Number theory is the study of the integers. Why anyone would want to study the integers is not immediately obvious. First of all, what’s to know? There’s 0, there’s 1, 2, 3 and so on, and there’s the negatives. Which one don’t you understand? After all, the mathematician G. H. Hardy wrote: "[Number theorists] may be justified in rejoicing that there is one science, at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean". What most concerned Hardy was that number theory not be used in warfare; he was a pacifist.Good for him, but if number theory is remote from all human activity, then why study it? We’ll
come back to that question later on...

Contents (27 pages)
1 Divisibility
2 Die Hard
3 The Greatest Common Divisor
4 The Fundamental Theorem of Arithmetic
5 Alan Turing
6 Turing’s Code
7 Modular Arithmetic
8 Turing’s Code (Version 2.0)
9 Turing Postscript
10 Arithmetic with an Arbitrary Modulus

Contents: (66 pages)
Chapter 1. Basic Number Theory
1. The natural numbers
2. The integers
3. The Euclidean Algorithm and the method of back-substitution
4. The tabular method
5. Congruences
6. Primes and factorization
7. Congruences modulo a prime
8. Finite continued fractions
9. Infinite continued fractions
10. Diophantine equations
11. Pell's equation
Problem Set 1
Chapter 2. Groups and group actions
1. Groups
2. Permutation groups
3. The sign of a permutation
4. The cycle type of a permutation
5. Symmetry groups 33
6. Subgroups and Lagrange's Theorem
7. Group actions
Problem Set 2
Chapter 3. Arithmetic functions
1. Definition and examples of arithmetic functions
2. Convolution and Mobius Inversion
Problem Set 3
Chapter 4. Finite and infinite sets, cardinality and countability
1. Finite sets and cardinality
2. Infinite sets
3. Countable sets
4. Power sets and their cardinality
5. The real numbers are uncountable
Problem Set 4
Index

Contents: (200 pages)
1 Lecture-wise break up
2 Divisibility and the Euclidean Algorithm
3 Fibonacci Numbers
4 Continued Fractions
5 Simple Infinite Continued Fraction
6 Rational Approximation of Irrationals
7 Quadratic Irrational(Periodic Continued Fraction)
8 Primes and ther Infinitude
9 Tchebychev's Theorem
10 Linear congruences, Chinese Remainder Theorem and Fermat's Little Theorem
11 Euler's function, Generalisation of FLT, CRT
12 Congrunces of Higher Degree
13 Lagrange's Theorem
14 Primitive Roots and Euler's Criterion
15 Quadratic Reciprocity
16 Applications of Quadratic Reciprocity
17 The Jacobi Symbol
18 Elementary Algebraic Concepts
19 Sylow's Theorem
20 Finite Abelian Groups & Dirichlet Characters
21 Dirichlet Products
22 Primes are in P
II Examples