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...