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1500 questions
67
votes
8 answers
How does a non-mathematician go about publishing a proof in a way that ensures it to be up to the mathematical community's standards?
I'm a computer science student who is a maths hobbyist. I'm convinced that I've proven a major conjecture. The problem lies in that I've never published anything before and am not a mathematician by profession. Knowing full well that my proof may be…
Balbanna
- 713
67
votes
4 answers
Calculate on which side of a straight line is a given point located?
I am a programmer without really good knowledge in math. :/ So I have to write an algorithm that changes the color of pixel(dot) P to opposite if it's on left side of the straigt line in coordinate system (and the line is not vertical, with that I…
Ritvars
- 773
67
votes
5 answers
What is the 'implicit function theorem'?
Please give me an intuitive explanation of 'implicit function theorem'. I read some bits and pieces of information from some textbook, but they look too confusing, especially I do not understand why they use Jacobian matrix to illustrate this…
Flying pig
- 887
67
votes
16 answers
How can I introduce complex numbers to precalculus students?
I teach a precalculus course almost every semester, and over these semesters I've found various things that work quite well. For example, when talking about polynomials and rational functions, in particular "zeroes" and "vertical asymptotes", I…
user641
67
votes
19 answers
What are the names of numbers in the binary system?
The names we use are very much related to the radix we use
$0 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9$
zero - one - two - three - four - five - six - seven - eight -nine
We repeat the names
$21$ twenty one, $22$ twenty two .. and so on.
This is not…
user37421
- 927
67
votes
29 answers
How to explain to my daughter that $\frac {2}{3}$ is greater than $\frac {3}{5}$?
I was really upset while I was trying to explain to my daughter that $\frac 23$ is greater than $\frac 35$ and she always claimed that $(3$ is greater than $2$ and $5$ is greater than $3)$ then $\frac 35$ must be greater than $\frac 23$.
At this…
Akam
- 639
67
votes
4 answers
Is it normal to treat Math Theorems as "Black Boxes"
It seems to me that as one goes higher up in mathematics, the proof of theorems get more involved and convoluted, that at some point one must postpone (or even give up?) understanding all prior theorems, and take them as "Black Boxes" instead? Is…
yoyostein
- 20,428
67
votes
2 answers
What is the average rational number?
Let $Q=\mathbb Q \cap(0,1)= \{r_1,r_2,\ldots\}$ be the rational numbers in $(0,1)$ listed out so we can count them. Define $x_n=\frac{1}{n}\sum_{k=1}^nr_n$ to be the average of the first $n$ rational numbers from the list.
Questions:
What is…
jdods
- 6,632
67
votes
12 answers
How is the derivative truly, literally the "best linear approximation" near a point?
I've read many times that the derivative of a function $f(x)$ for a certain $x$ is the best linear approximation of the function for values near $x$.
I always thought it was meant in a hand-waving approximate way, but I've recently read that:
"Some…
jeremy radcliff
- 4,933
67
votes
11 answers
Undergraduate algebraic geometry textbook recommendations
What are the best algebraic geometry textbooks for undergraduate students?
tobias
67
votes
6 answers
How to avoid perceived circularity when defining a formal language?
Suppose we want to define a first-order language to do set theory (so we can formalize mathematics).
One such construction can be found here.
What makes me uneasy about this definition is that words such as "set", "countable", "function", and…
IssaRice
- 1,285
67
votes
17 answers
Good "history of mathematical ideas" book?
All too often, mathematical history books include far too much material on the private lives of the personalities involved and not enough information on the actual ideas. Mathematics is a living subject in itself, which is not enhanced by knowing…
67
votes
7 answers
Is the sum and difference of two irrationals always irrational?
If $x$ and $y$ are irrational, is $x + y$ irrational? Is $x - y$ irrational?
Miguel Mora Luna
- 3,243
67
votes
12 answers
Easy way of memorizing values of sine, cosine, and tangent
My math professor recently told us that she wanted us to be able to answer $\sin\left(\frac{\pi }{2}\right)$ in our head on the snap. I know I can simply memorize the table for the test by this Friday, but I may likely forget them after the test. So…
James Smith
- 1,779
67
votes
2 answers
How do different definitions of "degree" coincide?
I've recently read about a number of different notions of "degree." Reading over Javier Álvarez' excellent answer for the thousandth time finally prompted me to ask this question:
How exactly do the following three notions of "degree"…
Jesse Madnick
- 32,819