Problem of the Week

Celebrate our #sigma with this week's summation Problem of the Week. Let us know how you did in the comments!

Find the solution below.

Super Bowl 50 Stats and Facts

Super Bowl 50

The outcome of the January 24th Conference championships left Patriot and Cardinal fans shocked and disappointed. Watching the game from a local pub in Boston, it felt as though the city came to a complete standstill when the final whistle blew with a 20-18 Bronco victory. If you are like any of the hard-core Patriot fans I know, you will most likely be boycotting the team until they deem themselves worthy again.

Of course, fans are always bitter after their team looses. However, it may have taken some of the edge off if the predictions were not so misleading. Statistics reported by Sportsbook, ODDS Shark, The Denver Post, Vegas Insider and FootballLocks all reported a Bronco-Cardinal face off.

Despite the fact that reports predicted a Bronco victory, a close game by the Patriots was not anticipated, straying fans toward false expectations. This being said, don't loose hope in the power of statistics! On February 7, the Carolina Panthers will face the Denver Broncos at Levi's Stadium in Santa Clara, California. In an interview with CNN, Panthers quarterback Cam Newton said: "I keep saying it: We're not finished" while Peyton Manning, Broncos quarterback emphasis his gratitude, "It's a great honor to be going back to the Super Bowl." As both teams and fans are confident in a Super Bowl 50 victory, listed below are February 7th's predictions: 

According to ESPN's Football Power Index:

                                             

The Bleacher Report also predicts a Panther victory: 31 to 17.

Shifting gears to website mediated polls, fans we're asked "Who's going to win Super Bowl 50?"

Result gathered by officials predict: 

Heavy

                                                      

LA Times 

As the Panthers are favored to win, lets hope Carolina fans aren't disappointed! 

If these statistics don't cut it for you, lets take a look at some celebrity predictions.

1. Pierre McGuire - Panthers 

"I think the (Cam) Newton factor is going to be huge. I know Denver's defense is obviously All-World. But I think the combination of (Greg) Olson and Newton make a big different for Carolina, so I give them the edge" 

2. Luc Robitaille - Broncos

"You know, I really like New England, so once Denver won, and I'm a fan of John Elway and how he built that team, and Peyton Manning is such a great story. I'll just say I'm probably going to be rooting for the old guy."

3. Timothy Bradley - Panthers 

"It's very clear to me - Carolina Panthers 31-27" 

4. John Scott - Panthers 

"Geez, I don't know. I don't know. That's a good question. I kind of want the Broncos to win just so Manning can go out (with a win) but I think the Panthers are going to win. They have a good team." 

With this information in mind, it is clear that a team is favored to win. However, odds can always go askew, and until February 7th's Super Bowl, fans will be on their toes. So go ahead and have a Super Bowl party, put on your favorite team's jersey and impress your friends with Super Bowl math facts!

1) Why is the phrase Super Bowl accompanied by a Roman numeral?

For starters, the NFL season spans two calendar years. Purely for aesthetic reasons, marketers decided that it would look better for Super Bowl to be accompanied with roman numerals rather than the years. For example, "Super Bowl XLVIII" - aka, Super Bowl 48 looks far better than "Super Bowl 2013-2014." This year, however, roman numerals were discontinued leaving "Super Bowl L" as "Super Bowl 50." "Some would ask, 'The letter L, what does that associate with?' NFL spokesman Brian McCarthy says; The answer, of course, is "Losing." Along with this, the creative team decided that L would not be aesthetically pleasing and the realm of creative design is much greater with the number "50." 

2) Does the coin toss that takes place before the Super Bowl actually matter?

In other words, if a team wins the coin toss does it increase the odds that they will win the game? In a few words, no, according to Jason Marshall, PhD, "the coin toss has no statically significant impact on the outcome of the game." No need to hold of bets till after the coin toss!

3) What scores are possible in football?

This is more of a puzzle than a fact, but we encourage you to try it out! In other words, are there any scores that are impossible?

You will need to know the difference number of points that can be awarded:

• 2 points for the relatively rare safety 
• 3 points for a field goal
• 6 points for a touchdown
• 7 points for a touchdown and a successful extra-point kick
• 8 point for a touchdown and a successful two-point conversation 

Is it possible for a team to score 13 points? How about 37? Try your best to prove why some scores are possible.. or impossible! 

Comment on our social media links or send us a message with your answer! 

Good luck Panthers and Broncos, may the odds be in your favor! 

Advanced Knowledge Problem of the Week

Try your hand at this analysis proof involving continuity and differentiability! It may help to draw a graph so you can visualize what is going on with the function near the origin.

See my solution below, and let us know how you did in the comments!

Problem of the Week

Check out this week's Problem of the Week, which involves a topic from differential equations, the Laplace transform. See if you can figure it out!

The solution can be found below the break.

Advanced Knowledge Problem of the Week

Test your knowledge of stability analysis in this week's Advanced Knowledge Problem of the Week. (hint: graphing sample phase planes may help with qualitative analysis!)

