Aljebra

Faili:Image-Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala.jpg

Ukurasa wa kitabu al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala cha Al-Khwārizmī.

Aljebra (kutoka katika Kiarabu "al-jabr", inamaanisha "muungano wa sehemu zilizovunjika") ni tawi mojawapo la hisabati pamoja na nadharia ya namba, jiometri na uchambuzi.

Sifa maalumu ya aljebra ni kwamba inatumia ishara kutatua matatizo ya hisabati, kwa mfano kupiga hesabu hata kama namba fulani ndani yake haijulikani.

Katika muundo wake wa kiujumla, aljebra ni somo la ishara za kihisabati na sheria za kuendesha ishara hizo; ni uzi unaounganisha karibu matawi yote ya hisabati. Inajumuisha kila kitu kutoka kwenye misingi ya kutatua milinganyo.

• Mfano mmoja ni mlinganyo ufuatao ambapo $x$ ni kutofautiana:

$\frac{7x+9}{4x+2}=2$

$7x+9=8x+4$

$9-4=8x-7x$

$x=5$

Marejeo

• Kigezo:Citation
• Donald R. Hill, Islamic Science and Engineering (Edinburgh University Press, 1994).
• Ziauddin Sardar, Jerry Ravetz, and Borin Van Loon, Introducing Mathematics (Totem Books, 1999).
• George Gheverghese Joseph, The Crest of the Peacock: Non-European Roots of Mathematics (Penguin Books, 2000).
• John J O'Connor and Edmund F Robertson, History Topics: Algebra Index. In MacTutor History of Mathematics archive (University of St Andrews, 2005).
• I.N. Herstein: Topics in Algebra. ISBN 0-471-02371-X
• R.B.J.T. Allenby: Rings, Fields and Groups. ISBN 0-340-54440-6
• L. Euler: Elements of Algebra Kigezo:Wayback, ISBN 978-1-899618-73-6
• Kigezo:Cite book

Viungo vya nje

• Khan Academy: Conceptual videos and worked examples
• Khan Academy: Origins of Algebra, free online micro lectures Kigezo:Wayback
• Algebrarules.com: An open source resource for learning the fundamentals of Algebra
• 4000 Years of Algebra Kigezo:Wayback, lecture by Robin Wilson, at Gresham College, October 17, 2007 (available for MP3 and MP4 download, as well as a text file).
• Kigezo:Cite SEP