On Thursday morning, as I had every other day this week and would for every day of this program, I walked from my room in Howard Hall to the classroom in Keller Hall where I had my class every morning.  I did not see any of the seven other students in the program leave, so I walked alone today.  It was cool and breezy, but the sky was blue, and I suspected it would warm up later.

Five others had arrived before I did.  In addition to Ivan Winn and Marcus Lee, whom I had met on Sunday when I arrived, Kirk Stone and Emily Sanders were already sitting in the room.  Emily was from upstate New York and pronounced some words in a distinct accent different from that of the West Coast.  She was a little shorter than average, slim with curly brown hair to her shoulders.   Kirk was one of two students in the program who actually attended Grandvale State, instead of having traveled here from elsewhere like me.  He was thin, with wavy brown hair and a build that I associated with typical Pacific Northwest outdoor activities like hiking or rock climbing.  Kirk, as a lifelong Oregonian, had made sure to educate all of us from out of state about how to pronounce local place names.  The last syllable of Oregon was pronounced more like “gun” than “gone,” and the Willamette, the river flowing through Grandvale, was pronounced with the accent on the second syllable.  “It rhymes with ‘damn it,’” he had said.  The beginning was not pronounced like actor Willem Dafoe, and it was definitely not pronounced like William.  I knew all of this, though.  I had relatives in the area on my grandfather’s side, and we took a road trip for a family reunion when I was eleven years old, in 1988.  My mother had corrected my pronunciation of Willamette on that trip.

I sat in an empty seat next to Ivan. “Hey, Greg,” Ivan said.  “What’s up?”

“Not much,” I replied.  “The guy who led that Bible study I went to on Tuesday said he has a bike I can borrow for the summer, so I’ll probably walk to his house and get that this afternoon.”

“Good.”

“That’ll be nice,” Emily said.  “You said you’re into cycling?”

“I don’t know if I’d call it ‘cycling,’” I explained.  “I don’t have a nice, expensive bike or anything.  But bicycles are really big in Jeromeville.  The newer parts of town have bike trails connecting the neighborhoods, and the campus extends into the rural area outside of town, since they do agricultural research there.  There are a lot of fun places to explore on a bike around Jeromeville.  And it’s flat, so it’s easy riding.  I started going for bike rides when I was bored freshman year, and I just never got out of that habit.  It’s pretty much the only exercise I get too.”

“I’m glad you found a bike, then,” she said.

The three missing students all arrived together about five minutes after I did.  Jeannie Lombard, the other student from Grandvale State, had long blonde hair and usually wore sandals, sort of a hippie look.  Julie Callahan was from Connecticut; she had chin-length brown hair, and was built like she might have played basketball or softball when she was younger, but had not kept it up into young adulthood.  And Marjorie Tanner, short and energetic with short curly brown hair, was a bit of a contradiction.  She was originally from California and talked like the stereotypical ditzy surfer girl, but she attended Harvard during the school year, so she was not actually ditzy, at least when it came to academics.

“Hey,” Julie said as the three of them entered.

“Hey, Julie,” Kirk said.  “What’s up?”

“Nothing.  What do you guys think of the presentations so far?  Any of them you really want to do?”

“I’m probably going to do one of the topology ones with Dr. Garrison.  But I want to look into applying topological methods to other areas,” Marcus explained.  “I didn’t think I was going to do topology this summer, but he had some very interesting things to say about that.”

After an introduction to the program on Monday, the rest of this week’s class time would be spent hearing the three professors working with the program talk about the areas of research that we could work on this summer.  Dr. Garrison had proposed some applications of topology, the study of properties of surfaces and how they are affected when they are stretched and twisted.  His talk focused on a surface called a punctured torus, a donut-like shape with one point missing.  I had not taken any classes about topology, so I was thinking that I would probably not do a topology-related project.