Check out my solution below, and comment with any other insights you may have!

Why are textbooks so expensive?

For college students, like myself, saving money is always high on the agenda. College apartments are stocked with utensils ‘borrowed’ from the dining hall, and it isn’t uncommon to eat Ramen three nights a week. While paying an exorbitant amount of money for tuition, students make sacrifices to save a few dollars here and there. These money-saving techniques can be as small as skipping on guacamole at Chipotle or as large as deciding not to purchase a text book for a class. Although it may be hard news to take, guac is probably a luxury we can forgo. But a textbook? That seems like a pretty significant part of college. We are here to get an education, right? To put it gently, the price of textbooks is not conducive with the life of a college student. The average price of tuition at a private institution is $32,405 per year. Multiply this number by 4 and you’re paying over $129,620 for 4 years. With this burden already associated with higher education, it would make sense for textbooks to be somewhat reasonable in price. Here at Worldwide Center of Math, the affordability and accessibility of textbooks is something we strive for. However, the majority of textbook publishers do not share the same idea.

According to students themselves, typically math and science books are the most detrimental to their bank account. Below is a chart that shows the price for a print and digital copy of one of the most expensive types of text books—Calculus.

  

These extravagant prices may be surprising (and alarming) to people who have been out of college for a few years, but for college students this is considered normal. In fact, when I reached out to students about the price of textbooks, about 50% answered that they have paid between 150-300+ for a textbook. Keep in mind, this is just one textbook for one semester. With four or five classes per semester, students may purchase up to 10 books in 1 school year. To avoid the cost of textbooks altogether, 58% of students admitted that they have ignored their teachers note to buy the required textbook. While some students felt this decision had no impact on their academic success, others (25%) felt that refusing to purchase the text did have a negative result on their grade.

Our logo, Sigmi, crying over $300 books

When asked about textbooks, some students laughed and confessed the great lengths they have gone to in order to avoid buying the text. A sophomore science major explained how she would visit the bookstore after class and take pictures of the homework problems assigned in her book. Unfortunately, she wasn’t as inconspicuous as she had hoped, and a book store employee put an end to her loophole. I had a similar experience in my freshman year math class, when one student in the class of 20 decided to purchase the book. A few of us decided to split the cost and pay her our portion of the price, and in return she would allow us to photograph the pages we needed. This worked for all parties, but when she was absent or forgot her book the whole class was at a stand still.

The tricks to avoid purchasing a textbook are pretty creative and highlight the dissatisfaction students feel about books. There is an underlying question that no one can seem to answer: Why are textbooks so expensive? 

Expensive is better? 

There is a common notion amongst consumers that more expensive goods must be of a higher quality. This imaged correlation between price and quality can help people justify paying more money for a specific brand or type of product. However, on many occasions, a more expensive product does not make it better. Only 7% of students feel that expensive textbooks are actually more beneficial to their education. The other 93%see no connection between price and quality in the textbook industry. 

Professors choose the text

Of course, there must be a unified syllabus with a textbook selection, made by the teacher. The problem is, most professors don't put too much thought into their students' wallets when selecting a textbook to assign. Professors don't pay for the text, so the price tag on the book isn't the first thing they look at. Publishing companies often convince professors to use the latest version of a textbook, which is almost always more costly. This brings us to the next point....

Publishers print new versions

Freshman typically spend more money on books than upperclassman, who learn to borrow books from friends that already took the same class. However, to eliminate this, publishers consistently publish updated versions. These versions may only have a few small changes, but can cost double an earlier version. 

The digital industry is still developing

Publishers often claim that the sole reason for the expense of textbooks is the cost of manufacturing. It may be true that textbooks are pricier to produce than other types of books, but why hasn't anything been done to change the industry standards? When every student has a laptop, cell phone, or iPod attached to their palm, why hasn't the digital textbook industry caught on more quickly? Over the past few years, several big name publishing companies have come out with digital editions, but very few students or professors are aware of digital options. Digital versions of textbooks are often less expensive and more accessible to students in this day in age. 

Don’t worry! The Center of Math is on your side!

David Massey, founder of The Worldwide Center of Mathematics, recognized this problem within the textbook industry. In hopes to combat the increasing rise in the cost of textbooks, the Center aims to create accessible and affordable mathematics materials for students and math enthusiasts alike. We recognized the benefits of the digital industry, and our digital books are only $9.95. Some students still prefer a hard copy, but don’t worry—that won’t break the bank either. Print copies only cost $29.95. Our goal is to help the math industry, so we have resources online that are open to the public, along with videos that accompany our books on our YouTube Channel.  (Almost at 10k subscribers—Go subscribe!). Along with academic texts, the Center is also involved in research. Massey’s Journal of Singularities is open source and accessible to anyone. In an industry that seems to be set on making learning more expensive for students, the Center of Math shows that it is possible to be affordable and educational.