Оставките в комисията за олимпиади по математика

    Всяка година, в България се провеждат няколко големи национални състезания по математика за ученици, които кулминират в излъчването и подоготвката на националния ни отбор за Международната олимпиада по математика (МОМ), еквивалента на олимпийските игри в тази наука. Преди около две седмици хората, които осъществяват този процес от десетки години, подадоха оставка от комисиите за провеждане на съответните състезания (източници тук и тук). Причината са съмнителните, несъгласувани със Съюза на математиците в България назначения в тези комисии за 2016/2017 от страна на Министерството на образованието и науката (МОН).

    В този текст споделям мнението си по този случай в качеството си на състезател в периода 2001-2010, помощник в подготовката в периода 2011-2016, и наблюдател на МОМ 2016.

    Interior point method, continued

    In this post, we continue the design and analysis of an interior point method algorithm to solve a linear program that we started last time.

    Logicomix

    This post collects some thoughts on the graphic novel “Logicomix” written by Apostolos Doxiadis and Christos Papadimitriou, with drawing from Alecos Papadatos and Annie Di Donna. Lots of spoilers ahead.

    Strong duality for linear programs

    In this post, we prove the strong duality theorem for linear programs, which says that if either the primal or dual is feasible, then their optimal values are equal.

    Interior point method

    In this post, we begin describing a basic interior point method to solve a linear program. We follow material from these notes by Professor Michel Goemans (relevant lectures are 6,7 and 8), filling in the details.

    Basic properties of the Laplacian

    In this post, we lay out the basics of spectral graph theory - the study of graph structure through the lens of linear algebra. Some of this material is based on a lecture for 6.854 given by Professor Aleksander Madry, and these notes by Professor Dan Spielman.

    IMO 2016: Overview

    This post details my overall experiences as an observer for Bulgaria at the 57th international math olympiad, which took place in Hong Kong, between July 6th and July 16th 2016; there will be a subsequent post listing day-to-day impressions, plus some photos.

    Moral disorder

    This post is a review of the short story collection “Moral disorder” by Margaret Atwood.

    The splitting lemma in abelian categories

    The splitting lemma in abelian categories is a basic tool for decomposing objects into biproducts. It is at the heart of some powerful structure theorems, such as the ones for finitely generated abelian groups and more generally finitely generated modules over a PID.

    Decomposing morphisms in abelian categories

    In this short post we state the basic decomposition result that any morphism in an abelian category decomposes canonically into an epimorphism followed by a monomorphism, and derive some very useful consequences.

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