Problem of the Week 12-26-17: License Plate [Probability]

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Math History Youtube Mini-Series: The History of Greek Mathematics

Mathematics has long been a unifying element across cultures around the globe. Beginning first as a tool used for counting and practical problems, Mathematics eventually came to be an intellectual interest producing theories and ideas that described the world. As one of the most pursued sciences, Math has built off itself creating new ideas on the backs of old ones. The study of Math history attempts to document and understand this path that Mathematics has taken from antiquity to now. Below you may watch this new mini-series on Math History which focuses on the breakthroughs made in the early years of Mathematics in Greece.


This series is meant to be a short introduction to Math History and as such covers only part of the Mathematical discoveries of one culture. Greek mathematicians as a whole did much to learn from and expand upon the knowledge established by the civilizations before it. Yet, within this series we have left out many Mathematicians that were instrumental in the development of Greek Mathematics in favor of focusing on three of the most well know Greek mathematicians: Pythagoras, Euclid, and Archimedes. This series in chronological order covers the beginning of Mathematics in Greece and the Greek numeral system, Pythagoras and his followers, Euclid and the Elements,  and Archimedes and the Method of Exhaustion.

If you are interested in this series and would like to learn more about Math History as a field or the cultures we did not cover in this series, there is a short list at the end of this post with resources and texts to look into. We also have another blog post with a short three part guide on the History of Babylonian Mathematics that you may read through. The history of Mathematics is populated with numerous individuals and ideas who helped to shape modern Mathematics today, and they are just as important as the ones we choose to include in this mini-series. Egyptian, Babylonian, Chinese, Roman, Islamic and countless other cultures contributed to the overall growth of Mathematical knowledge.

We hope you enjoy this mini-series on the History of Greek Mathematics!

Math History Guide: The History of Babylonian Mathematics

Mathematics has long been a unifying element across cultures around the globe. Beginning first as a tool used for counting and practical problems, Mathematics eventually came to be an intellectual interest producing theories and ideas that described the world. As one of the most pursued sciences, Math has built off itself creating new ideas on the backs of old ones. The study of Math history attempts to document and understand the path that Mathematics has taken from antiquity to now. Below you may read our guide series on the History of Babylonian Mathematics in three parts.

These documents are meant to be a quick introduction to some of the themes and ideas from one of the early civilizations of Math History. Within this series we have left out minor discoveries or examples in preference for ideas that are important in the context of modern Mathematics. Babylonian Mathematics was essential in helping to spread ideas that led to the further development of Math in later civilizations. This series is separated into three parts, the Babylonian writing system and its modern translation, general arithmetic problems and how they were solved, and mathematical results relating to modern day notions.

If you are interested in this series and would like to learn more about Math History as a field or the cultures we did not cover in this series, there is a short list at the end of this post with resources and texts to look into. We also have another blog post introducing our YouTube mini-series on the History of Greek Mathematics that you may watch. The history of Mathematics is populated with numerous individuals and ideas who helped to shape modern Mathematics today, and they are just as important as the ones we choose to include in this short guide. Egyptian, Greek, Chinese, Roman, Islamic and countless other cultures contributed to the overall growth of Mathematical knowledge.

We hope you enjoy this short guide on the History of Babylonian Mathematics!

Problem of the Week 12-19-17: Find a Function [Differential Equations]

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Problem of the Week 12-12-17: Vectors [Linear Algebra]

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Problem of the Week 12-5-17: Integration by Substitution [Calculus]

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Think Thursday 11-30-17: Nine Digit Number [Algebra]

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Problem of the Week 11-28-17: A Form of a+bi [Complex Algebra]

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Think Thursday 11-23-17: Thanksgiving Edition

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Problem of the Week 11-21-17: Partial Fractions [Calculus]

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Think Thursday: Committee [Algebra]

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Problem of the Week 11-14-17: Tossing a Coin [Probability]

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Think Thursday 11-9-17: Change [Logic]

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Problem of the Week 11-7-17: Span of Subspace [Linear Algebra]

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Think Thursday 11-2-17: Multiples [Discrete]

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Problem of the Week 10-31-17: Halloween Spooky Scare

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Think Thursday 10-26-17: Number of Students [Discrete Math]

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Problem of the Week 10-24-17: Rolling Dice [Probability]

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Think Thursday 10-19-17: Chessboard and Dominoes

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Problem of the Week 10-17-17: Positive Integer Triple

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Think Thursday 10-12-17: Rays through Squares

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Problem of the Week 10-10-17: Marking the Grid [Configurations]

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Think Thursday 10-5-17: Cheryl's Birthday [Deductive Reasoning]

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Problem of the Week 10-3-17: Folding a Piece of Paper [Geometry]

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Think Thursday 9-27-17: Bridge Crossing [Logic]

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This problem was originally posted by MAA online.

