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Conditional Proofs

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As an undergraduate, following a mathematics major degree, I have seen many of my friends using proof techniques without having a clear understanding. Once you understand something really well, then you can get the maximum from it. In mathematics, understanding the concepts correctly is one of the major keys. Proving a conditional statement by writing a conditional proof is a very powerful technique in proof writing. I hope I can give you,the reader, some bit of understanding about what we really do in a conditional proof, at the end of this article. Before jumping into conditional proofs, we must first look into the question: "what is a conditional statement?" .  Simply a conditional statement is of the form " if...,then... ".  There are five logical connectives we discuss in mathematics.(actually in logic). They are, NOT AND OR IF-THEN IF AND ONLY IF In mathematics, the statements we use to discuss is of special kind. That is, any mathematical...
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Are We Going Back in Time?

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"We are not makers of history, we are made by history" is a great statement said by Martin Luthur King,Jr. Great civilizations in the past, created what we are doing now and who we are now. Communication, science and technology, dresses, food and almost everything are what we got from the past. Civilizations which evolved from time to time, gathering, sharing and documenting knowledge, created the world where we live today. This article is not focusing something about history that someone has already revealed. I am going to present my own point of view on what I felt a few days ago. Communication, which makes humans unique, is not something happened suddenly. It was developed step by step in different ways, during different civilizations.  Discovery of clay tablets belonging to Mesopotamian civilization points out that the documenting could be done easily using real world pictures, what we see each and every day . And when it comes to Egyptian c...
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Goldbach's Conjecture

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Primes are a wonderful and amazing set of numbers which is quiet difficult to formulate, find relationships with each other and indeed really mysterious. A conjecture is an unproved proposition. Goldbach's conjecture is related with primes and upto date it is not proved. First let's try to figure out "What is Goldbach's conjecture?" . In simple form, Goldbach's conjecture points out that any even number greater than 2 can be written as a sum of two prime numbers. For example consider number 4. Clearly, as we all know, 4 is an even number. And also 4 can be written as 2+2, where 2 is prime. Let's take another example, somewhat big even number. Hmmm...what about 34. Obviously 34= 31+3, where 31 and 3 are both primes. Someone might say there may exist an even number which cannot be written as a sum of two primes. In fact, if someone can find such an even number Goldbach's conjecture will be disproved. Such an even number is commonly known as a ...
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