Michael Penn

the why of the determinant

a very special knights tour

the strangeness of transfinite arithmetic

generalizing the Gaussian Integral

a great proof of my favorite identity

on the prime counting function

The exact solution to any quintic equation

Have you seen this definition of Euler's number??

trigonometry like you have never seen it!

on the "product" of all natural numbers.

You can divide by zero.

Math's most viral equation

Putnam Exam | 2018: A1

Putnam Exam | 1995:B4

An awesome Putnam problem with a number theory twist!

Putnam Exam | 2010: A2

Putnam Exam 2004 | B5

Abstract Algebra | Subgroups and quotient groups of the quaternions.

why there is no four dimensional cross product.

Abstract Algebra | Units and zero divisors of a ring.

Fibonacci squares are rare!

An example of classic Japanese geometry -- Sangaku

Abstract Algebra | The third isomorphism theorem for groups.

Abstract Algebra | First Isomorphism Theorem for Groups

Abstract Algebra | The Second Isomorphism Theorem for Groups

a nice factorial equation.

Number Theory | Rational Points on the Unit Circle

a math problem from the most famous computer programming book??

Abstract Algebra | The inner automorphisms of a group.

A cruel limit for a beginning calculus class

On means of binomial coefficients.

there is always a trick with cubic polynomials...

Number Theory | Primitive Pythagorean Triples

I’m not anti-Goldbach but this conjecture is

The SPICIEST math challenge!

Abstract Algebra | Cosets of a subgroup.

Abstract Algebra | Direct product of groups.

Abstract Algebra | The division algorithm for polynomials.

Eulers universal formula for continued fractions.

a continued fraction for pi

a continued fraction for pi

DIFFERENTIATING a CONTINUED FRACTION?!

the REAL second derivative test

Real Analysis | The Mean Value Theorem

Solving a friendly algebra problem.

A nice algebra problem.

an absurd approach to a simple mathematics problem

Writing Proofs | Principle of Mathematical Induction Example 1

proving the power rule for any exponent!!

The unreasonable effectiveness of linear algebra.

How to multiply matrices of ANY size -- the Kronecker product.

Real Analysis | Riemann Integrability

Integrate to make trig identities.

know this classic group theory exercise.

Real Analysis | The Supremum and Completeness of ℝ

a matrix inverse homework problem

Real Analysis | Introduction to differentiability.

Multivariable Calculus | Differentiability

The number theory you need to learn abstract algebra.

Geometry and Number Theory from Norway!

Evaluate an infinite series

Primes and Composites -- Number Theory 6