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Problem of the Week 9-26-17: Choosing balls from Urns [Probability]

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Think Thursday 9-21-17: Twelve Coins

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Problem of the Week 9-19-17: Four Digit Numbers

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Think Thursday 9-14-17: Tiling with Dominoes

Welcome to our first Think Thursday Problem!

This series aims to introduce logic based problems, puzzles, and other tricky brain teasers. The problems featured here are Math related, but do not require a extensive knowledge of Mathematics to solve. We hope you enjoy this new series!

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Solution below.

Problem of the Week 9/12/1: Variables [Algebra]

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Why did the variable break up with the constant?

Because the constant was incapable of change.

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Solution below.

Episode 10: Prime Number Theorem [#MathChops]

          This episode of #MathChops focuses on prime numbers and their theorem. The prime number theorem describes the distribution of prime numbers becomes much more sparse and numbers get bigger. This theorem helps us quantify how many prime numbers there are less than a specific number n. The proof itself for this theorem is quite extensive, but it is still fascinating to learn about. Watch our video below to learn more about the prime number theorem.

Problem of the Week 9-5-17: Find P(0) [Algebra]

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Episode 9: The Limit Definition of e [#MathChops]

The history of ‘e’ is a tangled one, one which would warrant an entire dedicated book to parse through mathematics to the original conception of the transcendental number. Even before e’s enigmatic beauty was fully unearthed, people using mathematics to solve real world problems encountered the number many times, and understood it enough to work it into their solutions. A good example of this is when e shows up in compound interest. Bankers found out that as the number of times one took annual compound interest grew to infinity, the rate of growth approached e! Watch the video to see two mathematical proofs of our statement, using two definitions of e.

Advanced Knowledge Problem of the Week: Drunkard's Walk [Probability]

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Problem of the Week 8-29-17: Pool Table

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Advanced Knowledge Problem of the Week: Finding a Perfect Square Solution [Algebra]

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Back to School Math Courses Review Guide

 Oh no, back to school is right around the corner!

We know it can be hard to jump straight back into Math classes during the first few days after a summer away. Lucky for you we have arranged some of of our Youtube channel videos into a helpful guide to make sure you are on your game in the first week of class. Check them out below!

Problem of the Week 8-21-17: Seven Pointed Star [Geometry]

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Episode 8: Infinite Primes [#MathChops]

Back in 300 BC, Euclid proved that there were an infinite number of primes. He used line segments to show that some line lengths could only be made up from single-unit line lengths and not lines with lengths of 2, 3, etc. These line lengths represented prime numbers. This proof has the same principle but is a little different than Euclid's and uses proof by contradiction. Take a look at this simple proof which shows that primes are infinite!

Advanced Knowledge Problem of the Week: Infinite Product of a Sequence [Convergence]

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Problem of the Week 8-15-17 [Algebra]

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Advanced Knowledge Problem of the Week: Website Traffic as a Poisson Process [Stochastic Processes]

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Problem of the Week 8-8-17 [Distance]

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Episode 7: Gauss and Triangular Numbers [#MathChops]

The mythology behind this fairly simple proof is what makes it one of the most popular proofs in math classes across the world. The story follows a young Carl Friedrich Gauss, whose first grade teacher asked the class to add up the numbers 1 to 100 in order to pass a good amount of time. Before the teacher had time to start grading papers, Gauss handed in his assignment. Watch the video to find out Gauss’ observation that is now one of the most famous math proofs out there.

Advanced Knowledge Problem of the Week: Is the vector in the span? [Linear Algebra]

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Problem of the Week 7/25/17 Math inspired Alphametic [puzzle]

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The two basic rules for solving alphametics are as follows:
Each letter must be represented by a different digit. If the letter is used more than once, it must be represented by the same digit.
Once you substitute digits for all your letters, you must end up with an accurate addition problem.

Solution below.

Episode 6: Area of a Circle [#MathChops]

This problem of determining the area of a circle, or better defined as the area inside of a circle, was a huge dilemma in the field of mathematics. It was not until the mid 200's BC when Archimedes began to anticipate modern calculus and analysis though concepts of infinitesimals and exhaustion, which he used to solve this major challenge of finding the area of a circle.

Archimedes' method of finding the area is described as "squaring the circle", which is trying to find the square that has the same enclosed area as a circle of a given radius. Using this and also using a method where he approximated the area of a circle with other, known shapes such as squares and hexagons, Archimedes was able to determine the area inside of a circle. Take a look at the proof to see how Archimedes came up with the formula we know today:

Advanced Knowledge Problem of the Week: Game of Thrones Committee [Combinatorics]

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Problem of the week 7/18/17 [geometry]

Check out this Problem of the week about Geometry and triangles within a circle. If you're interested in learning more about how you draw circles and what it says about your cultural background, read this article: 

How do you draw a circle? We analyzed 100,000 drawings to show how culture shapes our instincts

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Solution below.