Notebook interfaceA notebook interface or computational notebook is a virtual notebook environment used for literate programming, a method of writing computer programs. Some notebooks are WYSIWYG environments including executable calculations embedded in formatted documents; others separate calculations and text into separate sections. Notebooks share some goals and features with spreadsheets and word processors but go beyond their limited data models. Modular notebooks may connect to a variety of computational back ends, called "kernels".
IntegralIn mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, the other being differentiation. Integration started as a method to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Today integration is used in a wide variety of scientific fields.
Proof theoryProof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature.
Three-sector modelThe three-sector model in economics divides economies into three sectors of activity: extraction of raw materials (primary), manufacturing (secondary), and service industries which exist to facilitate the transport, distribution and sale of goods produced in the secondary sector (tertiary). The model was developed by Allan Fisher, Colin Clark, and Jean Fourastié in the first half of the 20th century, and is a representation of an industrial economy. It has been criticised as inappropriate as a representation of the economy in the 21st century.
LaptopA laptop computer or notebook computer, also known as a laptop or notebook for short, is a small, portable personal computer (PC). Laptops typically have a clamshell form factor with a flat panel screen (usually in diagonal size) on the inside of the upper lid and an alphanumeric keyboard and pointing device (such as a trackpad and/or trackpoint) on the inside of the lower lid, although 2-in-1 PCs with a detachable keyboard are often marketed as laptops or as having a "laptop mode".
Proof (truth)A proof is sufficient evidence or a sufficient argument for the truth of a proposition. The concept applies in a variety of disciplines, with both the nature of the evidence or justification and the criteria for sufficiency being area-dependent. In the area of oral and written communication such as conversation, dialog, rhetoric, etc., a proof is a persuasive perlocutionary speech act, which demonstrates the truth of a proposition.
Proof by contradictionIn logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally valid. More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved.
Chain ruleIn calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g. More precisely, if is the function such that for every x, then the chain rule is, in Lagrange's notation, or, equivalently, The chain rule may also be expressed in Leibniz's notation. If a variable z depends on the variable y, which itself depends on the variable x (that is, y and z are dependent variables), then z depends on x as well, via the intermediate variable y.
Finite element methodThe finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).
Project JupyterProject Jupyter (ˈdʒuːpɪtər) is a project to develop open-source software, open standards, and services for interactive computing across multiple programming languages. It was spun off from IPython in 2014 by Fernando Pérez and Brian Granger. Project Jupyter's name is a reference to the three core programming languages supported by Jupyter, which are Julia, Python and R. Its name and logo are an homage to Galileo's discovery of the moons of Jupiter, as documented in notebooks attributed to Galileo.
Proof calculusIn mathematical logic, a proof calculus or a proof system is built to prove statements. A proof system includes the components: Language: The set L of formulas admitted by the system, for example, propositional logic or first-order logic. Rules of inference: List of rules that can be employed to prove theorems from axioms and theorems. Axioms: Formulas in L assumed to be valid. All theorems are derived from axioms. Usually a given proof calculus encompasses more than a single particular formal system, since many proof calculi are under-determined and can be used for radically different logics.
Peer supportPeer support occurs when people provide knowledge, experience, emotional, social or practical help to each other. It commonly refers to an initiative consisting of trained supporters (although it can be provided by peers without training), and can take a number of forms such as peer mentoring, reflective listening (reflecting content and/or feelings), or counseling. Peer support is also used to refer to initiatives where colleagues, members of self-help organizations and others meet, in person or online, as equals to give each other connection and support on a reciprocal basis.
