By Thomas Beth, D. Jungnickel, H. Lenz

ISBN-10: 0521444322

ISBN-13: 9780521444323

ISBN-10: 0521772311

ISBN-13: 9780521772310

This quantity concludes the second one variation of the normal textual content on layout idea. because the first version there was large improvement of the idea and this booklet has been completely rewritten to mirror this. particularly, the starting to be significance of discrete arithmetic to many components of engineering and technological know-how have made designs a useful gizmo for purposes, a proven fact that has been stated the following with the inclusion of an extra bankruptcy on purposes. the amount is acceptable for complicated classes and for reference use, not just for researchers in discrete arithmetic or finite algebra, but additionally for these operating in desktop and communications engineering and different mathematically orientated disciplines. positive aspects comprise workouts and an intensive, up-to-date bibliography of good over 1800 citations.

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Méthode 1 : posons j = i − n, alors 2n (−1)k ak = k=0 11 n j=0 j=0 n(n + 1) + n(n − 0 + 1) 2 3 n(n + 1) = 2 = k=1 V = 1 + 2 + · · · + 97 − 2(2 + 4 + · · · + 96) 97 (2n)(2n + 1) (n − 1)(n − 1 + 1) − 2 2 n(4n + 2 − (n − 1)) = 2 3 = n(n + 1) 2 k=1 97 × 98 48 × 49 −4 2 2 = 49 Remarque – On a aussi V = (1 − 2) + (3 − 4) + · · · + (95 − 96) + 97 = (−1) + (−1) + · · · + (−1) +97 48 termes = −48 + 97 = 49. 15 (1000 + 10k) W = (2i − 1) = 19 + 21 + · · · + 57 + 59 et cette somme a k=0 15 = 1000 i=10 30 − 10 + 1 = 21 termes.

On peut considérer alors l’application ]1, +∞[ → √ R , f : x → ln(x) mais on pourrait aussi considérer ]1, +∞[ → √R+ , ou bien x → ln(x) [2, +∞[ → √R+ ... x → ln(x) 43 2 COURS & MÉTHODES Ensembles et applications Exemple Les mathématiciens rêveraient de connaître une formule pour l’application qui à l’entier n de N∗ associe le n-ième nombre premier, mais cela n’existe pas ... 2 Opérations sur les applications Définition – Restriction/Prolongement Soient E1 , E2 , F des ensembles tels que E1 ⊂ E2 , g : E1 → F et f : E2 → F deux applications.

La définition se généralise aux n-uplets : E1 , . . , En étant n ensembles, on note E1 × · · · × En l’ensemble des n-uplets (x1 , . . , xn ) où, pour tout i ∈ {1, . . , n}, xi ∈ Ei . 1 Définition Définition – Application On définit une application (souvent appelée fonction) f en donnant un ensemble E dit de départ, un ensemble F dit d’arrivée et, pour tout x élément de E, un unique élément de F noté f (x) et appelé image de x par f . x est alors appelé un antécédent par f de f (x). L’ensemble des applications de E dans F est noté F E ou F (E, F).

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Design theory by Thomas Beth, D. Jungnickel, H. Lenz


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