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

- Finite Fields, R. Lidl and H. Niederreiter, Cambridge University Press

- Finite Fields and applications, G. L. Mullen and C. Mummert, AMS MASS

- Monday [T] (16.30--17.30)
- Tuesday (15.30--16.30)
- Wednesday (14.30--15.30)

- Thursday (16.30--17.30)

- Assignment 1
- Assignment 2
- Assignment 3
- Assignment 4
- Assignment 5
- Assignment 6

- Quiz 1
- Quiz 2
- Quiz 3

- 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

Attend all the lectures and tutorials, Do the homeworks, ask questions. Talk to me if you have any problem.

Good Luck... |