A finite-state machine (FSM) or finite-state automaton, finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of states at any given time. The FSM can change from one state to another in response to some external inputs; the change from one state to another is called a transition. An FSM is defined by a list of its states, its initial state, and the conditions for each transition. Finite state machines are of two types – deterministic finite state machines and non-deterministic finite state machines. A deterministic finite-state machine can be constructed equivalent to any non-deterministic one.
Mathematics includes the study of such topics as quantity, structure, space, and change.
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
The term phase transition is most commonly used to describe transitions between solid, liquid, and gaseous states of matter, as well as plasma in rare cases. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change, often discontinuously, as a result of the change of external conditions, such as temperature, pressure, or others. For example, a liquid may become gas upon heating to the boiling point, resulting in an abrupt change in volume. The measurement of the external conditions at which the transformation occurs is termed the phase transition. Phase transitions commonly occur in nature and are used today in many technologies.
Hidden Markov Model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved states.
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science and discrete mathematics. The word automata comes from the Greek word αὐτόματα, which means "self-acting".
A Petri net, also known as a place/transition (PT) net, is one of several mathematical modeling languages for the description of distributed systems. It is a class of discrete event dynamic system. A Petri net is a directed bipartite graph, in which the nodes represent transitions and places. The directed arcs describe which places are pre- and/or postconditions for which transitions. Some sources state that Petri nets were invented in August 1939 by Carl Adam Petri—at the age of 13—for the purpose of describing chemical processes.
Without loss of generality is a frequently used expression in mathematics. The term is used before an assumption in a proof which narrows the premise to some special case; it implies that the proof for that case can be easily applied to all others, or that all other cases are equivalent or similar. Thus, given a proof of the conclusion in the special case, it is trivial to adapt it to prove the conclusion in all other cases.
In physics, the terms order and disorder designate the presence or absence of some symmetry or correlation in a many-particle system.
Gateway STEM High School is a public magnet high school in St. Louis, Missouri, USA.
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n. In this more precise terminology, a manifold is referred to as an n-manifold.
A track transition curve, or spiral easement, is a mathematically-calculated curve on a section of highway, or railroad track, in which a straight section changes into a curve. It is designed to prevent sudden changes in lateral acceleration. In plane, the start of the transition of the horizontal curve is at infinite radius, and at the end of the transition, it has the same radius as the curve itself and so forms a very broad spiral. At the same time, in the vertical plane, the outside of the curve is gradually raised until the correct degree of bank is reached.
In theoretical computer science, a transition system is a concept used in the study of computation. It is used to describe the potential behavior of discrete systems. It consists of states and transitions between states, which may be labeled with labels chosen from a set; the same label may appear on more than one transition. If the label set is a singleton, the system is essentially unlabeled, and a simpler definition that omits the labels is possible.
Genetic epistemology or 'developmental theory of knowledge' is a study of the origins (genesis) of knowledge (epistemology) established by Jean Piaget.
Michael Aizenman is a mathematician and a physicist at Princeton University, working in the fields of mathematical physics, statistical mechanics, functional analysis and probability theory.
Jennifer Tour Chayes is a Technical Fellow and Managing Director of Microsoft Research New England in Cambridge, Massachusetts, which she founded in 2008, and Microsoft Research New York City, which she founded in 2012. Chayes is best known for her work on phase transitions in discrete mathematics and computer science, structural and dynamical properties of self-engineered networks, and algorithmic game theory. She is considered one of the world's experts in the modeling and analysis of dynamically growing graphs. Chayes has been with Microsoft Research since 1997, when she co-founded the Theory Group. She received her Ph.D. in mathematical physics at Princeton University in 1983. She is Affiliate Professor of Mathematics and Physics at the University of Washington, and was for many years Professor of Mathematics at UCLA. She is an author on almost 120 scientific papers and the inventor on more than 25 patents.
Jürg Martin Fröhlich is a Swiss mathematician and theoretical physicist.
Judit Nora Moschkovich is a professor in mathematics education and the learning sciences. She works in the Education Department at the University of California, Santa Cruz. Professor Moschkovich's research uses sociocultural approaches to study mathematical thinking and learning, mathematical discourse, and language issues in mathematics education. Her research has focused on the transition from arithmetic to algebraic thinking, mathematical discourse, and learning/teaching mathematics in classrooms with students who are bilingual, Latino/a, and/or learning English.
Mary Winston Jackson was an African American mathematician and aerospace engineer at the National Advisory Committee for Aeronautics (NACA), which in 1958 was succeeded by the National Aeronautics and Space Administration (NASA). She worked at Langley Research Center in Hampton, Virginia, for most of her career. She started as a computer at the segregated West Area Computing division. She took advanced engineering classes and, in 1958, became NASA's first black female engineer.
