Algebra and Number Theory detailed syllabus for Cyber Security (Cyber Security) for 2021 regulation curriculum has been taken from the Anna Universities official website and presented for the Cyber Security 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 Cyber Security 7th Sem scheme and its subjects, do visit Cyber Security 7th Sem 2021 regulation scheme. For Open Elective-III scheme and its subjects refer to Cyber Security 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 Cyber Security 7th Sem, visit Cyber Security 7th Sem subject syllabuses for 2021 regulation.
For all Cyber Security results, visit Anna University Cyber Security all semester results direct link.