Neologic Math School

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  • Home
  • 2025 Courses
    • Introductory Courses
    • AMC 10 Training
    • AIME Algebra/Precalculus
    • Number Theory & Counting
    • Advanced Geometry
    • AIME Prep (Short term)
  • Sign Up/ Register
  • Blogs
  • Contact Us
  • FAQ
  • More
    • Home
    • 2025 Courses
      • Introductory Courses
      • AMC 10 Training
      • AIME Algebra/Precalculus
      • Number Theory & Counting
      • Advanced Geometry
      • AIME Prep (Short term)
    • Sign Up/ Register
    • Blogs
    • Contact Us
    • FAQ

Neologic Math School

Neologic Math SchoolNeologic Math SchoolNeologic Math School
  • Home
  • 2025 Courses
    • Introductory Courses
    • AMC 10 Training
    • AIME Algebra/Precalculus
    • Number Theory & Counting
    • Advanced Geometry
    • AIME Prep (Short term)
  • Sign Up/ Register
  • Blogs
  • Contact Us
  • FAQ

Number Theory & Counting (AIME)

Course Format

  • All courses are online, live via Zoom. 
  • Each week 2 hours of lectures  

Prerequisite

  • Students who have finished AMC 10 training.
  • AIME qualifier

Course Material

  • Lecture Notes
  • Elementary Number Theory by David Burton
  • AOPS Intermediate Counting & Probability
  • Introductory Combinatorics by Richard Brualdi

Difficulty Level

  • AIME level primarily
  • We will study many methods of solving introductory proof problems
  • If you are already capable of solving MO problems, then you are overqualified.

Goal

To improve AIME score, and to be able to solve some problems at the JMO level.

Meeting Time for Number Theory (Starting Feb 2025)

  • Class Time: Wednesday Eastern time 7:30 PM - 9:30 PM 

Meeting Time for Counting (Fall 2025)

  • Class Time: to be determined 

Syllabus

Number Theory

Discrete Math and Combinatorics

Discrete Math and Combinatorics

Divisors and Multiples

Prime Numbers

Modular Congruence

Wilson and Fermat's theorems

Euler's Theorem

Binomial Coefficients

Order, Primitive Roots and LTE

Quadratic Congruence

Polynomial Congruence Introduction

Fibonacci Numbers

Floor Functions


Discrete Math and Combinatorics

Discrete Math and Combinatorics

Discrete Math and Combinatorics

Mathematical Induction

Parity

Inclusion Exclusion Principle

State Diagrams

Combinatorial Identities

Recursive Sequences

Counting with Recursions

Generating Functions

Burnside's Lemma

Mobius Inversion

Miscellaneous Case Studies


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