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A million dollars a year in textbooks

Just received this request for a donation to Williams:

Dear Diana,

Did you know that Williams provides a book grant to cover all required texts and course materials for students receiving financial aid?

Prior to 2010, financial aid students would queue up before dawn with the hopes of borrowing textbooks from the 1914 Library. For decades, the 1914 provided financial aid students access to textbooks without having to purchase them outright. […] All of that changed in the spring of 2010: no more standing in line, no more choosing courses or majors based on the availability of textbooks. Since 2010, the Alumni Fund has made it possible for the college to help purchase approximately $7.5 million in textbooks for financial aid students. […]

Perhaps you’d like your Alumni Fund gift to buy the books for students taking “MATH 150: Multivariable Calculus” this semester. (You can read more about the course here.)

Thank you so much for all you do for Williams!

Lisa Russell-Mina ‘79
Co-Chair, Alumni Fund

Thoughts:

Some problems I wrote about Mount Greylock, the Mountain Day T-shirt, Cricket Creek farm, and the Williams Outing Club are below the break. The whole textbook is here.

A problem about the gradient vector and level curves, which also builds insights toward the method of Lagrange Multipliers:

 

A problem to build understanding of the multivariable Chain Rule:

 

An applied problem about (finite) geometric series:

 

A problem about optimizing a function under a constraint:

Solutions welcome! :)

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#1 Comment By PTC On September 7, 2018 @ 6:49 am

DDF-

It is good policy to pay for books. That way you know that students on financial aid will have the basic material that is relevant to the mission.

Not sure why the 11 million dollar bookstore was a good idea in the age of Amazon and the internet?

Much less expensive way to handle that than taking on those construction, taxation, and maintenance costs.

What are your thoughts on the hotel? You think that earns for Williams, or loses money?

How do you factor in alumni happiness and giving when considering things like a new bookstore/ pro shop, the log, the hotel?

Is there an economic model for giving as it pertains to expenditure on visiting alumni happiness?

#2 Comment By David Dudley Field ’25 On September 7, 2018 @ 7:25 am

This post was by Diana (welcome back!), not by me.

#3 Comment By PTC On September 7, 2018 @ 7:53 am

DDF-

Thanks.

Good times. I still want your opinion on this. Do commercial buildings like the bookstore, the log, and the hotel add to gains in giving?

Diana- Good to see you “here.” What is your opinion on giving and items such as the new hotel- does that factor into how much you give?

I have no idea on the math you asking. Although I have read a lot of maps, and hiked all over the world. So if no one else answers 5 &6, 6 and 4 please do.

#4 Comment By Diana On September 7, 2018 @ 11:05 am

PTC, I give the same amount every year, a token donation to help with the participation numbers.

At some point I hope to be able to give a lot of money to an organization (TBA) that makes a lot of people’s lives better. It’s not going to be a private institution of higher education. There is just too much administrative bloat, excessively fancy construction, so many things they spend money on where that same dollar would do a lot more good elsewhere.

I don’t have particular opinions about the hotel or the bookstore. I liked the Log when it was operated by Hops & Vines, because the food was great and affordable. Now I think it’s a pizza restaurant.

There are things that Williams should do, to change the culture to make it a better and healthier place for students and faculty (who are the heart of the College). None of these things require millions of dollars, but they would require changing the culture, which is harder than raising and spending money.

#5 Comment By Arch Stanton ’62 On September 7, 2018 @ 11:14 am

Welcome back, Diana. I love that you posted some math problems, though most of the math is over my head,I’m afraid. It tried to answer the parts I could without. Am I close? I do love math, but that C+ in calculus freshman year dissuaded me from going any further with it. On 6a, the flat parts should be the sections where the green line runs along the contour lines, I believe. The steepest part would be the ascent/descent on the east side of Stony Lodge, because the contour lines are closest together there.

3a. $53,354
3b. $73,351
3c.
2046-47 $148,799
2047-48 $154,156
2048-49 $159,705
2049-50 $165,455
3d. 1904 (112 years prior to 2016-17)
(was I allowed to use an amortization calculator for that one?)

On 4, I think a silo where the ratio of the height to the radius is 2:1 would maximize the volume available to store grain with a fixed amount of aluminum for the surface area. I arrived at that conclusions using polynomial equations and testing various solutions to compare the volume vs surface area. Here, that would mean a height of 20 feet and radius of 10 feet. But, that would increase the footprint of the silo, and land is generally more expensive than aluminum. Also, in a flatter silo, it will be harder for grain inside to flow out.

#6 Comment By David Dudley Field ’25 On September 7, 2018 @ 11:57 am

1) I love these math problems! Diana: Maybe post one each day next week? (No worries if you are too busy to waste time which such shenanigans.)

2) Arch: You should join us as an author. We need more writers. Some for you Interloper! Although PTC provides nice local coverage, especially his photos, our readers want more.

#7 Comment By Jon Cole On September 7, 2018 @ 12:11 pm

My $100 more than pays for the books for the intro major seminar in my major.

The sentiment of the original post has an unattractive aroma to it imo (Since I can’t buy a complete text in subject x, I’m less likely to /won’t contribute anything towards the goal).

The math problems are interesting but don’t change my opinion, even though I don’t think one must feel obligated to buy books for financial aid students.

#8 Comment By Diana On September 18, 2018 @ 4:28 pm

Arch Stanton, sorry for my late response. All of your answers are correct! For anyone who is reading, this means the total 4-year tuition will be $628,000. Wow! As for the amortization calculator, I’m not sure. I did 51,500 * 1.036^-104 and got less than $1000, and with -103 got more than $1000, so your answer is correct. :) As for why the silo is taller and thinner than optimal, this question was somewhat of an obsession of mine. The reason seems to be that silage requires weight on top of it in order to ferment properly, and the smaller the surface area, the taller the height of the silage inside.

Dave, sure, I’d be happy to post a short series. I will do it as soon as time allows. It’s good to be back!

Jon, sorry for the late response. I didn’t mean to imply the sentiment you stated. My opinion is: I would rather my $100 pay for the printing and binding texts for all 50 or 100 of the students, than for my $100 to go towards only one (or 1/2, or 2, etc) textbook.

#9 Comment By David Dudley Field ’25 On September 18, 2018 @ 4:50 pm

Welcome back!