How can calculus help you survive the zombie apocalypse? Colin Adams, humor columnist for the Mathematical Intelligencer and one of today's most outlandish and entertaining popular math writers, demonstrates how in this zombie adventure novel.
Zombies and Calculus is the account of Craig Williams, a math professor at a small liberal arts college in New England, who, in the middle of a calculus class, finds himself suddenly confronted by a late-arriving student whose hunger is not for knowledge. As the zombie virus spreads and civilization crumbles, Williams uses calculus to help his small band of survivors defeat the hordes of the undead. Along the way, readers learn how to avoid being eaten by taking advantage of the fact that zombies always point their tangent vector toward their target, and how to use exponential growth to determine the rate at which the virus is spreading. Williams also covers topics such as logistic growth, gravitational acceleration, predator-prey models, pursuit problems, the physics of combat, and more. With the aid of his story, you too can survive the zombie onslaught.
Featuring easy-to-use appendixes that explain the book's mathematics in greater detail, Zombies and Calculus is suitable both for those who have only recently gotten the calculus bug, as well as for those whose disease has advanced to the multivariable stage.
|Publisher:||Princeton University Press|
|Product dimensions:||5.60(w) x 8.50(h) x 0.90(d)|
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Zombies & Calculus
By Colin Adams
PRINCETON UNIVERSITY PRESSCopyright © 2014 Princeton University Press
All rights reserved.
Up until April of this year, I was a math professor at Roberts College, in the tiny town of Westbridge, Massachusetts, on the far western border of the state. Roberts was a small liberal arts college, endowed with excellent students, a beautiful New England campus, and deep pockets. I couldn't imagine a better job than teaching those highly motivated students the mathematics that I love, and also having the time to work on my own research in mathematics. It was a dream job. On top of that, Roberts was set in the Berkshire Mountains, which by anyone else's standards are not mountains at all, but they are still some of the prettiest hills you have ever seen.
Spring break ended at the beginning of April, and we had just returned for the last six weeks of the semester. It was a Friday, and I was reviewing for my calculus class the fact the derivative f'(x) of a function f(x) is the slope of the tangent line to the graph of the function at x. I had drawn this picture (Fig. 1.1) on the board.
Megan, one of those students who always sits in the first row, and who really has a true appreciation for the beauty of mathematics, had asked the perfect set-up question.
"But Professor Williams, what if the graph isn't smooth? What if it has a kink? How do you know which tangent line to use?"
I smiled. "Great question, Megan. I'm glad you asked." She returned the smile, pleased with the compliment. Megan tended to dress on the conservative side, and that day, she was wearing a tan cashmere sweater over a white blouse, with pearls and a matching tan skirt. Thora, who was sitting just behind Megan, and who had chopped purple hair and more piercings than I could easily count, gave a barely audible groan.
"Suck up," she muttered, just loud enough for Megan and me to hear. I ignored Thora's interjection. In fact, Thora was just as talented as Megan, but she did her best to hide it.
I drew this next picture (Fig. 1.2) on the board.
"At this point, any of these lines could be valid tangent lines. So there's no well-defined slope, and therefore no well-defined derivative. So the derivative doesn't exist at this point." Megan nodded as I spoke.
It was at this moment that through the window I noticed one of my perennially late students shambling toward class. He was looking particularly disheveled, and I wondered to myself about the appropriate tack to take when he entered the classroom. Charlie wasn't a bad kid, and he wasn't bad at the math either. He was just a serious flake who was too disorganized to attend class regularly or turn homework in when it was due. If I had to guess, I suspected the reason he was late this Friday was a drunken binge the night before. Thursday night parties were becoming more and more of a problem.
Although I anticipated the door opening, I continued on. "At all the other points on the graph other than the kink point, there is a perfectly good tangent line, and therefore, everywhere else the derivative is defined." Charlie still didn't enter. This distracted me to the extent that I finally crossed to the door and opened it. Charlie was standing in the lobby facing away from me.
"Are you going to join us, Charlie?" I asked.
He turned to look at me, his expression suggesting he didn't register who I was. But then his lips pulled back into what might have been a grimace and what might have been a bizarre smile. There was definitely something off-kilter about him. His eyes looked filmy, and his posture seemed all wrong. Spittle hung off his chin. That must have been some party.
He shuffled forward and I backed into the room, not sure what to make of him. He stopped when he saw row after row of students staring at him. I tried to regain my composure.