Today, a professor named Dr. Schneider was talking about Monte Carlo integration.  I learned how to calculate definite integrals in calculus in high school, but for some functions, the values of its definite integrals cannot be calculated exactly.  Various methods for approximating these values existed, with varying levels of complexity, efficiency, and accuracy.  The simpler methods tended to be less efficient, less accurate, or both.  I had studied some of these methods last year in a class called Numerical Analysis.  Monte Carlo integration used random numbers to produce a reasonably accurate result for these integral problems; the method was named for the famous gambling resort in Monaco, because of its reliance on random numbers.  Such methods could be improved upon; by choosing certain other sequences of numbers in place of the random numbers, a more accurate result can be obtained with fewer calculations.  This project sounded more interesting than the others that had been presented so far, mostly because I could actually follow what was going on in the talk.

The eight of us in the Research Experiences for Undergraduates program were given the use of a study room with couches, tables, and three computers.  I went there after our morning class ended, to check my email.  The most interesting message I had was from my mother, updating me on everything going on with her, my father, my 15-year-old brother Mark, and other people back home I might know.  I began typing a reply, telling my mother about my last few days, about the Bible study I had been to and the possible research projects for this summer.  I was staring at the wall trying to think of ways to explain Monte Carlo integration to someone with no knowledge of calculus when Kirk, Marjorie, and Julie walked in.  I said hi to them, and they said hi back.

As I was typing my email to Mom, I was vaguely aware of the other three playing Hangman on the chalkboard on the wall to the left of me.  After I sent the email, I walked to the others.  Marjorie stood at the board, with Kirk and Julie guessing letters.  Marjorie had written the category as “thing,” and her puzzle had two words, of nine and five letters, respectively.  The first word had an N for the third letter, and an E in the second to last position, and the second word had an O in the second position and ended with S.  The letters A, L, and H had been guessed and were not in the word.

_ _ N _ _ _ _ E _
_ O _ _ S

“I,” Julie guessed.

“No I,” Marjorie replied, writing I with the other letters not in the puzzle.

“No I?” Julie exclaimed.  “Where are all the vowels?  What is this?”

“I know,” I said.

“What?”  Kirk replied.

“I know what the puzzle is.”

“How do you know?” Julie asked.  “What is this word with no vowels?”

“You haven’t guessed all the vowels,” I said slyly.

“Fine,” Kirk replied indignantly.  “U.”   Marjorie filled in the blanks for the three Us in the puzzle.

_ U N _ _ U _ E _
_ O _ U S

“There are the vowels,” Julie said, “but I still don’t know it.”

“I don’t want to interrupt your game,” I said.  “You guys were trying to figure it out.”

“You can play if you want.”

“I’ll play the next one.  I’ll let you guys figure this one out.”

I turned my attention to a bookshelf next to the chalkboard.  The bookshelf contained the proceedings from previous years’ REU projects; I grabbed one at random and began flipping through the pages.  This one was from 1996, last year’s program.  Since I still had no idea what I was doing this summer, I thought that looking through these might help me get some ideas of what my final report should look like, even if the mathematics itself would end up being wildly different.  Each book contained a different number of reports, depending on how many students worked on each project.  Some students who worked with the same professor wrote separate reports, and others seemed to work together, with multiple names on one report.  Most likely, the nature of the research being done dictated whether it required separate reports or a collaborative report.

Kirk guessed T in the Hangman game.    Marjorie filled in the two Ts in the puzzle, and Kirk groaned when he realized that the answer was “punctured torus,” a word from yesterday’s math presentation.  Kirk took the next turn, and as he stood at the chalkboard thinking of a word, I picked up a different book of REU proceedings.  This one was from 1994; Dr. Garrison was still the lead professor, and Dr. Schneider worked on this one too, but the other two professors were names I did not recognize.  I glanced at the list of participating students and the universities that they were from, to see if any of them were from anywhere interesting, and I felt that weird jolt pass through my body as I read a name that I recognized.

“Hey,” I said.  “Someone I know is in here.”

“What is that?” Marjorie asked.

“The proceedings from this program in 1994.”  I turned the book to the others so that they could see what I was pointing to: Mary Heinrich, University of Jeromeville.

