To make students competent in proving and applying the theory of congruence in establishing different theorems of Fermat, Wilson and little theorem. To enhance the skills of applying Euler’s generalization to find quadratic reciprocity. To make students competent in applying theorem of perfect number to establish Fermat theorem, Pythagorean triples and Fibonacci number in continued fraction. Specific Objectives and Contents Specific Objectives Content Prove the validity of Unit 1: Review on mathematical preliminaries statements consideration of number theory (4) by Induction. Test Pascal’s induction rules Binomial Sketch the theorem development Early number of number theory theory in earlier day. Compute gcd by Euclidean algorithm. Unit II: Divisibility Solve the Theory (10) Euclidean Diophantine algorithm equation Diophantine with integral equation ax+by=c solution. Fundamental the theorem of fundamental arithmetic theorem of Goldbach’s arithmetic conjecture Verify the Goldbach’s Conjecture. Prove the Unit III: Theory of properties of Congruence and its congruence. Application Validate and (12) apply famous Properties of conjectures congruence in number Linear theory. congruence Prove Fermat’s different theorem theorems Little theorem based on the Wilson’s theory of theorem congruence. Identify the Unit IV: Euler’s phi-function. Generalization and its
To make students competent in proving and applying the theory of congruence in establishing different theorems of Fermat, Wilson and little theorem. To enhance the skills of applying Euler’s generalization to find quadratic reciprocity. To make students competent in applying theorem of perfect number to establish Fermat theorem, Pythagorean triples and Fibonacci number in continued fraction. Specific Objectives and Contents Specific Objectives Content Prove the validity of mathematical statements by Induction. Test Pascal’s rules Sketch the development of number theory in earlier day. Unit 1: Review on preliminaries consideration of number theory (4) induction Binomial theorem Early number theory Compute gcd by Euclidean algorithm. Solve the Diophantine equation with integral solution. the fundamental theorem of arithmetic Verify the Goldbach’s Conjecture. Unit II: Divisibility Theory (10) Euclidean algorithm Diophantine equation ax+by=c Fundamental theorem of arithmetic Goldbach’s conjecture Prove the properties of congruence. Validate and apply famous conjectures in number theory. Prove different theorems based on the theory of congruence. Unit III: Theory of Congruence and its Application (12) Properties of congruence Linear congruence Fermat’s theorem Little theorem Wilson’s theorem Identify the phi-function. Unit IV: Euler’s Generalization and its
BICT-2nd-Semester-final.docx