field

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics.
The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers. Many other fields, such as fields of rational functions, algebraic function fields, algebraic number fields, and p-adic fields are commonly used and studied in mathematics, particularly in number theory and algebraic geometry. Most cryptographic protocols rely on finite fields, i.e., fields with finitely many elements.
The relation of two fields is expressed by the notion of a field extension. Galois theory, initiated by Évariste Galois in the 1830s, is devoted to understanding the symmetries of field extensions. Among other results, this theory shows that angle trisection and squaring the circle cannot be done with a compass and straightedge. Moreover, it shows that quintic equations are, in general, algebraically unsolvable.
Fields serve as foundational notions in several mathematical domains. This includes different branches of mathematical analysis, which are based on fields with additional structure. Basic theorems in analysis hinge on the structural properties of the field of real numbers. Most importantly for algebraic purposes, any field may be used as the scalars for a vector space, which is the standard general context for linear algebra. Number fields, the siblings of the field of rational numbers, are studied in depth in number theory. Function fields can help describe properties of geometric objects.

View More On Wikipedia.org
Recent contents

  1. Field Officer Supervisor at VisionFund Tanzania Microfinance Bank Ltd (VFT MFB) September, 2023

    Work reference no: 008/2023 Position: Field Officer Supervisor Reporting to: FAST Product Manager Responsibility: Setting/Agreeing targets with Field officers Agreeing daily activity plan with Field officer Monitor Field Officer Performance on regular basis. Continuously coach and train FOs...

  2. Tuna Nafasi Moja Kwa Clinical Officer Kufanya Field Au Volunteer

    Natural Skin Solution yenye makao yake Kibaha Tanzania, tunapenda kutangazia wahitimu wa Clinical Officer au wanafunzi wa fani ya Clinical medicine ,tuna nafasi moja tu ya field au volunteer. Wasiliana nasi kwa 0713 039 875 kwa maelezo zaidi. (Siko hapa jukwaani muda mwingi, tumia Simu)...

  3. Field Compressor Technician (02 Vacancies) at Bulyanhulu Gold Mine

    Position: Field Compressor Technician (02 Vacancies) Reporting to: Process Mechanical Foreman Duration: Permanent Location: Kahama, Shinyanga Responsibilities: Ensure safe work practices, i.e., attending compulsory safety courses and meetings, use of required PPE, incident/accident reporting...
  4. A

    Maoni yangu jinsi ya kuboresha Sekta ya Elimu nchini

    Habari wana bodi ni matumaini Yangu kuwa wote ni wazima wa afya. Mimi ni Kijana wa kitanzania miaka 23 pia mwanafunzi wa shahada ya kwanza ya ualimu sayansi. Siku ya Leo nimewaza Sana ambayo yanaweza boresha sekta ya elimu na maisha ya walimu kwa ujumla kama ifuatavyo; 01. Kuwe na Kodi ya...
  5. M

    Field ya IT yenye uhitaji mkubwavtanzania

    Wakubwa I hope mko powa! Nilikuw na uliza Kwa wale wenye enough understanding na maswali ya information technology ni field ipi inauhitaji mkubwa tanzania Kati ya hizi 1.networking 2.database 3.cybersecurity 4.programming 5.web development 6.data science
  6. M

    Wanafunzi wa chuo wanaokwenda TANESCO kufanya field huwa wanalipwa?

    Hey

  7. Msaada: Napata mtihani kupata field

    MREJESHO: Nimefanikiwa kusaidiwa kupata field wakuu, mungu awabariki wote mliotoa mchango wenu wa kimawazo katikabuzi huu. 🙏 Wakuu habari za wakati huu, Wakuu habari za wakati huu, Nakuja kwenu kwa ombi la unyenyekevu: Msaada katika kutafuta fursa ya mafunzo kwa vitendo. (FIELD). Kwa sasa...
  8. K

    Field Zanzibar

    Hi, jamani niko natafuta Hotel ya kufanyia field zanzibar, msaada please 🙏🙏

  9. Wanafunzi wa kichawi wanapokuwa internship "Field" au mafunzo kwa vitendo

    WANAFUNZI WA KICHAWI WANAPOKUWA INTERNSHIP "FIELD" AU KWENYE MAFUNZO KWA VITENDO. Anaandika, Robert Heriel Baada ya kupokea kozi fupifupi au ndefu katika taaluma ya Uchawi na ulozi ni muhimu kwenda Internship au field au Kwa Kiswahili fasaha tunasema kwenda kwenye mafunzo Kwa vitendo for...

