M463: Finite  Fields
Syllabus:
• Structure of finite fields: characterization, roots of irreducible polynomials,traces, norms and bases, roots of unity, cyclotomic polynomial, representation of elements of finite fields, Wedderburn’s theorem;
• Polynomials over finite field: order of polynomials, primitive polynomials, construction of irreducible polynomials, binomials and trinomials, factorization of polynomials over small and large finite fields, calculation of roots of polynomials;
• Factorization of polynomials
• Equations over Finite Fields
• Exponential Sums
• Linear recurring sequences
• Applications of Finite fields
References:
• Finite Fields,  R. Lidl and H. Niederreiter, Cambridge  University Press
• Finite Fields and applications, G. L. Mullen and C. Mummert, AMS MASS
Lectures:
• Monday [T] (16.30--17.30)
• Tuesday (15.30--16.30)
• Wednesday (14.30--15.30)
• Thursday (16.30--17.30)
Assignment:
• Assignment 1
• Assignment 2
• Assignment 3
• Assignment 4
• Assignment 5
• Assignment 6
Quiz:
• Quiz 1
• Quiz 2
• Quiz 3
Examination:
• Mid- Semester
• End- Semester

There will be three quizzes carrying 10 marks each,  a mid-semester examination of 30 marks and one final end-Semester exam of 40 marks (Total 100). The final grading will be done based on the performance in the quizzes, mid-semester and end-semester examination.  Suppose the total marks obtained by a  student is x out of 100.  Then the grading will be as follows:
• 0<=x< 30---FR
• 30<=x<40---DD
• 40<=x<50---CD
• 50<=x<60---CC
• 60<=x<70---BC
• 70<=x<80---BB
• 80<=x<90---AB
• 90<=x<=100---AA
Keys to Success:
Attend all the lectures and tutorials,  Do the homeworks, ask questions. Talk to me if you have any problem.

 Good Luck...