Advanced Knowledge Problem of the Week 3-1-18: An Improper Integral [Complex Analysis]

Check out this Advanced Knowledge Problem of the Week.
Be sure to let us know how you solved it in the comments below or on social media!

Solution below.

Equations of Math: Null Curl [Vector Calculus]

Problem of the Week 2-27-18: Minimizing a Number [Inequalities]

Check out this Problem of the Week.
Be sure to let us know how you solved it in the comments below or on social media!

Solution below.

Advanced Knowledge Problem of the Week 2-22-18: Inner Automorphisms [Group Theory]

Check out this Advanced Knowledge Problem of the Week.
Be sure to let us know how you solved it in the comments below or on social media!

Solution below.

Combinatoric Identities

Here are a couple neat combinatorial identities.

Problem of the Week 2-20-18: Set Painting [Set Theory]

Check out this Problem of the Week.
Be sure to let us know how you solved it in the comments below or on social media!

Solution below.

Advanced Knowledge Problem of the Week 2-15-18: Modular Arithmetic and Factorials [Number Theory]

Check out this Advanced Knowledge Problem of the Week.
Be sure to let us know how you solved it in the comments below or on social media!

Solution below.

Valentine's Day Theorem

Here is a neat little theorem referred to as the "Happy ending problem" by Paul Erdős, due to it resulting in the marriage of two mathematicians. Happy Valentines Day!

Problem of the Week 2-13-18: Polynomial Root Averages [Polynomials]

Check out this Problem of the Week.
Be sure to let us know how you solved it in the comments below or on social media!

Solution below.

Generating Functions

Here are some neat generating functions for different notable sequences of numbers.

Advanced Knowledge Problem of the Week 2-8-18: Nilpotent Elements [Abstract Algebra]

Check out this Advanced Knowledge Problem of the Week.
Be sure to let us know how you solved it in the comments below or on social media!

Solution below.

Problem of the Week 2-6-18: Powers of Five [Number Theory]

Check out this Problem of the Week.
Be sure to let us know how you solved it in the comments below or on social media!

Solution below.