Mathematics
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics).Mathematics involves the description and manipulation of abstract objects that consist of either abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to prove properties of objects, a ''proof'' consisting of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of the theory under consideration.
Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation. Some areas of mathematics, such as statistics and game theory, are developed in close correlation with their applications and are often grouped under applied mathematics. Other areas are developed independently from any application (and are therefore called pure mathematics) but often later find practical applications.
Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics, most notably in Euclid's ''Elements''. Since its beginning, mathematics was primarily divided into geometry and arithmetic (the manipulation of natural numbers and fractions), until the 16th and 17th centuries, when algebra and infinitesimal calculus were introduced as new fields. Since then, the interaction between mathematical innovations and scientific discoveries has led to a correlated increase in the development of both. At the end of the 19th century, the foundational crisis of mathematics led to the systematization of the axiomatic method, which heralded a dramatic increase in the number of mathematical areas and their fields of application. The contemporary Mathematics Subject Classification lists more than sixty first-level areas of mathematics.
Provided by Wikipedia
-
1
-
2
-
3
-
4
-
5
-
6
-
7by University of Alaska (College). College of Mathematics, Physical Sciences, and EngineeringGet access
Published 1969
Journal/Newspaper -
8by University of Alaska (College). College of Mathematics, Physical Sciences, and EngineeringGet access
Published 1969
Journal/Newspaper -
9by University of Alaska (College). College of Mathematics, Physical Sciences, and EngineeringGet access
Published 1968
Journal/Newspaper -
10
-
11
-
12
-
13
-
14by Langford, Zachary L. Oak Ridge National Lab. , Oak Ridge, TN . Computer Science and Mathematics Division. Climate Change Science Inst.; Pennsylvania State Univ., University Park, PA . Dept. of Civil and Environmental Engineering, Gooseff, Michael N. Colorado State Univ., Fort Collins, CO . Dept. of Civil and Environmental Engineering, Lampkin, Derrick J. Univ. of Maryland, College Park, MD . Dept. of Atmospheric and Oceanic ScienceGet access
Published in Antarctic Science (2021)
Get access
Get access
-
15by Seydoux, Léonard, Balestriero, Randall Rice Univ., Houston, TX . Electrical and Computational Engineering, Poli, Piero Univ. of Grenoble Alpes, Saint-Martin-d-Heres . ISTerre, équipe Ondes et Structures, Hoop, Maarten de Rice Univ., Houston, TX . Computational and Applied Mathematics, Campillo, Michel Univ. of Grenoble Alpes, Saint-Martin-d-Heres . ISTerre, équipe Ondes et Structures, Baraniuk, Richard Rice Univ., Houston, TX . Electrical and Computational EngineeringGet access
Published in Nature Communications (2023)
Get access
Get access
-
16Геоинформационные технологии экспертной системы GIS-ENDDB («Базы данных природных катастроф Земли»).by Институт вычислительной математики и математической геофизики СО РАН, Институт нефтегазовой геологии и геофизики им. А. А. Трофимука СО РАН, Новосибирский государственный университет, Высший колледж информатики НГУ, Сургутский государственный университет, Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS, Novosibirsk State University, Higher School of Informatics of NSU, Surgut State University, Михеева, Анна Владленовна, Дядьков, Петр Георгиевич, Марчук, Андрей Гурьевич, Егоров, Александр Алексеевич, Mikheeva, Anna Vladlenovna, Dyadkov, Petr Georgiyevich, Marchuk, Andrey Gurjevich, Egorov, Aleksandr AlekseevichGet access
Published 2016
