![\begin{align}
e^{ix} &{}= 1 + ix + \frac{(ix)^2}{2!} + \frac{(ix)^3}{3!} + \frac{(ix)^4}{4!} + \frac{(ix)^5}{5!} + \frac{(ix)^6}{6!} + \frac{(ix)^7}{7!} + \frac{(ix)^8}{8!} + \cdots \\[8pt]
&{}= 1 + ix - \frac{x^2}{2!} - \frac{ix^3}{3!} + \frac{x^4}{4!} + \frac{ix^5}{5!} - \frac{x^6}{6!} - \frac{ix^7}{7!} + \frac{x^8}{8!} + \cdots \\[8pt]
&{}= \left( 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \frac{x^8}{8!} - \cdots \right) + i\left( x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots \right) \\[8pt]
&{}= \cos x + i\sin x \ .
\end{align}](taylor.gif)
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Examples from programming classes:
Recommended literature | websites on the other universities for algorithms:
Vazirani, Algorithms - use Google to find a pdf. It was free for download till 2015. In 2021, I have found this.
Jeff Erickson - Programming, Algorithms (better than previous one).
Missing in those books/texts:
Tutorials point: Typical attacks, RSA infrastructure
Sorting, and another algorithms on the algoritmy.net
Some basics in C++: studytonight.com
Individual algoritms named after: see Stigler's law of eponymy.
Linked lists: prof. Adamchik, ...
Trees ... Daniel Jimenez
Youtube: Dijkstra's Algorithm, Prim's Algorithm (the second author is better)
Huffman coding: Youtube, sentence example from Wikipedia, Daniel Jimenez,
FFT - Wikipedia, Youtube, seminar preparation, correlation-with-cos. Excell example. Taylor series (source: Wikipedia):
Modular arithmetic: xls, jpg, PKI, MIM, gcd, prime, Fermat's little theorem, power (an). Coprime, Chinese remainder. Arbitrary precision arithmetic, RSA.
Netbeans environment: history, download.
Graphs for the distant students.
