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Thursday, December 13, 2018

Problem of the Week: 12:13-18: Taylor Series Approximation and Remainder Estimation [Calculus]

Today is Taylor Swift's birthday.


Surely, we had to take this opportunity to do a problem that involves a Taylor series.

Side note: Taylor series was formulated by the Scottish mathematician James Gregory and formally introduced by the English mathematician Brook Taylor . 

We have no idea what T-Swizzle's background in mathematics is.



Solution:



Video:

Thursday, December 6, 2018

Problem of the Week: 12-06-18: Math Test [Combinatorics]

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Solution:



Video:

Thursday, November 29, 2018

Problem of the Week: 11-29-18: Find their Birthdays [Algebra]

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:


Video:
Sorry guys, the woman was born in 1983 not 1973. I'm still living in 2008. The solution above is correct,

Wednesday, November 21, 2018

Problem of the Week: 11-21-18 Thanksgiving Banquet

Happy Thanksgiving!

Solution:

Video:

Edit: At 2:25, the inequality is between five hundred and *SIX HUNDRED* not 16 :)

Thursday, November 15, 2018

Problem of the Week 11-15-18: Harry Potter Currency [Arithmetic]

Tomorrow marks 17 years since Harry Potter and the Sorcerer's Stone was released in theaters.


Obviously we needed to do a Harry Potter themed Problem of the Week. 

 Does Hogwarts teach math? 


Solution



Video:

Thursday, November 8, 2018

Problem of the Week: 11-08-18: Prove Pasch’s Postulate as a Theorem [Geometry]

Happy 175th birthday Moritz Pasch! The German mathematician was born on November 8, 1843. Pasch specialized in the foundations of geometry. He is best remembered for Pasch's axiom, which he discovered in 1882. 


Although axioms do not require proofs, in this week's problem we celebrate Pasch's birthday by- you guessed it- proving Pasch's axiom. Why? Because proofs are FUN    


Solution:


Video:

Thursday, November 1, 2018

Problem of the Week: 11-01-18: Election Exit Polls [Probability]

Midterm elections are just around the corner. Don't forget to go out and VOTE! In the meantime, give this election-edition problem a try!
Solution 



Video

Thursday, October 25, 2018

Problem of the Week: 10-25-18: Halloween Monster Party [Logic Puzzle]

Halloween is less than a week away! Celebrate early with this Halloween themed Problem of the Week. 

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


Solution:


Video:

Thursday, October 18, 2018

Problem of the Week: 10-18-18: Prove that the Fraction is Irreducible [Number Theory]

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Solution:


Video:

Thursday, October 11, 2018

Problem of the Week: 10-11-18: Baseball Bet [Probability]

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


Solution



Video:

Thursday, October 4, 2018

Problem of the Week: 10-04-18: Arc Length [Calculus]

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


Solution



Video

Thursday, September 27, 2018

Problem of the Week: 09-27-18: Comparing Numbers [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


Video:

Thursday, September 20, 2018

Problem of the Week: 09-20-18: Separation of Variables [Differential Equations]

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Solution:



Video:

Thursday, September 13, 2018

Problem of the Week: 09-13-18: Two Independent Events [Probability]

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Solution:


Video:

Thursday, September 6, 2018

Thursday, August 30, 2018

Problem of the Week 08-30-18: Solving Equation for Variables [Algebra]

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Solution:



Video:

Thursday, August 23, 2018

Problem of the Week 08-23-18: Solving a Trigonometric Equation [Trig]

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Solution:


Video:

Thursday, August 16, 2018

Problem of the Week 08-16-18: Nullspace of a Matrix [Linear Algebra]

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

Solution:



Video:

Thursday, August 9, 2018

Problem of the Week 08-09-18: Logarithmic Differentiation [Calculus]

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

Solution below:



Video:

Thursday, August 2, 2018

Problem of the Week 8-02-18: Double Integral [Calculus]

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

Solution below:



Video:
*Edit: there is not suppose to be a constant of integration at the end since this is a definite integral.

Wednesday, August 1, 2018

The Fields Medal

Today, Peter Scholze, Caucher Birkar, Alessio Figalli, and Akshay Venkates won the Fields Medal- the highest honor a mathematician can receive

To celebrate their victory, we compiled a list of important facts about the award:

1. The Fields Medal is awarded to two, three, or four mathematicians under the age of 40.
Image result for fields medal
The Fields Medal

2. It has been awarded every four years since 1950 at the International Congress of Mathematicians. 

3. The award “recognizes outstanding mathematical achievement for existing work and for the promise of future achievement.” 