“Oh, wow,” Marjorie observed.  “Someone else from Jeromeville.”

“And you actually know her?” Kirk asked.

“She was a senior when I was a freshman,” I explained.  “And she was President of the Math Club that year.  I didn’t know her well, but that year I knew her to say hi to.”

“That’s cool,” Marjorie said.

As we guessed letters in Hangman, I thought about what it meant that Mary Heinrich had also done the REU at Grandvale State.  Probably nothing, in the grand scheme of things.  Dr. Thomas had probably recommended the REU to many promising mathematics students, as she had done with me.  Mary probably noticed the same thing I had, that Jeromeville gets out for the summer a month after most other universities, and after many REU programs begin.  Students from Jeromeville doing an REU would be limited as to which ones they could apply to without missing spring quarter finals, so maybe REU students from Jeromeville tended to end up at the same few programs.  Still, it was interesting that, although I had never heard of this program until a few months ago, and only a few students participate each year, I knew someone else who had been in the program.

I arrived in Grandvale four days ago, in the late morning on a Sunday, and I quickly found a church that had an evening service.  I had told the greeter at church about my situation, that I was only in town for two months for a research internship at the university, and she forwarded my contact information to the college and young adult pastor, a man in his thirties named Joe Ferris.  He invited me to the weekly Bible study for that age group that met on Tuesdays, and it was at Bible study that he mentioned that he had a bicycle I could borrow.

After playing a few more rounds of Hangman, I went back to my room and made a sandwich, then I called Joe Ferris and asked if I could walk to his house and pick up the bicycle now.  He said that he and his family might be leaving the house for a bit around the time I got there, but they would leave the bicycle in the side yard with the gate unlocked for me.

The Ferrises, a family of five, lived in the central part of Grandvale on 16th Street.  I walked the route that had become very familiar to me over the last few days, as if I were going to class in Keller Hall, but when Keller approached to my right, I continued walking north to Maple Street, the boundary between the campus and city.  I then crossed Maple Street and walked north on 21st Street, past small apartment complexes and old houses.  I had been this way once before, to go grocery shopping on Monday.  This was a major thoroughfare leading to the northern part of Grandvale, but in this old neighborhood, the street was narrow, with only one lane for cars in each direction.

I passed a commercial area about half a mile past the university, with a pizza place, the grocery store I had gone to earlier in the week, a coffee shop, and other stores.  Beyond this was a traffic light at Cedar Street.  I crossed the street at the light and then turned east.  As I walked down Cedar Street, I heard honking from an approaching car.  I looked up and saw the Ferrises driving west.  Joe waved at me from the driver’s seat, and I could see his wife, Anne, in the passenger seat, and their three daughters waving from the back.  I waved back.

When I arrived at the Ferrises’ house, the bicycle was on the side of the garage, just as Joe had said it would be.  It was green, a cruiser-style bicycle with a chain guard and clunky fenders, although the fenders would come in handy if it rained again.  It looked like it was probably at least over a decade old.  It was not pretty or sleek in any way, but it was a bicycle, and it was free to use.

I rode back down 16th Street and turned on Cedar the way I came.  I was pedaling fast and not getting very far, so I shifted the front dérailleur to a higher gear.  I heard the chain make a funny noise, then suddenly felt no resistance in my pedaling.  The chain had slipped off of the gears.

No problem, I thought.  This happened all the time with Schuyler, my bike back in Jeromeville, and usually I can just pedal while I shift the front to its highest gear, and the chain will drag back into place.  But this slip happened when I was in the process of shifting to a higher gear, so now I was not sure what to do.  I tried pushing the shift lever as far as it would go, and the chain did not reattach.  I tried frantically moving both dérailleurs as I pedaled, and nothing seemed to want to make the chain reattach.

