LaTeX math cheatsheets
My girlfriend asked for LaTeX cheatsheets. There are many of them online, but she was specifically looking for notational commands for algebra and number theory. You need to be aware that notation is...
View ArticleMapping lexicographical comparison to integer comparison
Claim (a, b) < (c, d) with a,b,c,d ∈ [0,M) ⇔ a · M + b < c · M + d (a, b) = (c, d) with a,b,c,d ∈ [0,M) ⇔ a · M + b = c · M + d (a, b) > (c, d) with a,b,c,d ∈ [0,M) ⇔ a · M + b > c · M + d...
View ArticleRunning Donald Knuth’s CWEB programs
I just realized that no-one documented how to quickly run Donald Knuth’s programs he publishes in his WEB system. Suppose you want to compile a program like commafree; a program he wrote between...
View ArticleMake 24 out of 1, 3, 4 and 6
Problem Give a mathematical expression which equals 24. This expression is only allowed to use the basic arithmetic operators +, -, * and /. The numbers 1, 3, 4 and 6 must occur exactly once. No magic...
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When is Tutte’s theorem in K₅ violated?
Theorem A graph, G = (V, E), has a perfect matching if and only if for every subset U of V, the subgraph induced by V − U has at most |U| connected components with an odd number of vertices. —Tutte’s...
View ArticleGolang hash digest sizes
Golang has several hash algorithms implemented in the crypto package. I needed their digest sizes. So it summed them up in this table: hash algorithm digest size MD4 128 MD5 128 SHA1 160 SHA224 224...
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I computed M74207281
On 7th of January 2016, GIMPS found Mersenne prime number M74207281. GIMPS is a project combining efforts of a large crowd of volunteers contributing computing power and a university server combining...
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Paper: “Mastering the game of Go with deep neural networks and tree search”
Most recently, a paper “Mastering the game of Go with deep neural networks and tree search” was published in Nature. It describes a neural network architecture which for the first time won against a...
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Project nihon ni ryuugakusei (日本に留学生)
Starting with October 2016 I am going to Japan for 1 year with my girlfriend. Both of us got granted a student’s exchange year at the same place. Setting I will attend classes as a math undergraduate....
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Boston Key Party: Graph 3-coloring with SAT solvers
The Boston Key Party was held between 4th and 6th of March 2016. A few colleagues of mine attended this event and asked for help with one particular problem: Given a graph with 683 vertices and 1253...
View ArticleTime management, an analysis
This semester I consciously decided to reduce my number of courses I take. As far as academic work is concerned I need to focus on finishing the first and second semester and finish my master thesis. I...
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Buchtipp: “Darum nerven Japaner”
Fig. 1. “Darum nerven Japaner – Der ungeschminkte Wahnsinn des japanischen Alltags” Der Autor Christoph Neumann erklärt erst im Nachwort wie er dazu kam dieses Buch zu schreiben. ここがヘンだよ日本人 (laut dem...
View ArticleUsing namespaces with lxml.etree
I need to admit, when I initiated and released ruledxml for the first time, I didn’t care much about namespaces. The usecase was not prevalent in my setting. This changed now. Time to implement it...
View ArticlePaper: “Engineering a Sort Function”
“Engineering a Sort Function” by John L. Bentley and M. Douglas McIlroy gives a nice insight how theoretical algorithm design is applied in software engineering. I think I came across the paper,...
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Buchtipp: “Simple Guide to Japan – Customs & Etiquette”
Cover of “Simple Guide to Japan” This booklet was published in the third edition in 1997 and authored by Helmut Morsbach. It features 80 pages in total with illustrations and a medium font size. So you...
View ArticleAn empty clause represents a contradiction
The problem I have just gone through many CNF files and come across the following file: p cnf 150 400 -3 -2 -1 0 3 2 -1 0 2 1 -3 0 [...] 150 149 98 0 150 -149 -98 0 149 -150 -98 0 98 -150 -149 0 0...
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My handwriting
Tidying up a few things at home, I came across all my documents from previous years. I thought it would be nice to document how my handwriting evolved over the year. I have been to school between the...
View ArticlePaper: “Bitcoin: A Peer-to-Peer Electronic Cash System”
The fundamental paper of crypto-currency bitcoin (PDF) was written by Satoshi Nakamoto. Who is Satoshi Nakamoto? We just don’t know. Nakamoto’s bitcoins currently yield a value of $4.2 billion USD, but...
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