Basics
Goldman Sachs loses profit after hits from GreenSky, real estate
Second-quarter profit fell 58% to $1.22 billion, or $3.08 a share, due to steep declines in trading and investment banking and losses related to...
Fundamental Counting Principle
We will introduce the fundamental counting principle with an example. This counting principle is all about choices we might make given many possibilities.
Multiplication principle
Suppose...
A generalized Cauchy-Schwarz inequality via the Gibbs variational formula
Let be a non-empty finite set. If is a random variable taking values in , the Shannon entropy of ...
The Battlestar Galactica Theory of Math Education – Math with Bad Drawings
Last month, as I read Christopher J. Phillips’ brief and engrossing The New Math: A Political History, I found myself reciting the ominous line...
How to Multiply 3-digit Numbers Having a Zero in the Tens Place
Use this trick to multiply 3-digit numbers having a zero in the tens place in 5 seconds or less.
A 3-digit number is any number...
Notes on the B+B+t theorem
A recent paper of Kra, Moreira, Richter, and Robertson established the following theorem, resolving a question of Erdös. Given a discrete amenable group...
Quotable Mathematics – Math with Bad Drawings
This summer, at MathFest 2024 in Indianapolis, I will be leading a session that combines my three passions:
Quotations
Mathematics
Leading sessions
“Okay, Ben,” you say. “The second...
What are Parallel Lines in Geometry? | Two Parallel Lines
In parallel lines when two lines do not intersect each other at any point even if they are extended to infinity.
What are parallel lines...
How to Solve a System of two Linear Equations Quickly
Solve a system of two linear equations quickly using this trick. It works 100% of the time and you waste no time, especially if...