ND 08.10.2023: Maths concepts with Medium and MathURLs

Good morning. This Sunday the digest will focus on the most recent postings of mathematics writers on Medium via MathURLs.

This article introduces the concept of counting pairs and explains a combinatorial theorem related to solving “number of ways” problems. It begins by discussing the idea of Stars and Bars in combinatorics. The example given involves distributing 10 identical cubes into 3 buckets, and the article illustrates how to represent this problem visually using lines and cubics. The formula for solving such problems is presented, where “n” represents the objects to be distributed, and “k” represents the containers. The article concludes by suggesting that readers can practice their understanding of Stars and Bars by solving a specific problem related to it – Stars and Bars (Medium)

The relationship between mathematics and programming is crucial because mathematics underpins the creation of algorithms, enabling programmers to dissect intricate problems into manageable steps. The Tower of Hanoi puzzle serves as a prime example of this interplay, challenging individuals to move disks while adhering to specific rules. This puzzle’s complexity is determined by the number of disks (2^n – 1), where “n” signifies the disk count. A Python code snippet is provided, showcasing a recursive solution to the Tower of Hanoi problem. It utilizes a function called hanoi with base conditions for single disk moves and recursive calls for multi-disk transfers, accepting user input for the number of disks to be manipulated – Math’s relation to programming (Medium)

The article discusses the importance of understanding and adhering to mathematical notations and their associated rules for interpreting expressions. It highlights the significance of agreed-upon rules to ensure consistent results when evaluating mathematical expressions. The article introduces different notations, including infix, postfix (Reverse Polish Notation), and a visual representation using mathematical expression trees. It explains how postfix notation simplifies computer evaluation through a stack-based algorithm. The author emphasizes the efficiency of choosing the right notation for human and computer comprehension and optimization – Between humans and computers: A tale of two notations (Medium)

The article underscores the importance of embracing numbers and mathematics, even if one doesn’t have a strong affinity for math. It provides real-world examples to illustrate this point, demonstrating how numbers can inform and influence decisions across different domains. Whether it’s understanding demographic statistics for career choices, redefining our perceptions of scale through revenue figures, making healthy dietary decisions based on Glycemic Index values, assessing the returns and risks in stock markets, or reevaluating the stability of fixed deposits, numbers play an integral role in making informed choices that impact various aspects of life. Thus, the article encourages individuals to not shy away from numbers but rather appreciate their significance in decision-making processes – Just look at the d@t@ (Medium)

The article explores the concept of Expected Value (E(X)) in statistics, highlighting its significance and origins. Expected Value is described as a weighted average that represents the arithmetic mean of outcomes from a random variable, emphasizing the need for a large sample size for accuracy. The historical problem of points, originating in the Renaissance era, serves as a foundation for understanding Expected Value. Various historical solutions to this problem, from Pacioli to Pascal, Fermat, and Huygens, are presented, shedding light on the evolution of probability theory. The article also delves into the Law of Large Numbers, discussing its weak and strong forms, and provides practical experiments with dice rolls to illustrate how larger sample sizes lead to results closer to the Expected Value, offering insights into predictive statistics and measurement uncertainty – To expect or not expect? (Medium)