Use the discount code CYBERWEEK19 to purchase English IT eBooks from Springer online for only 7 Euro. Go to the checkout and enter the code. Afterwards, you can proceed browsing the book list and it automatically shows if the code was applied.
Note: At the checkout read again if the discount...
Springer math books are 40% off till Nov 30. Coupon code is MATH19PE.
I bought Linear Algebra by Axler , the analysis books by Pugh and Abbott.
Any further recommendations for good books?
You are asking about the difference between "Proof by contraposition" and "Proof by contradiction", and here is an example.
To prove p \rightarrow q:
- In proof by contraposition you start by assuming that \neg q is true and derive the statement \neg p. Here, the path is clear, i.e. you start...
Go has been considered one of the games in which the human is superior to any AI. However in a first match Google's AI has beaten world Go champion Lee Se-dol. Earlier this year the AI beat the European Go champion.
Try to get an intuitive feeling for what the Kronecker-Delta \delta_{ij} does.
Consider this sum:
\sum_{j=1}^{n} c_j = c_1 + c_2 + \dots + c_n
Now observe what happens if we multiply with the Kronecker-Delta:
\sum_{j=1}^{n} \delta_{ij} c_j = \delta_{i1} c_1 + \delta_{i2}c_2 + \dots +...
For a sequence (a_n)_{n \in \mathbb{N}} you can form the series \sum_{n=0}^\infty a_n = a_0 + a_1 + a_2 + \dots.
If you take the sequence a_n = 1 and plug it into the expression above,
then you get the series \sum_{n=0}^\infty a_n = \sum_{n=0}^\infty 1 = 1 + 1 + 1 \dots .
Or consider the...
This nature article mentions that other interferometers such as Geo600 in Germany and Virgo in Italy were not operating at the time . Is it known whether Geo600 would have detected the gravitational waves?
What happens with gravitational waves? Do they exist forever or can they be absorbed or...
Here is a proof mentioned on math.stackexchange using the "sign-preserving property" of continuous functions:
http://math.stackexchange.com/a/543800
And two more links for the proof of the sign-preserving property:
https://math.la.asu.edu/~dajones/class/371/ch4.pdf...
One way to understand this is to interpret it as a two-player game, let's say between you and me. The game works as follows:
I give you a number \epsilon > 0, and your task is to find a number \delta > 0 such that a certain condition is fulfilled.
You can read about this two-player game...
Here is a definition of what the limit means when it involves infinity:
\lim_{x \to +\infty}f(x) = +\infty
if for every number M>0 there is a corresponding number N such that
f(x)>M whenever x>N.
Intuitively this means, if I give you a positive number M, then you can find a number N such that...
Here are some nice videos that explain the time and frequency domain:
Intro to Fourier Transform, see also the website http://www.thefouriertransform.com/#introduction
Fourier Transform Introduction
Fourier transform explained with an oscilloscope
Approved textbooks by The American Institute of Mathematics (the books are open-access):
1) A Gentle Introduction to the Art of Mathematics by Joe Fields
2) Mathematical Reasoning: Writing and Proof by Ted Sundstrom
Do you mean by surface the purple curve? If yes, you could rotate this curve around the "x-axis" as shown here. You would have to adjust the jpeg to make the balloon symmetrical around the x-axis.
The idea is to http://calculus-geometry.hubpages.com/hub/Disk-Method-Volume-of-Solid-of-Revolution...
The purple vector is the projection of \vec{u} onto \vec{v}.
Now, you have to think of how the purple vector is defined. It has (i) a length and (ii) a direction.
(i) The length of the purple vector is | \vec{u}| \text{cos}(\theta).
(ii) The direction of the purple vector is the same as that of...
In case you are asking for the derivation of the formula I've drawn a sketch (see attachment). You can see that it is indeed just expressing the cosine in terms of the dot product.