Mathematics

/ˈbuːliən/

adjective … “Relating to true/false logic.”

Boolean refers to a data type, algebra, or logic system based on two possible values: true and false. Boolean concepts underpin digital electronics, logic gates, computer programming, and decision-making systems. Named after mathematician George Boole, Boolean logic allows complex conditions to be expressed using operators like AND, OR, and NOT.

Key characteristics of Boolean include:

/ˈsɜːr.fɪs ˈɪn.tɪ.ɡrəl/

noun … “summing quantities over a curved surface.”

/ˈvɛk.tər fiːld/

noun … “direction and magnitude at every point.”

Vector Field is a mathematical construct that assigns a vector—an entity with both magnitude and direction—to every point in a space. Vector fields are fundamental in physics, engineering, and applied mathematics for modeling phenomena where both the direction and strength of a quantity vary across a region. Examples include velocity fields in fluid dynamics, force fields in mechanics, and electromagnetic fields in physics.

/ˈmækswɛlz ɪˈkweɪʒənz/

noun … “the laws that choreograph electricity and magnetism.”

/ɛnˈtrəpi/

noun … “measuring uncertainty in a single number.”

Entropy is a fundamental concept in information theory, probability, and thermodynamics that quantifies the uncertainty, disorder, or information content in a system or random variable. In the context of information theory, introduced by Claude Shannon, entropy measures the average amount of information produced by a stochastic source of data. Higher entropy corresponds to greater unpredictability, while lower entropy indicates more certainty or redundancy.

/ˈbraʊ.ni.ən ˈmoʊ.ʃən/

noun … “random jittering with a mathematical rhythm.”

/ˈmɑːr.kɒv ˈprəʊ.ses/

noun … “the future depends only on the present, not the past.”

Markov Process is a stochastic process in which the probability of transitioning to a future state depends solely on the current state, independent of the sequence of past states. This “memoryless” property, known as the Markov property, makes Markov Processes a fundamental tool for modeling sequential phenomena in probability, statistics, and machine learning, including Hidden Markov Models, reinforcement learning, and time-series analysis.

/ˈmæksɪməm ˈlaɪk.li.hʊd ˌɛstɪˈmeɪʃən/

noun … “finding the parameters that make your data most believable.”

/ˈsɪŋ.ɡjʊ.lər ˈvæl.ju dɪˌkɑːm.pəˈzɪʃ.ən/

noun … “disassembling a matrix into its hidden building blocks.”

/ˈfʊr.i.ɛr ˌtrænsˈfɔːrm/

noun … “the secret language of frequencies.”