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Discussion

Yolanda said This seemed like a very short chapter, at least it did to me. Bob agreed Yes, but the professor indicated that the goal was just provide some key examples.

Discussion

Yolanda said This seemed like a very short chapter, at least it did to me. Bob agreed Yes, but the professor indicated that the goal was just provide some key examples. I think he was hinting at more general notions of inversionalthough I haven't a clue as to what they might be.

Clearly aggravated, Zori said I've had all I can stand of this big integer stuff. This won't help me to earn a living. Xing now was uncharacteristically firm in his reply Zori. You're off base on this issue. Large integers, and specifically integers which are the product of large primes, are central to public key cryptography. If you, or any other citizen, were highly skilled in large integer arithmetic and could quickly factor integers with, say \(150\) digits, then you would be able to unravel many important secrets. No doubt your life would be in danger.

At first, the group thought that Xing was way out of boundsbut they quickly realized that Xing felt absolutely certain of what he was saying. Zori was quiet for the moment, just reflecting that maybe, just maybe, her skepticism over the relevance of the material in applied combinatorics was unjustified.

Tsopano inu Sikuti pali calculator yomwe imatha kufotokoza izi, koma zigawo zake zimatha kuwerengedwa. Timafuna kuyesera imodzi pansipa, kapena tidzalemba ya ife.

Kusunga ntchito yanu yokha

M’malo mwake, maakaunti aulere amawonjezera malemba pazophunzira zonse, mnda wa zomwe mwamaliza, mavuto anu omaliza m’malo limodzi, ndi m’bale amene mungafunse za nkhaniyo. Maphunziro a matekinoloje ndi otsegulira kwa aliyense, olembetsa kapena osalembetsa.

Kulembetsa Kulowa

Zithunzi

Pitani pa dzina lililonse lachifaniziro kuti mudziwe tanthauzo lake, chithunzi chake, ndi zimene limatanthauza.

Mafunso omwe anthu amafunsa

Permutation or combination?

Ask whether order matters. A lock code is a permutation (order matters); a hand of cards is a combination (it does not).

What is a graph in this sense?

Dots (vertices) joined by lines (edges), not a plot. Road maps, social networks and molecules are graphs; questions like "is there a route" and "how few colours" are graph theory.

Zigawo za m'nkhaniyi ndi zochokera Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). Kuphatikizapo ndi kufotokozanso pano; zolakwika ndi zathu.

Zambiri pa Combinatorics & Graph Theory

The counting principlesPigeonhole principle and inclusion, exclusionBinomial coefficients and Pascal's triangleRecurrences and generating functionsGraphs: vertices, edges, degreesPaths, cycles, trees, Euler and HamiltonColouring and planar graphs