  10. Akumbukwe John Okello, Baba wa Taifa la Zanzibar. Bila huyu leo Zanzibar wangekuwa bado Utumwani

    Huyu ni Mmoja wa Mashujaa wa miaka ile aliyeshiriki kuwaondoa Makoloni huko Zanzibar. Kama ambavyo Bara nao walikuwa wameondoa wao. Anasimulia mzee wangu ambaye alikuwa Mwalimu Chuo Kikuu cha Dar es Salaam miaka hiyo Che Guavera alikuja Tanzania mwaka 1965. Anasema Che alijaribu kuulizia habari...
  11. A

    Mwalimu wa field aliyesambaza picha za watoto wamekaa chini kufukuzwa (uhaba wa madawati)

    Mwalimu aliyesambaza picha hizi kufukuzwa JUMATANO , 8TH FEB , 2023 NA MWANDISHI WETU Kaimu Mkurugenzi wa Jiji la Mbeya, Wakili Triphonia Kisiga, amesema Mwalimu wa kujitolea katika shule ya sekondari Sinde, Evarist Chonya, aliyesambaza picha za uongo za wanafunzi wakiwa wamekaa chini...
  12. H

    I'm seeking for an employment opportunity on any field

    Greetings, My name is Harrison Munuo, a 28 years old . A holder of a bachelor degree in Education(IT& Geography). I'm seeking for an employment opportunity on any field that my particulars fit. I am energetic and open to learn new skills. I am willing to work in remotely environment and minimal...

  13. Natafuta field ya IT diploma

    Greetings guys of JF nimepost Uzi huu natafuta field ya IT katioa level ya diploma nimetafuta field jimekosa nimeona nije umu kwa ajili ya msaada wenu mkoa was Dar au Dodoma Niko tayari kwenda.

  14. Field Project Team Assistant at UNIDO

    Requisition ID: 1056 Grade : SB2 – Local support Country: Tanzania, united republic of Duty Station : Dar-es-Salaam Category: Local Support Personnel Type of job Posting: Internal and External Employment Type: NonStaff-Regular Duration (tentative): 3 months Application deadline: 26-Sep-2022...

  15. Chief Field Office,(NO-3) at UNICEF

    Job no: 552517 Contract type: Fixed Term Appointment Duty Station: Kibondo Level: NO-3 Location: United Republic of Tanzania Categories: Programme Management UNICEF works in some of the world’s toughest places, to reach the world’s most disadvantaged children. To save their lives. To defend...
  16. N

    Kazi kubwa anayoifanya Rais Samia katika ziara za mikoani

    Rais Samia anaendelea kupita katika kila Mkoa kukagua utekelezaji wa miradi mbalimbali na kutatua kero za wananchi. Licha ya kufanya ziara katika nchi mbalimbali zilizoleta tija kubwa, Rais hapumziki na kungojoea ripoti yuko "FIELD" katika Mikoa, Wilaya, Kata hadi Vijijiji. Baadhi ya mambo...

  17. Naomba kujuzwa kuhusu cheo cha Field Marshall, ni aina Gani ya mtu anaitwa cheo hicho?

    Katika pekua pekua pamoja na simulizi za hapa na pale nimeambiwa kwamba Dunia nzima ma-Field Marshall hawazidi kumi akiwemo hayati Fidel Castro na Ally Zaqawi . Je, ni kweli kuwa mafied marshall hawafiki kumi Dunia nzima ? Je, cheo hiki hutumikaje katika majeshi?

  18. Field Supervisors (Multiple Positions) at ICAP

    Job Overview Field Supervisors (multiple positions) Job no: 496339 Position type: Regular Full-Time Location: Tanzania – Dar es Salam Division/Equivalent: Tanzania School/Unit: Technical Department/Office: PHIA Categories: Program Management/Implementation/Support, Technical/Clinical/Quality...
  19. M

    kutolewa kwa ela za field (HELSB) baadhi ya vyuo vikuu Tanzania inaumiza wanafunzi wa hali ya chini (watoto wa wakulima)

    Bodi ya mkopo ya elimu ya juu hutoa mikopo kwa wanafunzi wenye vigezo na sifa zinazo stahili kupokea ambapo fedha hizo hujumuisha Ada , field, book and stationary na research ambapo kama mwanafunzi akibahatika kupata vyote huwa ni nafuu kwa mzazi. Lakini mwaka huu 2022 kwa wanafunzi wengi wa...

  20. Agricultural Field Officer II at (ASA) 55 posts

    POST AGRICULTURAL FIELD OFFICER II – 55 POST EMPLOYER The Agricultural Seed Agency (ASA) APPLICATION TIMELINE: 2022-07-23 2022-08-05 JOB SUMMARY NA DUTIES AND RESPONSIBILITIES i.To plan for field labor force for various field activities; ii.To allocate and supervise daily tasks to the field...
Menu
Log in
Register
Cookies are required to use this site. You must accept them to continue using the site. Learn more…