by Gaurav Tiwari | Oct 28, 2013 | Education, Featured, Learning, Recreations, Science, Study Notes

Every student or graduate knows how hard the first experience of passing exams is. Preliminary preparation starves the nervous system and the physical condition of the human body, however, the exam itself is always a stressful situation, which requires a candidate a...
by Gaurav Tiwari | Oct 8, 2013 | Featured, Math, Number Theory, Research, Status Updates, Study Notes

This is a continuation of the series of summer projects sponsored by department of science and technology, government of India. In this project work, I have worked to collect and expand what Ramanujan did with Nested Radicals and summarized all important facts into...
by Gaurav Tiwari | Aug 12, 2013 | Algebra and Topology, Math, Real Analysis, Science, Study Notes

Sequence of real numbers A sequence of real numbers (or a real sequence) is defined as a function $ f: \mathbb{N} \to \mathbb{R}$ , where $ \mathbb{N}$ is the set of natural numbers and $ \mathbb{R}$ is the set of real numbers. Thus, $ f(n)=r_n, \ n \in \mathbb{N}, \...
by Gaurav Tiwari | Aug 10, 2013 | Algebra and Topology, Math, Real Analysis, Study Notes

SETS In mathematics, Set is a well defined collection of distinct objects. The theory of Set as a mathematical discipline rose up with George Cantor, German mathematician, when he was working on some problems in Trigonometric series and series of real numbers, after...
by Gaurav Tiwari | Mar 26, 2013 | Algebra and Topology, Math, Number Theory, Recreations, Study Notes

The greatest number theorist in mathematical universe, Leonhard Euler had discovered some formulas and relations in number theory, which were based on practices and were correct to limited extent but still stun the mathematicians. The prime generating equation by...
by Gaurav Tiwari | Feb 14, 2012 | Algebra, Algebra and Topology, Calculus, Math, Number Theory, Real Analysis, Recreations, Study Notes

“Irrational numbers are those real numbers which are not rational numbers!” Def.1: Rational Number A rational number is a real number which can be expressed in the form of where $ a$ and $ b$ are both integers relatively prime to each other and $ b$ being...