MA8551 ALGEBRA AND NUMBER THEORY
Prepared by
S.Santhosh (Admin)
Important questions
share it a link alone
Don't waste my hardwork and valuable time
Don't share as screenshot kind request
based on views next exams questions are yet to be updated
most viewed dept will get update at first So Dont screenshot and share
most viewed dept will get update at first So Dont screenshot and share
Unit-1
1.Lagrange’s theorem
2.Ring homomorphism.
3. Cyclic groups And related all theories
Unit 2 1.Factorization of polynomials over finite fields.
or
2.Irreducible polynomials over finite fields
Unit 3
1.GCD* , Euclidean algorithm**
2.Fundamental theorem of arithmetic** ,LCM.
Unit 4
1.Chinese remainder theorem*
2.LDE **
Unit 5
1. Euler‘s theorem,Wilson‘s theorem
2.Tau and Sigma functions(rare)
**Very important questions are bolded and may be asked based on this topic
don't waste my hardwork and valuable time
As Engineer i think you know how to respect another
Share it as link alone . don't share it as screenshot or any text material if u found this anywhere kindly report me . #Admin WhatsAppContact uS
*These questions are expected for the exams This may or may not be asked for exams All the best.... from admin Santhosh
Thanks for your love and support guys keep supporting and share let the Engineers know about Us and leave a comment below for better improvements If there is any doubt feel free to ask me I will clear if I can or-else I will say some solutions ..get me through WhatsApp for instant updates ~$tuff$£ctorSYllabuS
Contact uS
*These questions are expected for the exams This may or may not be asked for exams
All the best.... from admin Santhosh
Thanks for your love and support guys keep supporting and share let the Engineers know about Us and leave a comment below for better improvements
If there is any doubt feel free to ask me I will clear if I can or-else I will say some solutions ..get me through WhatsApp for instant updates ~$tuff$£ctorUNIT I GROUPS AND RINGSGroups : Definition – Properties – Homomorphism – Isomorphism – Cyclic groups – Cosets – Lagrange’s theorem. Rings: Definition – Sub rings – Integral domain – Field – Integer modulo n – Ring homomorphism.
UNIT II FINITE FIELDS AND POLYNOMIALSRings – Polynomial rings – Irreducible polynomials over finite fields – Factorization of polynomials over finite fields.
UNIT III DIVISIBILITY THEORY AND CANONICAL DECOMPOSITIONSDivision algorithm – Base – b representations – Number patterns – Prime and composite numbers – GCD – Euclidean algorithm – Fundamental theorem of arithmetic – LCM.
UNIT IV DIOPHANTINE EQUATIONS AND CONGRUENCESLinear Diophantine equations – Congruence‘s – Linear Congruence‘s – Applications: Divisibility tests – Modular exponentiation-Chinese remainder theorem – 2 x 2 linear systems.
UNIT V CLASSICAL THEOREMS AND MULTIPLICATIVE FUNCTIONSWilson‘s theorem – Fermat‘s little theorem – Euler‘s theorem – Euler‘s Phi functions – Tau and Sigma functions.
UNIT I GROUPS AND RINGS
Groups : Definition – Properties – Homomorphism – Isomorphism – Cyclic groups – Cosets – Lagrange’s theorem. Rings: Definition – Sub rings – Integral domain – Field – Integer modulo n – Ring homomorphism.
UNIT II FINITE FIELDS AND POLYNOMIALS
Rings – Polynomial rings – Irreducible polynomials over finite fields – Factorization of polynomials over finite fields.
UNIT III DIVISIBILITY THEORY AND CANONICAL DECOMPOSITIONS
Division algorithm – Base – b representations – Number patterns – Prime and composite numbers – GCD – Euclidean algorithm – Fundamental theorem of arithmetic – LCM.
UNIT IV DIOPHANTINE EQUATIONS AND CONGRUENCES
Linear Diophantine equations – Congruence‘s – Linear Congruence‘s – Applications: Divisibility tests – Modular exponentiation-Chinese remainder theorem – 2 x 2 linear systems.
UNIT V CLASSICAL THEOREMS AND MULTIPLICATIVE FUNCTIONS
Wilson‘s theorem – Fermat‘s little theorem – Euler‘s theorem – Euler‘s Phi functions – Tau and Sigma functions.