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Mathematics

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A map of the Tricki. This is an attempt to give a quick guide to the top few levels of the Tricki.

A map of the Tricki

It may cease to be feasible when the Tricki gets bigger, but we might perhaps be able to automate additions to it. Clicking on arrows just to the right of the name of an article reveals its subarticles. If you want to hide the subarticles again, then you should click to the right of them rather than clicking on the name of one of the subarticles themselves, since otherwise you will follow a link to that subarticle. What kind of problem am I trying to solve? General problem-solving tips Front pages for different areas of mathematics How to use mathematical concepts and statements. EyA Recordings of the ICTP Diploma Programme.

Combinatorics

Logic. Algebra. Topology. Analysis. Lists of mathematics topics. This list is incomplete; you can help by making it inconsistent.

Lists of mathematics topics

This article itemizes the various lists of mathematics topics. Some of these lists link to hundreds of articles; some link only to a few. The template to the right includes links to alphabetical lists of all mathematical articles. This article brings together the same content organized in a manner better suited to browsing. The purpose of this list is not similar to that of the Mathematics Subject Classification formulated by the American Mathematical Society. Areas of basic mathematics[edit] These lists include topics typically taught in secondary education or in the first year of university. Areas of advanced mathematics[edit] See also Areas of mathematics. As a rough guide this list is divided into pure and applied sections although in reality these branches are overlapping and intertwined. Pure mathematics[edit] Algebra[edit] Calculus and analysis[edit] Geometry and topology[edit] Combinatorics[edit] Logic[edit] Computing[edit] Areas of mathematics. Mathematics has become a vastly diverse subject over history, and there is a corresponding need to categorize the different areas of mathematics.

Areas of mathematics

A number of different classification schemes have arisen, and though they share some similarities, there are differences due in part to the different purposes they serve. In addition, as mathematics evolves, these classification schemes must evolve as well to account for newly created areas or newly discovered links between different areas. Classification is made more difficult by some subjects, often the most active, which straddle the boundary between different areas. A traditional division of mathematics is into pure mathematics, mathematics studied for its intrinsic interest, and applied mathematics, mathematics which can be directly applied to real world problems.[1] This division is not always clear and many subjects have been developed as pure mathematics to find unexpected applications later on.

Classification systems[edit] Model theory.

Category theory

List of mathematical proofs. Proof assistance. List of rules of inference. This is a list of rules of inference, logical laws that relate to mathematical formulae.

List of rules of inference

Introduction[edit] Rules of inference are syntactical transform rules which one can use to infer a conclusion from a premise to create an argument. A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following list, as many of the rules are redundant, and can be proven with the other rules.

Discharge rules permit inference from a subderivation based on a temporary assumption. Indicates such a subderivation from the temporary assumption to Rules for classical sentential calculus[edit] Sentential calculus is also known as propositional calculus. Rules for negations[edit] Reductio ad absurdum (or Negation Introduction) Reductio ad absurdum (related to the law of excluded middle) Noncontradiction (or Negation Elimination) Double negation elimination Modus tollens. MR: Search Publications database.