### BASIC LOGIC AND NUMBER THEORY

Logic, the study of principles of techniques and reasoning, is fundamental to every branch of learning. The first module discusses the fundamentals of logic, its symbols and rules. This enables one to think systematically, to express ideas in precise and concise mathematical terms and also to make valid arguments. How to use logic to arrive at the correct conclusion in the midst of confusing and contradictory statements is also illustrated. The classical number theory is introduced and some of the very fundamental results are discussed in other modules. Successful completion of the course enables students to

• Prove results involving divisibility, greatest common divisor, least common multiple and a few applications.

•  Understand the theory and method of solutions of LDE.

•  Understand the theory of congruence and a few applications.

•  Solve linear congruent equations.

• Learn three classical theorems viz. Wilson’s theorem, Fermat’s little theorem and Euler’s theorem and a few important consequences.