I turned the bike upside down to see what was happening closer up.  With Schuyler, it would have been easy to push the rear dérailleur loose, grab the chain, slip it around the gears, and then let the rear dérailleur spring back into place.  But this bicycle had a chain guard, so I could not easily grab the chain from that side.  I tried grabbing it from the side that was normally on the bottom, away from the chain guard.  A thick layer of black grease immediately covered my hand; at this point, I did not care, I just had to be careful not to stain or damage any of my clothes permanently.  I tried to move the chain into position, but I could not get it in place no matter how hard I pulled.  I tried again, pulling in a slightly different direction, and I felt a tooth of one of the gears scratch my skin.  I was bleeding now, and I was going to need another shower when I got home.

After about ten minutes of fiddling, shifting, and swearing, I finally felt the chain start to catch on a gear as I pushed the pedal forward with my hands.  I slowly continued turning the pedal, and the chain clicked into place.   Finally.  I turned the bike right side up on its wheels and began pedaling home.

Now how could I make sure that this did not happen every time I rode the bike?  I had been shifting gears on the rear dérailleur repeatedly before I attempted to shift the front, and nothing had gone wrong.  Maybe I was going to have to spend the entire summer only shifting gears in the back.  I supposed I could get used to that.

Now that I had a mode of transportation, I wanted to explore more of Grandvale.  But I was dirty, and still bleeding a little, and getting cleaned up and staying in my room seemed like a much more appealing way to spend the evening.  I had work to do, books to read, and letters to write.  I walked the bike into the Howard Hall elevator and got off on the third floor; Emily was walking past when I got out of the elevator.

“Hey, Greg,” Emily said.  “Is that the bike you’re borrowing?”

“Yeah,” I replied.  “I learned the hard way that it doesn’t shift properly in the front.”  I showed her my right hand, still covered in black grease with a few small blood stains.

“Wow.  Are you okay?”

“I will be.  Just grease and scratches.  I have Band-Aids in my room.”

“Okay.  Be careful.”

“I will.”

Mom had told me in her email earlier that she would be sending my package of things I needed for the summer, but was not able to pack on the plane, on Friday morning.  That was tomorrow, so I called Mom later that night and told her to send the bike lock in the package.  That way, if I had to ride to the grocery store or anywhere else, I would be able to leave the bike unattended.

I saw the Ferrises at church on Sunday, and Joe told me that they had seen me on the side of the road trying to fix the chain as they returned home. “I thought about honking and waving again, but I didn’t. We had a good laugh at that, though, since that bike always does that.”

“I got it eventually,” I said. “A reminder not to shift the front would have been helpful, though.”

“Sorry. I just forgot. Didn’t think to say anything.”

It was fun being on a different campus in a different state, but it was starting to get difficult being this far out of my comfort zone.  I missed my normal life in Jeromeville.  I missed my friends.  I missed Jeromeville Christian Fellowship and the youth group kids at Jeromeville Covenant Church.  I missed having a computer in my room.  I missed riding Schuyler on the bike trails in Jeromeville.  Of course, I still had no idea what experiences waited for me in the time I had left in Grandvale; maybe I would be surprised at everything that would happen.

Also, many of my Jeromeville friends were also leaving their comfort zones this summer.  Brian Burr, my roommate last year, was moving to New York later this summer to start medical school.  Taylor Santiago left in March to work at an urban ministry center in Chicago, volunteering with church youth groups from around the country that take week-long trips to Chicago to do urban ministry projects.  Jennifer Dawson, an acquaintance from another church in Jeromeville who knew the people who had the coffee house party in April, was going on a mission trip to Brazil this summer; I had donated money to her mission trip at that party.  And Eddie Baker, Melinda Schmidt, Tabitha Sasaki, Evan Lundgren, and seven of my other friends from JCF were leaving this week to spend a month in China, preaching the good news of Jesus to university students in a very hostile country.  If all of these people could handle being that far away from home to serve the Lord, surely I would be just fine spending eight weeks in Oregon doing mathematics.  Especially since I had already found a Bible study full of brothers and sisters in Christ who could help me with things like finding a used bicycle.  God would be with me wherever I went, according to several passages in the Bible.

Readers: Tell me an interesting story about a time you were away from home for an extended period.

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