Kozi ya Abstract algebra inafaida gani ?

[JPM605]

Wakuu kuna kozi za hesabu hazina manufaa kabisa. Mfano abstract algebra yaani ni kutesana bila kuleta mafanikio.

Mlioisoma popote pale tubadilishane uzoefu maana mi ningekuwa senete ya chuo ningeiweka iwe optional kwa wanaoitaka.

 

[Munguwatosha]

Siku moja kwenye lecture nilimuuliza dk Kakiko pale udsm faida ya kusoma hiyo course alisema ina umuhimu wakati ukitaka kusoma masters ya mathematics.

 

[KATUMBACHAKO]

Isomophirsm... homomorphism.. rings.. and fields

 

[kasahunga]

ktk maisha ya chuo kozi ninazoziheshimuni topology na abstract algebra

 

[Jeho]

ktk maisha ya chuo kozi ninazoziheshimuni topology na abstract algebra

Ukiwa Tanzania course yoyote ya hesabu haina manufaa, maana inachukulika kila anayesoma hesabu anapaswa kuwa mwalimu. Lakini kwa nchi za wenzetu, course zote za pure mathematics zina manufaa. Mleta uzi, ili ujue manufaa ya abstract algebra,

jaribu kuifanyia project kama katika shahada yako kuna project, ndipo utapata mwanga wa matumizi ya abstract algebra. Nazipenda sana course za pure mathematics kama hiyo abstract, topolgy and measure theory.

 

[Jeho]

Isomophirsm... homomorphism.. rings.. and fields

ongezea na groups

 

[marooo]

Just Google "What are some real-life applications of abstract algebra?"

Au soma hapa:

Codes

Error Correcting Codes are used in almost all forms of digital storage and communication, from DVD players to satellite communication. The theory and practice of constructing good error correcting codes rely heavily on the abstract notions of finite fields and vector spaces (see e.g. Huffman[1]), and more recently on even deeper and more abstract algebraic concepts like function fields and algebraic curves (Stichtenoth[2]).

Expander Graphs

Expander graphs can be used to design sparse communication networks with very strong connectivity features. "Sparse" means that every node in the network is connected to just a few other nodes; "strong connectivity" means that in order to sever the connection between two substantial pieces of the network you'd have to cut lots of individual connections. Expander graphs are useful also in a variety of algorithms where one needs to simulate "randomness" in a deterministic way.

Constructing good expander graphs is hard. The best known constructions rely on very deep results in representation theory, see e.g. Lubotzky[3].

3D Modeling and Animation

Representing rotation in 3D space, particularly when one wants to interpolate between two rotation states as in 3D animation, is usually done using the algebraic concept of quaternions [4]. It's amusing to find chapters on "quaternions" in the user manuals of software such as Maya and 3d studio.

Block Designs

In a sense this is a generalization of the "Codes" example. Block designs are very symmetric finite set systems; a nice concrete example to keep in mind is the following little challenge: find a set of 7 triplets of numbers in the range 1..7 such that every pair of numbers in this range belongs to precisely one triplet (look up the Fano Plane).

Such symmetric designs are useful in a variety of real-life contexts such as the design of experiments (it's a good way to choose sample sets without biases) and - says Wikipedia[5] - software testing, though I'm not really familiar with how they're used for that.

Once again, constructing block designs relies heavily on tools from abstract algebra, specifically finite fields (especially projective and affine geometries based on finite fields) and finite groups.

[1] Huffman and Pless: Fundamentals of Error Correcting Codes.

[2] Stichtenoth: Algebraic Function Fields and Codes.

[3] Lubotzky: Discrete Groups, Expanding Graphs and Invariant Measures.

Hakuna course isiyokuwa na manufaa.

 

[Mgumu04]

Abstact algebra ina matumizi makubwa sana kwa nchi zilizo endelea katika maswala ya TEHAMA maana katika information security lazima abstract uijue ila kibongo it is useless