Mathematics

Writing a Formal Mathematical Report

General Information   Your analytical work in solving problems is of no value if you cannot communicate it to others. A written report is just one method of doing this. The ability to write clear, concise, accurate, and professional looking reports is as important as the analysis that goes into problem solving.   It is…

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Teach Yourself Limits in 8 Hours: Part 1

Introduction While looking at certain limit problems posed in math.stackexchange.com (henceforth to be called MSE) I found that most beginners studying limits are living in a fantasy world consisting of vague notions, infinities and what not. I too had my share of such experiences during my time as a student learning calculus but I was…

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A Continued Fraction for Error Function by Ramanujan

Today's post is inspired by this question I asked sometime back on MSE. And after some effort (offering a bounty) I received a very good answer from a user on MSE. This question was asked for the first time by Ramanujan in the "Journal of Indian Mathematical Society" 6th issue as Question no. 541, page…

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Ramanujan’s Generating Function for Partitions Modulo 7

Ramanujan's Partition Congruences Based on the empirical analysis of a table of partitions Ramanujan conjectured his famous partition congruences $$boxed{begin{align}p(5n + 4)&equiv 0pmod{5}notag\ p(7n + 5)&equiv 0pmod{7}notag\ p(11n + 6)&equiv 0pmod{11}notagend{align}}tag{1}$$ and gave some of the most beautiful proofs for them (see here). In addition to these proofs he gave the following generating functions for…

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Measuring An Angle

Today we will focus on a topic from elementary geometry namely the concept of measurement of angles. The idea of an angle is a simple one namely in the sense that it is made by two rays emanating from the same point. But the measurement of angles is not that simple as it appears. Many…

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