Fermat's Last Theorem is one of the most celebrated problems in mathematics. It is a problem in the field of Number Theory that's very simple to understand, yet extremely difficult to solve. In fact, it's so difficult that it remained unsolved for 358 years even though it got a lot of attention from some of … Continue reading Chasing Fermat’s Last Theorem
Dissecting Diophantine Equations
The word Diophantine refers to Diophantus, the third century mathematician from Alexandria. Numbers are the fundamental building blocks of mathematics, so he started thinking about problems for which we need integer solutions. For example, how many horses do we need to achieve a particular task? Even if the exact answer is 15.5, we cannot really … Continue reading Dissecting Diophantine Equations
Understanding Catalan’s Conjecture
Numbers are deceptively simple. We use them everyday in a variety of contexts. It's beautiful how there are so many mysteries hidden inside these numbers. Catalan's Conjecture is a mathematical problem that's really easy to understand, but extremely difficult to prove. In fact, it took around 158 years to come up with a mathematical proof. … Continue reading Understanding Catalan’s Conjecture
What is Empirical Risk Minimization
Even though it has an ornate name, the underlying concept is actually quite simple and intuitive. The concept of Empirical Risk Minimization becomes relevant in the world of supervised learning. The actual goal of supervised learning is to find a model that solves a problem as opposed to finding a model that best fits the … Continue reading What is Empirical Risk Minimization
Measuring the Stability of Machine Learning Algorithms
When you think of a machine learning algorithm, the first metric that comes to mind is its accuracy. A lot of research is centered on developing algorithms that are accurate and can predict the outcome with a high degree of confidence. During the training process, an important issue to think about is the stability of … Continue reading Measuring the Stability of Machine Learning Algorithms
Ergodicity In The World Of IoT
Ergodicity is one of the most important concepts in statistics. More importantly, it has a lot of real world applications. In this case, it's applicable to the staggering number of internet connected devices in the world of Internet of Things (IoT). Most of the experiments conducted by research labs, businesses, and marketing agencies often rely on … Continue reading Ergodicity In The World Of IoT
Cauchy Sequences In The Real World
Sequences occur everywhere in our daily life. Some of the examples include sensor data, stock market quotes, speech signals, and many more. A sequence is a collection of elements where each element is indexed. Repetitions are allowed in this case, which means any element can reappear in a given sequence. If we look closely, we can … Continue reading Cauchy Sequences In The Real World
Measuring The Memory Of Time Series Data
Time series data has memory. It remembers what happened in the past and avenge any wrongdoings! Can you believe it? Okay the avenging part may not be true, but it definitely remembers the past. The "memory" refers to how strongly the past can influence the future in a given time series variable. If it has a … Continue reading Measuring The Memory Of Time Series Data
What Is Pareto Optimality
Let's consider a business deal where there are multiple parties negotiating the terms. In such a situation, it's usually not possible for every single party to get everything it wants. They need to optimize their demands so that everyone comes out with something positive. Similar situations arise across many areas of engineering where we have to … Continue reading What Is Pareto Optimality
What Is Long Memory In Time Series Analysis
We encounter time series data very frequently in the real world. Some common examples include real time sensors, surveillance video, stock market, astrophysics, speech recognition, and so on. In order to study time series data, we try to extract various characteristics that tend to define it. One of the most important things to think about … Continue reading What Is Long Memory In Time Series Analysis
Perpetual Enigma 