Algebra and Number Theory detailed syllabus for Mechanical Engineering Sandwich (Mech Sandwich) for 2021 regulation curriculum has been taken from the Anna Universities official website and presented for the Mech Sandwich 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 Mechanical Engineering Sandwich 9th Sem scheme and its subjects, do visit Mech Sandwich 9th Sem 2021 regulation scheme. For Open Elective-III scheme and its subjects refer to Mech Sandwich 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.
For detailed syllabus of all the other subjects of Mechanical Engineering Sandwich 9th Sem, visit Mech Sandwich 9th Sem subject syllabuses for 2021 regulation.
For all Mechanical Engineering Sandwich results, visit Anna University Mech Sandwich all semester results direct link.