"Nice of you to join us, Charlie. Perhaps you would like to take a seat." I motioned to the front row.
Charlie lurched forward and instead of taking the seat I had intended, he fell on top of Megan. Initially I and all the other students assumed Charlie had tripped, and there was a broad giggle from the class. But almost immediately, Megan started shrieking, and suddenly blood was spurting out. Charlie made guttural snarling noises as Megan flailed about. It took me a moment to register what was happening, but then I leaped forward.
"Get off her!" I screamed. Grabbing at Charlie's arm, I tried to pull him back, but his teeth were embedded deep in Megan's neck. I pulled harder, putting all my weight into it, and the three of us toppled back onto the floor, with me on the bottom and Megan on the top. Charlie never released his grip as he climbed back on top of her and continued to chew on her neck.
Tom and Manuel, two of the biggest students in the class, both members of the front line of the football team, leaped up from their seats at the front of the room. They tended to sit near the door to make their escape as soon as possible. Tom grabbed Charlie around the waist and Manuel held onto Megan as Tom tried to pull Charlie away. There was a ripping sound and much of Megan's neck came off in Charlie's mouth. By now there was lots of screaming.
Charlie then turned around as Tom was struggling with him and bit Tom's nose off. At this point, people started bolting for the door, knocking each other over in an attempt to get out. Tom fell over backward screaming, and Charlie fell upon him.
"Get out, everyone get out," I cried over the tumult. Shrieking students scrambled out the door. Thora sat frozen in her seat. I grabbed her by the arm and pulled her up. "Run!" I screamed, as I pushed her through the door ahead of me.
Charlie continued to feast on Tom. I slammed the door behind me, and ran across the lobby to the department's administrative assistant's office. Having heard the commotion, Marsha was standing in her doorway. She was dressed in her usual color-coordinated manner. Today it was red high heels, red dangly earrings, red lipstick, and a short red skirt with matching red stockings.
"What's going on, Craig? Give back an exam today?"
I pulled her into her office and shut the door. "Call security! Call the Westbridge police! Call a SWATteam from somewhere! A student's gone completely insane. He's killed two students."
Marsha laughed. "It's a little late for April Fool's."
"No April Fool's," I said, handing her the phone. "Call! Call now!" She could tell by the tone of my voice that I wasn't kidding and she began to dial. I peeked out the door, but the lobby remained empty. All the students from my class had gotten as far away as possible. I realized I had to clear the building as quickly as I could. Cautiously, I stepped out into the lobby and pulled the fire alarm on the wall. As the alarm sounded, flashing blue lights strobed on and off in the lobby. Almost immediately students and faculty poured out of the classrooms into the lobby.
"Get away from the building," I yelled. "This is a real emergency. Get far away from the building." Within five minutes, the lobby was again empty. I then cautiously crossed to the door of the classroom to check that it was still latched shut. I could hear slurping sounds emanating from inside. Slipping out the front door of the building and keeping low, I snuck around the outside to the window I had looked out when I had first spotted Charlie. I peered in, and saw Charlie still chomping on Tom, blood oozing down his jaw.
I reentered the lobby as Marsha came out of her office.
"Security and cops are on the way," she said.
"Thank God," I said.
"What's going on in there?" she asked.
"You don't want to know," I replied.
"Actually, I do want to know," she said.
Before I could explain, we heard someone coming down the hall that connected the back door of the building to the lobby. It was Hoyle, the Westbridge police chief. Stuffed into his uniform like a sausage in its casing, he had a perpetually angry expression on his face. I had never been a particular favorite of his since the time I stood up at a town meeting and argued that we should cut the town's police budget. I didn't see the point of having three on-duty police officers for a town that averaged one crime every six months.
"What the hell is going on?" demanded Hoyle over the fire alarm. He ignored me and turned to Marsha. "Did you make that call?"
Marsha nodded and pointed at me.
"There's a crazy student in 106," I said as calmly as I could muster.
"So call Psych Services. Why're you calling me?"
"Umm, because he's killed two students."
"You're the one who sounds crazy right now," said Hoyle. "Did you pull the fire alarm?"
"Yes," I replied. "I had to get everyone out of the building."
He walked over to the alarm box, inserted a key and silenced the alarm. Then he walked over to the door to the classroom.
"Really!" I said. "He bit them, and then started eating them."