4. An individual cannot win a Fields Medal more than once.

5. Many describe the Fields Medal as the mathematician's "Nobel Prize."

6. There is a monetary award of about $15,000 Canadian dollars.

7. The award is named after Canadian mathematician John Charles Fields.
Image result for john charles fields
John Charles Fields

8. Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas were the first recipients in 1936.

9. Maryam Mirzakhani became the first woman to win the Fields Medal in 2014

10. Jean-Pierre Serre became the youngest recipient at the age of 27. 

11. In 2006, Grigori Perelman, refused his Fields Medal. He said, "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo.”

12. So far, 4 mathematicians under the age of 30 have won.

Source: 

Thursday, July 26, 2018

Problem of the Week 7-26-18: 2nd Order Nonhomogenous Linear Differential Equation [Differential Equations]

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


Video:

Thursday, July 19, 2018

Problem of the Week 7-19-18: Invertible Matrix [Linear Algebra]

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

Solution below:


Video:
*Note: In the video, k- 1 - 6(k - 1) reduces to k2- 6k + 5 NOT k2 - 6k - 5

Friday, July 13, 2018

Unlucky Numbers Around the World



Friday the 13th is upon us!  Across the nation, there are people avoiding black cats, spilled salt, ladders, and broken mirrors. Not everyone, however, is scared of 13 because they have other numbers to fear. 


In honor of today, here are 6 unlucky numbers from around the world.


4 - China
In China, the number 4 is considered unlucky because it is homophonous to the word "death." Similar to how the 13th floor is absent in many buildings in the West, the 4th floor is often left out in China.


9 - Japan
Just like the number 4 in China, the number 9 is a bad omen in Japan because it sounds similar to the Japanese word for “torture.”


17 - Italy
The Roman numeral for 17 is XVII, and an anagram for XVII is "VIXI.” This translates to “I lived," aka “my life is over."


26  - India 
For India, tragedies and disasters have the pattern of striking on the 26th (the 2008 Mumbai terror attack, the 2001 Gujarat earthquake, the 2004 Indian Ocean tsunami, 2008 Ahmedabad bomb blasts). For this reason, India doesn't really like the number 26. Can you blame them?


39 - Afghanistan
The number 39 is considered cursed in Afghanistan due to the fact that 39 translates to  ‘morda gow’ which means ‘dead cow” - which is slang for pimp. Since 39 is linked to prostitution, the number is largely avoided.


0888 888 888 - Bulgaria
After three people in Bulgaria with the phone number 0888 888 888 died within ten years, a Bulgarian mobile company suspended the phone number because they believed it was cursed. If you are in Bulgaria, try calling the number. Surely, no one will pick up. 




Thursday, July 12, 2018

Tuesday, July 10, 2018

Thursday, July 5, 2018

Tuesday, July 3, 2018

Problem of the Week 7-3-18: Invariant Sums of Digits [Number Theory]

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Solution below.

Thursday, June 28, 2018

Advanced Knowledge Problem of the Week 6-28-18: Conjugates of a Subgroup [Group Theory]

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




Solution below.

Tuesday, June 26, 2018

Problem of the Week 6-26-18: Integers and Quartics [Number Theory]

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



Solution below.

Thursday, June 21, 2018

Tuesday, June 19, 2018

Problem of the Week 6-19-18: A Polynomial Inequality [Inequalities]

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


Solution below.

Thursday, June 14, 2018

Tuesday, June 12, 2018

New Video Series on Integration Tricks

Integration is a vast topic with many diverse techniques meant to help find the integrals of functions. Many delightful and elegant methods are used to tackle difficult integrals. This video series talks about a few of the less common, but still very useful, techniques. These videos cover topics such as the tangent half-angle substitution, integration with a parameter, and how symmetry in integrals can be useful. 


Problem of the Week 6-12-18: Making Polynomials Prime [Number Theory]

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Solution below.

Thursday, June 7, 2018

Advanced Knowledge Problem of the Week 6-7-18: Order of an Element [Abstract Algebra]

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


Solution below.

Tuesday, June 5, 2018

Problem of the Week 6-5-18: A Composite Polynomial [Number Theory]

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Solution below.

Thursday, May 31, 2018

Tuesday, May 29, 2018

Problem of the Week 5-29-18: Numbers with Certain Divisors [Number Theory]

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Solution below.

Thursday, May 24, 2018

New Video Series on Complex Analysis

Interested in learning a bit more about complex variables and some theorems about them? Then check out this new video series covering some of the basics of complex analysis! Complex analysis is an immensely useful subject that is found in many branches of mathematics. The residue theorem is especially well known as being an extremely important method for the integration of functions (real or complex!). Some other topics discussed include complex differentiation, Cauchy's Integral Formula, Liouville's theorem, the Möbius transformation, and much more!


Advanced Knowledge Problem of the Week 5-24-18: A Metric Space [Topology]

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





Solution below.