Gaurav Sharma's Blog

Author: gvs139

  • Leetcode: Two Sum

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    Inputs Problem 1: Two Sum Description Given an array of integers nums and an integer target, return the indices of the two numbers such that they add up to target. Each input is guaranteed to have exactly one solution. You may not use the same element twice. The answer can be returned in any order.…

  • Welcome

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    Welcome to my blog. I’m Gaurav Sharma. On this blog I write and share articles on mathematics, machine learning and functional programming.

  • Flow – The Psychology of Optimal Experience

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    Book excerpts from the book: He concludes that the most important trait of survivors is a “nonself-conscious individualism,” or a strongly directed purpose that is not self-seeking. People who have that quality are bent on doing their best in all circumstances, yet they are not concerned primarily with advancing their own interests. Because they are…

  • Raising Abstraction Level in SAS

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    In the following codes an attempt is made to raise the abstraction level available to the sas programmer by providing list manipulation macros: This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.…

  • The Need For MapReduce and NoSQL

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    The Need for MapReduce Relational Database Management Systems have been in use since 1970s. They provide the SQL language interface. They are good at needle in the haystack problems – finding small results from big datasets. They provide a number of advantages: A declarative query language Schemas Logical Data Independence Database Indexing Optimizations Through Use…

  • Introduction to Hadoop

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    Apache Hadoop is a software framework for distributed processing of very large datasets. It provides a distributed storage system Hadoop Distributed File System (HDFS)), and a processing part of the system MapReduce. The system is so designed so as to recover from hardware failures in some nodes that make up the distributed cluster. Hadoop is…

  • Quotients

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    1. Motivation Consider the set of rational numbers. We say that a rational number is of the form where . But all numbers of the form, where are also the same rational number. Thus, the elements of are not really numbers of the form where , but “equivalence classes” of numbers, where two numbers and…

  • Difference Equations

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    1. Difference Equations 1.1. Introduction Time series analysis deals with a series of random variables. 1.2. First Order Difference Equations We will study time indexed random variables . Let be a linear function of and . Equation 1 is a linear first-order difference equation. It is a first-order difference equation because only depends on and…

  • Misconceptions About P Values and The History of Hypothesis Testing

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    1. Introduction The misconceptions surrounding p values are an example where knowing the history of the field and the mathematical and philosophical principles behind it can greatly help in understanding. The classical statistical testing of today is a hybrid of the approaches taken by R. A. Fisher on the one hand and Jerzy Neyman and…

  • The Development of Mathematical Analysis

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    1. Reasons Behind The Creation of Analysis Newton had approached his calculus with fluxions and flows while Leibniz had done with differentials. Both methods however had to deal with infinities and infinitely small quantities, specifically to find methods that combine infintely many infinitely small quantities to get finite quantities. The reasoning used to arrive at…