Recreational Mathematics

Advanced 8 chapters 24 lessons 3 hr 39 min

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.

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

Number Theory Adventures 3 lessons

Explore divisibility, modular arithmetic, and the surprising properties of integers through engaging problems.

  1. Fermat Numbers: Prime Generators That Fooled a Genius 8 min read Free
  2. Prime-Generating Formulas: Euler, Heegner, and the Ulam Spiral 8 min read
  3. The Collatz Conjecture: Simple Rules, Infinite Mystery 9 min read

The Distribution of Primes 3 lessons

Study how prime numbers are distributed among the integers, from the Prime Number Theorem to open conjectures.

  1. Counting Primes: From Eratosthenes to Chebyshev 10 min read
  2. The Riemann Zeta Function: From Euler Products to the Critical Strip 9 min read
  3. The Prime Number Theorem and Open Frontiers 9 min read

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 2 11 min read
  2. The Irrationality of e and Pi 9 min read
  3. Irrationality Measure and Liouville Numbers 11 min read

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 Number 9 min read
  2. e and Pi Are Transcendental 10 min read
  3. Beyond e and Pi: Frontiers of Transcendence 10 min read

Continued Fractions 3 lessons

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

  1. Euclid's Algorithm and Convergents 8 min read
  2. Pell's Equation and Quadratic Irrationals 10 min read
  3. Ramanujan, Ford Circles, and the Stern-Brocot Tree 9 min read

Ramanujan's Nested Radicals 3 lessons

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

  1. Introduction to Nested Radicals 7 min read
  2. Deriving Ramanujan's Formulas 6 min read
  3. Nested Radicals and Continued Fractions 7 min read

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 Functions 7 min read
  2. Ramanujan's Partition Congruences 8 min read
  3. The Circle Method and Exact Formulas 12 min read

Bhaskaracharya's Lilavati 3 lessons

Solve recreational arithmetic and geometry puzzles from the 12th-century Sanskrit classic Lilavati.

  1. Arithmetic and Word Problems from Bhaskara's Lilavati 12 min read
  2. Algebra and Combinatorics in the Lilavati 8 min read
  3. Geometry and the Chakravala Method 10 min read