x^2,...,x^{2^n},...\}$ dense in $C([0,1])$ for the uniform norm?
While looking for a short proof for Weierstrass' theorem, I came across this justification(*) (which shows this result)...
- 4,074
0
votes
1
answer
125
views
Are there search algorithms that are competitive against (gradient based) optimization routines for continuous problems?
Suppose that $f: \mathbb{R}^n \to \mathbb{R}$ is a continuous function for which we want to minimize. We may arbitrarily impose good conditions for $f$, such as Lipschitzness, smoothness, convexity, ...
- 479
0
votes
1
answer
552
views
Teaching profession:Differential Equations and Mean Value Theorems
Usually I teach Algebra,Algebra and Geometyry, Topology, at various University levels. This semester (Spring 2014) I have to teach Differential Equations to University second year students (4th ...
- 1,422
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votes
1
answer
1k
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Alternative proofs of Euclid-Euler theorem
What are some alternative methods of proof for the necessity direction of the above theorem, ie $n$ an even perfect number $\Rightarrow n$ is of form $2^{a-1} (2^a - 1)$ where $2^a - 1$ is a Mersenne ...
-1
votes
1
answer
771
views
Are manifolds typically taught to undergraduates outside mathematics (and possibly theoretical physics) tracks? [closed]
I'm writing my dissertation on symplectic structure-preserving algorithms for Hamiltonian systems simulation, and I'm trying to figure out how much exposition is necessary for it to be readable by ...
- 151
-4
votes
2
answers
228
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An elementary-looking integral inequality
This might seem a bit easy but I still like to ask it for pedagogical reasons.
QUESTION. Is this inequality true for non-negative integers $n$?
$$\frac{\pi}2\int_0^1x^n\sin\left(\frac{\pi}2x\right)dx\...
- 43.2k
-4
votes
1
answer
550
views
Amount of mathematical knowledge required for starting Ph.D. in pure mathematics [closed]
How much mathematics should one know before starting a Ph.D. program in pure mathematics? For example what topics one must understand well to pursue a Ph.D. in US University in Number Theory (...
- 310
-5
votes
1
answer
2k
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V.I. Arnold's high school problem [closed]
According to his interview to the Notices of the AMS, when Vladimir I. Arnold was 12 years old (in 1949) his teacher I.V. Morozkin, gave to his classroom (apparently 6th grade of a soviet primary ...
- 2,933
-8
votes
1
answer
378
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Why is it impossible to find work of John Tate online? [closed]
The work of John Tate belongs to mankind. Why is not online in pdf´s? Who is dirty enough to earn money on HIS work?
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