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Thursday, November 16, 2017

Think Thursday: Committee [Algebra]

Check out this logic based Think Thursday Problem!
Be sure to let us know how you solved it in the comments below or on social media!


Solution below.

Tuesday, November 14, 2017

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

Check out this Problem of the Week.
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Solution below.

Thursday, November 9, 2017

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

Check out this logic based Think Thursday Problem!
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Solution below.

Tuesday, November 7, 2017

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

Check out this Problem of the Week.
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Solution below.

Thursday, November 2, 2017

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

Check out this logic based Think Thursday Problem!
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Solution below.

Tuesday, October 31, 2017

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

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Solution below.

Thursday, October 26, 2017

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

Check out this logic based Think Thursday Problem!
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Solution below.

Tuesday, October 24, 2017

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

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Solution below.

Thursday, October 19, 2017

Think Thursday 10-19-17: Chessboard and Dominoes

Check out this logic based Think Thursday Problem!
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Solution below.

Tuesday, October 17, 2017

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

Check out this Problem of the Week.
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Solution below.

Thursday, October 12, 2017

Think Thursday 10-12-17: Rays through Squares

Check out this logic based Think Thursday Problem!
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Solution below.

Tuesday, October 10, 2017

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

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Solution below.

Thursday, October 5, 2017

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

Check out this logic based Think Thursday Problem!
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Solution below.

Tuesday, October 3, 2017

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

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Solution below.

Thursday, September 28, 2017

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

Check out this logic based Think Thursday Problem!
Be sure to let us know how you solved it in the comments below or on social media!
This problem was originally posted by MAA online.

Solution below.

Tuesday, September 26, 2017

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

Check out this Problem of the Week.
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Solution below.

Thursday, September 21, 2017

Think Thursday 9-21-17: Twelve Coins

Check out this logic based Think Thursday Problem!
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Solution below.

Tuesday, September 19, 2017

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

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Solution below.

Thursday, September 14, 2017

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!

Be sure to let us know how you solved it in the comments below or on social media!

Solution below.

Tuesday, September 12, 2017

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

Check out this Problem of the Week and enjoy this math joke.

Why did the variable break up with the constant?
Because the constant was incapable of change.

Be sure to let us know how you solved it in the comments below or on social media!

Solution below.

Friday, September 8, 2017

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.


Image result for prime number theorem


Tuesday, September 5, 2017

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

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Solution below.

Thursday, August 31, 2017

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

Screen Shot 2017-06-27 at 3.19.13 PM.png



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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Solution below.

Tuesday, August 29, 2017

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

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Solution below.

Thursday, August 24, 2017

Wednesday, August 23, 2017

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!


Tuesday, August 22, 2017

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

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


Solution below.

Friday, August 18, 2017

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!



Thursday, August 17, 2017

Tuesday, August 15, 2017

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

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


Solution below.

Tuesday, August 8, 2017

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

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Solution below.

Friday, August 4, 2017

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.



Tuesday, July 25, 2017

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

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

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.

Friday, July 21, 2017

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:



Tuesday, July 18, 2017

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


Be sure to let us know how you solved it in the comments below or on social media!

Solution below.

Friday, July 14, 2017

Episode 5: Königsberg Bridge Problem (Seven Bridges) [#MathChops]

The advent of graph theory, from the mind of Leonhard Euler, came from a long-standing problem for the people of Königsberg. The problem was that no couple had a long and happy marriage, if they were married in Königsberg. As tradition dictated, a newlywed couple had one chance to travel across Königsberg’s four land masses using each of the seven bridges once and only once. If the two lovers could complete this seemingly simple task, their marriage would be long and happy. Years went by and nobody could complete to task, until Euler constructed a mathematical object that broke the curse of Königsberg… a graph!



Watch the proof proposed by Euler below to learn how mathematical abstraction created a whole new field of math, which is now regarded as an important predecessor to topology. Euler’s invention itself is remarkable, but the implications to mathematical philosophy reveals something very deep in the heart of mathematics. Namely, the art of abstraction to gain a better understanding of certain truths inherent in life’s situations.

The Königsberg Bridge Problem, and its solving:

Thursday, July 13, 2017

Tuesday, July 11, 2017

Problem of the Week: 7-11-17 [Calculus I]

Be sure to let us know how you solved it in the comments below or on social media!

Solution below.

Thursday, July 6, 2017

Episode 4: Uncountability of Real Numbers [#MathChops]





This week’s Top Pop Math Chop comes from Georg Cantor, who first solved this piece of set theory in 1891. He presented this as a mathematical proof which showed it was impossible to link infinite sets with an infinite set of the natural numbers. This is known today as Cantor’s diagonal argument, which he proved using binary numbers.



Cantor showed that if he has a list of binary numbers, takes one digit from each going diagonally, produces a new number, and swaps every single digit with a corresponding 1 or 0 (if is a 1 it becomes 0 and vice versa), that the number will be different than every other binary number listed before it. This is because in the first number the first digit is different, so it’s definitely different than the new number; in the second number the second digit is different than the second digit in the new number and so on.


You can do this same thing with real numbers, and produce infinite decimals between 0 and 1. This shows the real numbers are uncountable.


Check out the video below explaining Georg Cantor’s proof:

Advanced Knowledge Problem of the Week: 7-6-17 [calculus]

Be sure to let us know how you did in the comments below or on social media!

This week's problem comes from our textbook, Worldwide Multivariable Calculus, so feel free to check it out or any other affordable texts we offer. Enjoy this problem and try to find its relation to July 4th!

Solution below.

Friday, June 30, 2017

Problem of the Week: 7-4-17 [Geometry]

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Solution below.

Episode 3: All Horses Are the Same Color -- Equine Monochromaticity [#MathChops]


Obviously, this theorem is false, but it is a good way to show off your math chops and confuse a friend who may be taking an introductory course in math reasoning. This ‘proof’ is purely for fun, but does point out an important part of inductive proofs, which is that the assumption for the ‘n’th case must imply our statement is true in the ‘n+1’th case for any arbitrary n. Take what you will from this proof, but it reminds me of a joke I heard once.


A mathematician, physicist, and engineer are on a train in spain and see a white horse. The engineer remarks, “all horses are white!” to which the physicist and mathematician shake their heads. “No no no,” says the physicist, “what this means is that some horses in spain are white.” to which the mathematician shakes his head. The mathematician thinks for a little, and says “In passing we saw a white horse grazing in the plains of spain; therefore, there exists at least one horse in spain, of which at least one side is white.” and the three go about their day.


Proof


Thursday, June 29, 2017

Tuesday, June 27, 2017

Problem of the Week: 6-27-17 [Linear Algebra]

Check out this #PotW about properties of orthogonal matrices! as always, let us know what you think about it in the comments below or on social media!



Solution below the break.