🧮 6-Week Roadmap to Math for Coding & Problem Solving

Hey there 👋

👋 Introduction

If you’ve been grinding LeetCode, Codeforces, or any kind of competitive programming, you probably noticed something sneaky:
👉 a lot of problems boil down to math.

Whether it’s GCD/LCM, modular arithmetic, prime numbers, or probability — math concepts show up everywhere. And the best part? You don’t need to be a “math genius” to use them. You just need the right toolkit and some practice.

That’s what this 6-week study plan is about. We’ll go step by step, learn the essentials, code them up in C++, and then apply them on real problems.

Each week is broken into daily blogs (Day 1, Day 2, …), so it’s bite-sized and fun. By the end of 6 weeks, you’ll feel way more confident when math sneaks into your coding interviews or contests.

🗓️ The Plan

Here’s what we’ll cover week by week:

Week 1: Number Theory Basics

GCD & LCM (the unsung heroes of many problems)
Modular arithmetic (mod, inverse, fast power)
Prime numbers, factorization, sieve of Eratosthenes
Applications in arrays, divisibility, and cycles

Week 2: Modular Math & Exponentiation

Modular exponentiation (fast power)
Modular inverses & Fermat’s little theorem
Extended Euclidean algorithm
Using modular math in coding challenges

Week 3: Combinatorics & Counting

Factorials & binomial coefficients
nCr and nPr (with modular math)
Inclusion-exclusion principle
Pigeonhole principle
Common LeetCode/Codeforces problems on counting

Week 4: Probability & Expectations

Probability basics for coding
Expected values
Randomized problems (hashing, rolling dice, etc.)
Classic problems from contests

Week 5: Advanced Number Theory Tools

Chinese Remainder Theorem
Euler’s Totient Function
Fast primality checks
Linear Diophantine equations

Week 6: Geometry & Miscellaneous Math Tricks

Basic computational geometry (lines, distances, orientation)
Vectors & dot product
Coordinate geometry in coding problems
Misc math tricks you see in CP (floor/ceil, logarithms, etc.)

Week 1 🔢 Number Theory Basics	Week 2 ✨ Modular Math & Powers	Week 3 🧮 Combinatorics
Day 1: GCD & LCM	Day 1: Fast exponentiation	Day 1: nCr basics
Day 2: Euclidean Algorithm	Day 2: Modular multiplication	Day 2: Pascal’s Triangle
Day 3: LCM applications	Day 3: Modular inverse	Day 3: nCr mod prime
Day 4: Sieve of Eratosthenes	Day 4: Fermat & Euler	Day 4: Inclusion-Exclusion
Day 5: Prime factorization	Day 5: Matrix exponentiation	Day 5: Counting problems

Week 4 🎲 Probability & Expectations	Week 5 🧩 Advanced Number Theory	Week 6 📐 Geometry & Misc
Day 1: Basic probability	Day 1: Chinese Remainder Theorem	Day 1: Dot product
Day 2: Expected value	Day 2: Euler’s Totient	Day 2: Cross product
Day 3: Probability in counting	Day 3: Extended Euclidean	Day 3: Convex hull
Day 4: Randomized algorithms	Day 4: Diophantine equations	Day 4: Bit manipulation tricks
Day 5: Mixed problems	Day 5: Primality testing	Day 5: Contest problems

🔑 Legend:

🔢 Number Theory
✨ Modular Arithmetic
🧮 Combinatorics
🎲 Probability
🧩 Advanced Number Theory
📐 Geometry & Misc

💡 How We’ll Learn

Concept First – A casual explanation with examples & intuition.
Visual/Mindmap – Sometimes an ASCII diagram or simple visualization.
Code in C++ – Short snippets to see the concept in action.
Practice Problems – Links to LeetCode, Codeforces, or AtCoder.
External References – Best articles/videos if you want to go deeper.

🎯 End Goal

By the end of 6 weeks, you’ll:

Know the core math concepts that show up in 90% of coding problems.
Have reusable C++ templates/snippets for math-heavy problems.
Feel confident applying math without overthinking it.

📌 Each daily blog will be linked here once it’s published. So think of this as the master roadmap.

Ready? Let’s dive in → Week 1, Day 1: GCD & LCM