Beginner's Georgian with 2 Audio CDs by Dodona Kiziria

By Dodona Kiziria

This publication is designed for either school room use and self-study. all of the thirteen classes opens with a discussion approximately a regular subject, via vocabulary lists, factors of grammar, and workouts. Audio CDs accompany the teachings, delivering right pronunciation of the dialogues and vocabulary, with pauses for repetition through the coed.


* An workout key
* Georgian-English and English-Georgian glossaries
* An creation to Georgian language, tradition, and heritage

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Extra info for Beginner's Georgian with 2 Audio CDs

Sample text

If'l U + and convex then Proof. 3. l !. 4I

Theorem 15. Proof. If E. a n > 0: a2 > - ~ n. if then i < j and a 1 < aj it is easily seen that a' a'. a' a' i i j > _J + + ai aj ai and so n a' . n a.

Theorem 20. If f: U + R is eonvex on the open eonvex set U in the f is Lipsehitz on every eompaet sub set of U, and has partial CHAPTERI 32 derivatives of the first order almost everywhere in U that are eontinuous on the set where they exist. Proof. See RV p. 93, 116-117. 'nleorem 2 1. p , n ~ 2, have f is eonvex on U is non-negative definite, if H is positive definite on U then f is strictly eonvex. Proof. See RV p. 103. SO-Sl. 3. 'nleorem 22. If'l U + and convex then Proof. 3. l !. 4I

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