I-Abstract algebra
I-Abstract algebra lolunye uhlobo lakwa-math olufunda nzulu ngezakhiwo ze-algebra nekuthiwa yi-algebraic structures. Ezi zakhiwo ziquka:
- amaqela abizwa ngokuba zii-groups
- Izazinge ekuthiwa zii-rings
- ii-fields
- ii-vector spaces
- ii-algebras
- i-Boolean algebra
Yinto eqhelekileyo ukwakhela i-theori kuhlobo olunye lwesakhiwo esinye, njengakwi-group theory okanye kwi-category theory.
Injongo yetheori kwi-concept nganye kukuza nenkcazo epheleleyo necacileyo nge- concept, imizekelo yayo, izakhiwana eziphuma kuyo, iindlela zokunxulumanisa imizekelo ye-concept eyahlukeneyo ngokwakwa-algebra(ically) (ezi ke zibizwa ngokuba zii-morphisms kwezinye iimeko), kunye nokusetyenziswa kwee-concepts, macalana omabini ngaphakathi kwitheori yayo, nangaphandle kwamanye amabakala amanye amabakala emathematics.
Ngexesha lembali, amabakala ngamabakala akwa-mathematics asebenzise ii--algebras. Ii-algebras zimalunga nokufumana okanye zixele ngokucacileyo nokuchanekileyo imigaqo yokubala ngee-formulas nangee-expressions ezithile kwamathematics. Olunye uhlobo lwe-algebra (nolungelilo olu-abstract) yi-elementary algebra, umzekelo.
Examples
[tshintsha | Yenza izilungiso kokubhaliweyo]- Ukusombulula ii-equations ngee-variables ezininzi. Oku kukhokelela kwii-matrices, ii-determinants kunye nee-linear algebra.
- Ukufumana ii-formulas ze-polynomial equations. Oku kukhokhelela ekufumaneni (amaqela) ii-groups, njege-expression ye-symmetry.
- I-Quadratic kunye ne-higher-degree equations kunye nee-Diophantine equations - ingakumbi xa i-Fermat's last theorem yayi-proved ikhokhelela kwinkcazo epheleleyo ye-rings, kunye nee-ideals.