Algebra and Number Theory detailed syllabus for Computer Science & Design (CSD) for 2021 regulation curriculum has been taken from the Anna Universities official website and presented for the CSD students. For course code, course name, number of credits for a course and other scheme related information, do visit full semester subjects post given below.
For Computer Science & Design 7th Sem scheme and its subjects, do visit CSD 7th Sem 2021 regulation scheme. For Open Elective-III scheme and its subjects refer to CSD Open Elective-III syllabus scheme. The detailed syllabus of algebra and number theory is as follows.
Course Objectives:
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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
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Unit IV
DIOPHANTINE EQUATIONS AND CONGRUENCES
Linear Diophantine equations – Congruence’s – Linear Congruence’s – Applications : Divisibility tests – Modular exponentiation – Chinese remainder theorem – 2×2 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.
Course Outcomes:
- Explain the fundamental ^concepts of advanced algebra and their role in modern mathematics and applied contexts.
- Demonstrate accurate and efficient use of advanced algebraic techniques.
- The students should be able to demonstrate their mastery by solving non-trivial problems related to the concepts, and by proving simple theorems about the, statements proven by the text
Text Books:
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Reference Books:
- San Ling and Chaoping Xing, “Coding Theory – A first Course”, Cambridge Publications, Cambridge, 2004.
- Niven.I, Zuckerman.H.S., and Montgomery, H.L., “An Introduction to Theory of Numbers” , John Wiley and Sons , Singapore, 2004.
- Lidl.R., and Pitz. G, “Applied Abstract Algebra”, Springer Verlag, New Delhi, 2nd Edition , 2006.
For detailed syllabus of all the other subjects of Computer Science & Design 7th Sem, visit CSD 7th Sem subject syllabuses for 2021 regulation.
For all Computer Science & Design results, visit Anna University CSD all semester results direct link.