Number Theory 1 Teaching Schedule

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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