Recreational Mathematics

A journey through recreational mathematics covering number theory adventures (Fermat numbers, prime-generating formulas, Collatz conjecture), prime distribution and the Riemann hypothesis, proofs of irrationality, transcendental numbers, continued fractions, Ramanujan's nested radicals, Ramanujan's partition function, and Bhaskaracharya's Lilavati.

Advanced 8 chapters 24 lessons 3 hr 39 min
Start with lesson 1 Browse the course content
Recreational Mathematics

What you'll learn

  • Explore Fermat numbers, prime-generating formulas, and the Collatz conjecture
  • Understand the Riemann zeta function, prime distribution, and the Prime Number Theorem
  • Prove irrationality of key constants and explore transcendental number theory
  • Work with continued fractions, Pell's equation, and the Stern-Brocot tree
  • Study Ramanujan's nested radicals, partition function, and Bhaskaracharya's Lilavati

Instructor

Gaurav Tiwari

Gaurav Tiwari

WordPress developer and content strategist with 16+ years of experience building performance-driven solutions for 800+ clients. Creator of multiple WordPress plugins with 10,000+ active installs.

Course content

24 lessons across 8 chapters. Follow them in order or jump to the section you need.

Chapter 3

Proofs of Irrationality 3 lessons

Walk through classic and modern proofs that certain numbers like the square root of 2 and e are irrational.

  1. The Irrationality of Square Root of 211 min read
  2. The Irrationality of e and Pi9 min read
  3. Irrationality Measure and Liouville Numbers11 min read

Chapter 4

Transcendental Numbers 3 lessons

Discover numbers that are not roots of any polynomial equation, including pi and Liouville constant.

  1. Liouville and the First Transcendental Number9 min read
  2. e and Pi Are Transcendental10 min read
  3. Beyond e and Pi: Frontiers of Transcendence10 min read

Chapter 5

Continued Fractions 3 lessons

Represent real numbers as continued fractions and explore their connections to approximation theory.

  1. Euclid's Algorithm and Convergents8 min read
  2. Pell's Equation and Quadratic Irrationals10 min read
  3. Ramanujan, Ford Circles, and the Stern-Brocot Tree9 min read

Chapter 6

Ramanujan's Nested Radicals 3 lessons

Unravel Ramanujan elegant identities involving infinitely nested square roots and their closed-form values.

  1. Introduction to Nested Radicals7 min read
  2. Deriving Ramanujan's Formulas6 min read
  3. Nested Radicals and Continued Fractions7 min read

Chapter 7

Ramanujan's Partition Function 3 lessons

Study the partition function p(n), Ramanujan congruences, and the Hardy-Ramanujan asymptotic formula.

  1. Integer Partitions and Generating Functions7 min read
  2. Ramanujan's Partition Congruences8 min read
  3. The Circle Method and Exact Formulas12 min read