Cheatsheets

Introduction to Alibaba Cloud Alibaba Cloud (also known as Aliyun) is China’s largest cloud service provider and a significant global player. Founded in 2009, it offers a full suite of cloud computing services including elastic computing, storage, database, networking, security, AI, and more. Alibaba Cloud is particularly important for businesses looking to establish or expand

Introduction to Big O Notation Big O Notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. In computer science, it’s used to classify algorithms based on their performance or space requirements as input size grows. Understanding Big O allows developers to

Introduction: What is Algorithmic Animation? Algorithmic animation refers to creating visual motion and transformation using mathematical functions, computational rules, and procedural techniques rather than traditional keyframing. Instead of manually specifying each frame, algorithms generate the animation based on defined parameters and rules. This approach offers greater flexibility, scalability, and often results in organic, complex, and

Introduction to Algorand Algorand is a high-performance, carbon-negative blockchain platform founded by Turing Award winner Silvio Micali. It offers a unique pure proof-of-stake (PPoS) consensus mechanism that provides security, scalability (thousands of TPS), and near-instant finality (< 4.5 seconds) without forking. The platform supports smart contracts, asset tokenization, and decentralized applications while maintaining low transaction

Introduction to Algorithmic Trading Algorithmic trading (algo trading) uses computer algorithms to execute trading strategies by automatically submitting orders to markets based on predefined criteria. It accounts for over 70% of trading volume in major markets and offers advantages including speed, accuracy, reduced emotional bias, and the ability to simultaneously monitor multiple markets. This systematic

Introduction to Algebraic Topology Algebraic Topology studies topological spaces by associating algebraic objects (like groups and rings) to them in a way that topological properties are reflected in algebraic properties. This powerful approach allows us to classify spaces, detect holes and obstructions, and solve problems that would be difficult using purely topological methods. Algebraic topology

Introduction to Algebraic Number Theory Algebraic Number Theory (ANT) studies algebraic structures related to algebraic numbers – numbers that are roots of non-zero polynomials with rational coefficients. It extends classical number theory by incorporating techniques from abstract algebra, especially field and ring theory. ANT is crucial for solving classical number-theoretic problems like Fermat’s Last Theorem

Introduction: What is Algebraic Geometry and Why It Matters Algebraic geometry studies geometric objects defined by polynomial equations. It represents a powerful fusion of algebra and geometry where: Geometric objects (curves, surfaces, higher-dimensional varieties) are defined by polynomial equations Algebraic techniques provide tools to study these geometric objects systematically Applications span pure mathematics (number theory,

Introduction to Algebraic Combinatorics Algebraic combinatorics is a field that uses algebraic methods to solve counting problems and, conversely, applies combinatorial techniques to understand algebraic structures. It sits at the intersection of several mathematical disciplines including combinatorics, algebra, representation theory, and geometry. Key areas of study include: Enumerative combinatorics Symmetric functions and symmetric groups Representation

Multiplication Shortcuts Multiplying by Powers of 10 Shortcut Example To multiply by 10, add a zero 45 × 10 = 450 To multiply by 100, add two zeros 45 × 100 = 4,500 To multiply by 1000, add three zeros 45 × 1000 = 45,000 Multiplying by 5 Shortcut Example Multiply by 10, then divide