This document is useful for current students. It contains teaching schedule for Number Theory 1.

## Overview:

Number Theory 1 is an introductory module. It is useful for beginner math olympiad aspirants (preparing for AMC, AIME, ARML, Duke Math Meet etc.)

- Number systems
- Prime numbers
- Arithmetic and geometric sequences
- Mathematical Induction
- Divisibility techniques
- Arithmetic of remainders
- Modular Arithmetic and Gauss’s theory
- Equivalence Relations
- Mathematical games

## Specifications

- Each session (day) is 2 hours long.
- It is followed by a homework assignment.
- Apart from regular theoretical work and problem-solving, each section consists of mathematical games
**Books:**- Challenges and Thrills of Pre-College Mathematics
- Mathematics can be Fun by Yakov Perelman
- Excursion Into Mathematics
- Mathematical Circles, Russian Experience by Fomin

## Sessions

### Session 1

- Formula for nth odd number and nth even number
- Sum of first n odd numbers and their visual treatment
- Arithmetic Progression

### Session 2 and 3

- Arithmetic Progression’s description (nth number)
- Gauss’s method for summing arithmetic progression (rewriting a finite sum in reverse order).
- Sum of n terms of an arithmetic sequence
- Geometric sequence
- Sum of nth term of a geometric sequence

### Session 4 and 5

- Mathematical induction
- Strong form of induction

### Session 6 and 7

- Divisibility and prime numbers
- Fundamental Theorem of Arithmetic

### Session 8

- Types of numbers
- Well ordering principles
- Irrationality of square root of 2 (and primes)

### Session 9 and 10

- Modular Arithmetic – similarity and differences with equality
- Notion of equivalence relation

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