Article in Journal/Newspaper -
17by Pernille Bronken Eidesen (Arctic Biology Department, University Centre in Svalbard), Eike Müller (Arctic Biology Department, University Centre in Svalbard), Christian Lettner (Department of Botany and Biodiversity Research, Faculty of Life Sciences, University of Vienna), Inger Greve Alsos (Department of Natural Sciences, Tromsø University Museum), Morgan Bender (School of Fisheries and Ocean Sciences, Institute of Arctic Biology, University of Alaska Fairbanks), Martin Kristiansen (Faculty of Biosciences, Fisheries and Economics, University of Tromsø), Bart Peeters (Faculty of Natural Sciences and Technology, Norwegian University of Science and Technology), Froukje Postma (Department of Plant Ecology and Evolution, Faculty of Biology, Uppsala University), Koen Frans Verweij (Community and Conservation Ecology Group, Faculty of Mathematics and Natural Sciences, University of Groningen)Get access
Published in Polar Research (2013)
Get access
Text -
18
-
19by Schulz, Kirstin, Janout, Markus, Lenn, Yueng‐Djern, Ruiz‐Castillo, Eugenio, Polyakov, Igor, Mohrholz, Volker, Tippenhauer, Sandra, Reeve, Krissy Anne, Hölemann, Jens, Rabe, Benjamin, Vredenborg, Myriel, Janout, Markus; 1 Alfred‐Wegener‐Institut Helmholtz‐Zentrum für Polar‐ und Meeresforschung Bremerhaven Germany, Lenn, Yueng‐Djern; 2 School of Ocean Sciences Bangor University Menai Bridge UK, Ruiz‐Castillo, Eugenio; 1 Alfred‐Wegener‐Institut Helmholtz‐Zentrum für Polar‐ und Meeresforschung Bremerhaven Germany, Polyakov, Igor; 3 International Arctic Research Center College of Natural Science and Mathematics University of Alaska Fairbanks Fairbanks USA, Mohrholz, Volker; 4 Leibniz Institute for Baltic Sea Research Rostock Germany, Tippenhauer, Sandra; 1 Alfred‐Wegener‐Institut Helmholtz‐Zentrum für Polar‐ und Meeresforschung Bremerhaven Germany, Reeve, Krissy Anne; 1 Alfred‐Wegener‐Institut Helmholtz‐Zentrum für Polar‐ und Meeresforschung Bremerhaven Germany, Hölemann, Jens; 1 Alfred‐Wegener‐Institut Helmholtz‐Zentrum für Polar‐ und Meeresforschung Bremerhaven Germany, Rabe, Benjamin; 1 Alfred‐Wegener‐Institut Helmholtz‐Zentrum für Polar‐ und Meeresforschung Bremerhaven Germany, Vredenborg, Myriel; 1 Alfred‐Wegener‐Institut Helmholtz‐Zentrum für Polar‐ und Meeresforschung Bremerhaven GermanyGet access
Published in Journal of Geophysical Research: Oceans (2021)
Get access
Article in Journal/Newspaper -
20by Langford, Zachary Univ. of Tennessee, Knoxville, TN . Bredesen Center for Interdisciplinary Research and Graduate Education; Oak Ridge National Lab. , Oak Ridge, TN . Environmental Sciences Division and Climate Change Science Inst., Kumar, Jitendra Univ. of Tennessee, Knoxville, TN . Bredesen Center for Interdisciplinary Research and Graduate Education; Oak Ridge National Lab. , Oak Ridge, TN . Environmental Sciences Division and Climate Change Science Inst., Hoffman, Forrest Oak Ridge National Lab. , Oak Ridge, TN . Computer Science and Mathematics Division and Climate Change Science Inst., Norby, Richard J. Univ. of Tennessee, Knoxville, TN . Bredesen Center for Interdisciplinary Research and Graduate Education; Oak Ridge National Lab. , Oak Ridge, TN . Environmental Sciences Division and Climate Change Science Inst., Wullschleger, Stan D. Univ. of Tennessee, Knoxville, TN . Bredesen Center for Interdisciplinary Research and Graduate Education; Oak Ridge National Lab. , Oak Ridge, TN . Environmental Sciences Division and Climate Change Science Inst., Sloan, Victoria L. Univ. of Bristol, Bristol . Dept. of Civil Engineering, Iversen, Colleen M. Univ. of Tennessee, Knoxville, TN . Bredesen Center for Interdisciplinary Research and Graduate Education; Oak Ridge National Lab. , Oak Ridge, TN . Environmental Sciences Division and Climate Change Science Inst.Get access
Published in Remote Sensing (2021)
Get access
Get access