Do you think this is just a bunch of meaningless numbers or something more? 9 \: 27 \: 12 \: 15 \: 22 \: 5 \: 27 \: 19 \: 3 \: 9 \: 5 \: 14 \: 3 \: 5 Later we’ll give you the answer. But before let’s talk about cryptography. Do you know what’s that? We’ll start with a bit of history. Cryptography is the science of secret writing. Its name comes from the Greek words Kryptos, meaning hidden, and graphene, which means writing. By the way, there is also steganography – the science and art of writing hidden messages. Don’t mix them up, though. Steganography and cryptography are not the same. Cryptography is the science of codes and ciphers. Steganography is the science of secure data transmission through the secrecy of the very fact of the transfer. (more…)
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Homework excuses that make your teacher believe
We are all aware that students are very busy people having little time to spare, even less for doing boring homework tasks. Moreover, as we have already mentioned, teachers often assign way too much leaving thus no way possible to do it all, if you are not a genius, or at least a nerd. So what to do? No one wishes to receive unsatisfactory grades. The only way out is to come up with a plausible excuse and spare yourself of performing homework or at least postpone it until better times. By the way, if you by accident decided to do the homework, check our tips how to save time and do it faster and better. (more…)
What is gamma function?
Today we’re going to discuss one of the non-elementary functions called gamma function and consider some of its properties. Gamma function is of great importance, it’s widely applied in math (in particular, when integrating certain types of expression gamma function helps greatly, we’ll see that later in examples), also gamma function is used in probability theory (possibly, you’ve heard about gamma distribution), etc. One of the most common representations of gamma function is the following:
\Gamma(p)=\int_0^{\infty}{e^{-x}x^{p-1}dx}, p>0
This is only true for positive values of parameter p. So to obtain value of gamma function in a certain point p we need to integrate over x the expression e^{-x} x^{(p-1)}, leaving p as a free parameter. Notice limits of integration – zero and infinity. This means that we’re dealing with improper integral. (more…)
Pigeonhole principle
Some time ago we’ve received a pretty interesting question from one of our visitors. It sounds as follows:
Let A be any set of 20 distinct integers chosen from the arithmetic progression 1, 4, 7, …, 100.
Prove that there must be two distinct integers in A whose sum is 104. (more…)
How to deal with Cauchy problem for differential equation?
In this section we’ll consider an example of how to deal with initial value problem (or Cauchy problem) for non-homogeneous second order differential equation with constant coefficients.
Initial value problem usually arises in the analysis of processes for which we know differential evolution law and the initial state. For example, consider the problem of counting human population. After years of observation and data processing scientists came up with some differential equations with which we can describe number of human beings on Earth. This is called a population model, and actually there are several various approaches concerning this problem. Suppose we want to find out how many people will be there up to 2120 year. And here comes initial value problem. We know current population (our initial value) and have a differential equation, so to find future number of humans we’re to solve a Cauchy problem.
Ok, back to math. (more…)
How to Do my Homework Fast and Well? Surviving Tips
Homework. Is it as useful as teachers claim? Really, doing loads of tasks reduces your time to sleep and to spend with family. Moreover, often homework prevents diligent students from sports training! That’s really terrible, not saying that long sitting hours lead to crooked spine and other health disorders. Do you need all this? Certainly no. Is there anyone who wants to become a homework slave? There again. (more…)
How to do Gauss elimination? Case of system with unique solution
In this section we offer one more example of how to solve system of linear algebraic equations using Gaussian elimination method. This example clearly shows that while doing Gaussian elimination you ought to notice when it’s convenient to swap rows in order to save time and reduce calculations. (more…)
