# Camp Lambda: Number Theory

At Camp Lambda, students will explore mathematical ideas focused on Number Theory.

## Overview

They will be exposed to a wide range of new mathematical knowledge and a deeper level of understanding in a collaborative environment. The curriculum is designed to include problems from various prestigious national and international math contests. The students will attend lectures, learn problem solving techniques, and work creatively and enthusiastically to tackle challenging problems.

**Dates: June 8 - June 12 [1 week].**

## Concepts

- Level 1 :
- Properties of Arithmetic
- Primes
- Fractions
- Parity and Divisibility
- Multiples and Divisors
- Counting Factors
- LCM and GCF
- Level 2 :
- GCF, LCM and their Applications
- Problem Solving Using Number Theory
- Multiples, Divisors and Remainders
- Factorials and Terminal Zeros
- Unit Digits
- Counting Factors
- Level 3 :
- Review of Level 2 Concepts
- Problem Solving using Counting Factors, Sum and Product of Factors
- Base Arithmetic
- Introduction to Modular Arithmetic
- Level 4 :
- Base Arithmetic
- Problems using Bases, Modular Arithmetic and Linear Congruences
- Euler’s totient function (The Phi function), Wilson's Theorem, Fermat's Theorem, Chinese Remainder Theorem
- Introduction to Diophantine Equations
- Level 5 :
- Solve difficult problems using Level 4 concepts
- Discussions of various techniques uses to prove Diophantine equations
- Proofs of Number theory problems - Residue classes, quadratic reciprocity, Fermat’s little theorem, Euler’s theorem, primitive roots, Lifting the Exponent (LTE)

### Notes

- Campers will be grouped based on assessments into five different levels before the start of the camp and may be moved from one to the other based on their progress during the camp.
- The concepts will be covered at different depth based on the student's comfort level.

## Fees

- $600 for full day session
- $400 for half day session (1st half - Number Theory)
- $400 for half day session (2nd half - Contest Preparation)

### Discount Policy

- The discounts are only applicable in the tuition fee for regular classes and accelerator program (practice sessions) till December 2020
- 10% discount in monthly tuition fee & accelerator program
- Discount starts on 1st of the month after receipt of full payment (e.g. full payment received on February 15, discount starts on March 1st
- Discount ends in the month of December 2020

### Refund Policy

- 80% of camp fee paid (discounts provided would also be deducted)