Algebra and Number Theory detail syllabus for Information Technology (It), 2017 regulation is taken from Anna University official website and presented for students of Anna University. The details of the course are: course code (MA8551), Category (BS), Contact Periods/week (4), Teaching hours/week (4), Practical Hours/week (0). The total course credits are given in combined syllabus.
For all other it 5th sem syllabus for be 2017 regulation anna univ you can visit It 5th Sem syllabus for BE 2017 regulation Anna Univ Subjects. The detail syllabus for algebra and number theory is as follows.”
Course Objective:
- To introduce the basic notions of groups, rings, fields which will then be used to solve related problems.
- To introduce and apply the concepts of rings, finite fields and polynomials.
- To understand the basic concepts in number theory
- To examine the key questions in the Theory of Numbers.
- To give an integrated approach to number theory and abstract algebra, and provide a firm basis for further reading and study in the subject.
Unit I
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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
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Unit V
Classical Theorems and Multiplicative Functions
Wilsons theorem – Fermats little theorem – Eulers theorem – Eulers Phi functions – Tau and Sigma functions.
Course Outcome:
Upon successful completion of the course, students should be able to:
- Apply the basic notions of groups, rings, fields which will then be used to solve related problems.
- 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.
- Demonstrate their mastery by solving non – trivial problems related to the concepts, and by proving simple theorems about the, statements proven by the text.
- Apply integrated approach to number theory and abstract algebra, and provide a firm basis for further reading and study in the subject.
Text Books:
- Grimaldi, R.P and Ramana, B.V., “Discrete and Combinatorial Mathematics”, Pearson Education, 5th Edition, New Delhi, 2007.
- Koshy, T., Elementary Number Theory with Applications, Elsevier Publications, New Delhi, 2002.
References:
- Lidl, R. and Pitz, G, “Applied Abstract Algebra”, Springer Verlag, New Delhi, 2nd Edition, 2006.
- Niven, I., Zuckerman.H.S., and Montgomery, H.L., An Introduction to Theory of Numbers, John Wiley and Sons , Singapore, 2004.
- San Ling and Chaoping Xing, Coding Theory – A first Course, Cambridge Publications, Cambridge, 2004.
For detail syllabus of all other subjects of BE It, 2017 regulation do visit It 5th Sem syllabus for 2017 Regulation.
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