"A little late for April Fool's isn't it?" he replied, as he pulled out his gun, and reached for the door handle.
"I wouldn't do that," I said, as he pushed open the door.
From my vantage point I could see blood coating the linoleum. I could also see Charlie kneeling over Tom's prone form. But the sight that was the most disturbing was Megan standing in front of her desk. Her head was tilted at a funny angle due to the chunk of her neck that was missing, but she was definitely up and about. She saw Hoyle, gave out a guttural moan, and immediately moved for him. Lucky for him, as she stepped forward, her foot slipped in the blood on the floor, and she went down hard, her head bouncing on the tile.
Charlie looked up at this point and realized a better meal had presented itself. As he rose from the floor, I could see Hoyle fiddling with the safety on his gun. Charlie reached him just as the gun went off. Both Charlie and Hoyle went down.
"Oh, shit," I mumbled. I could see Megan struggling to get up, as Charlie sank his teeth into Hoyle's leg.
"Holy crap," cried Hoyle. "Help me!" He reached imploringly in my direction.
Hoyle's gun lay on the floor just out of his reach.
"Don't," said Marsha, but I couldn't just watch the rest of this scene unfold. I ran across the lobby and grabbed up the gun. Pointing it at Charlie's chest, I pulled the trigger. There was a loud explosion and the force of the bullet knocked him flat on his back. Hoyle started to crawl away. As I reached down to help him, Charlie inexplicably lifted his head off the tile. He seemed unfazed by the gaping wound in his chest as he reached out and grabbed at Hoyle again.
"What the hell," I uttered incredulously.
"Shoot him again," screamed Hoyle. I lined the gun up on the side of Charlie's face and pulled the trigger. Brains flew out the other side of his head, and he collapsed. Hoyle crawled out from under him and pulled himself through the doorway. I just stood there with the gun held limply in my hand. In the meantime, Megan had managed to regain her footing. She slowly stepped forward, seemingly aware that a fast movement would put her back on the floor. As she was reaching for us, I grabbed hold of the door handle and slammed the door shut. I was shaking uncontrollably. I had never shot a gun before, let alone at a student, crazed or not.
"Jesus Christ, that was some messed up student," said Hoyle wincing. "Help me up."
Hoyle wrapped an arm over my shoulder and I hoisted him to his feet. He motioned for his gun, which he reholstered. Then, as I supported him, he used his shoulder radio to call the police station.
"Chuck, pick up. We need serious backup ... Chuck. Come on. Pick the hell up. Where the goddamn hell are you?" He clicked off his radio in frustration.
"There's always supposed to be someone there," he said to me. With my support, he hobbled across the lobby.
Marsha motioned to the glass door of the lobby.
"Thank God. Here's campus security," she said. I saw Hollister, one of the college security guards, heading toward the building. Marsha clattered on her high heels to the door and pushed it open.
"Hurry!" she yelled as she held the door for him. At that moment, I noticed that Hollister's gait looked peculiar. He was not bending at the knee as he shuffled forward.
"Marsha, let the door go," I screamed as I pointed at Hollister. As he was reaching a crabbed hand for her, she suddenly grasped the reality of the situation and ducked back into the building, slamming the door. Hollister's face smashed up against the glass as he flailed about, desperate to sink his teeth into her.
Marsha sank back, horrified.
"What the hell is going on?" I asked to no one in particular, staring as Hollister continued to ram his face into the glass door.
"Oh, my God," whispered Marsha in horror. We watched as he tried to bite through the smooth surface, his saliva smearing the glass.
"We have to get out of here," said Marsha.
"Not sure that's such a good idea," I said.
"What do you mean?" demanded Hoyle. "Of course we have to get out of here."
"Look," I said. "In the last fifteen minutes, three people have either tried or succeeded in killing and eating others."
"So, that seems to be an argument for getting as far away as possible," said Marsha.
"Actually, it's not," I replied. "The point is that if two of the three people who have tried to enter the building are crazy, it is very unlikely that they are the only two who are crazy. But if a whole lot of people are crazy, then it's not so surprising that two who tried to come in are crazy. It's probability."
"So you're trying to say that there are lots of others who are nuts?" asked Hoyle. "And if we go outside, our chances of survival plummet?"
"That's exactly what I'm trying to tell you," I said. "Come on. We can check it out from the windows upstairs."
With Marsha on one side and me on the other, we managed to help Hoyle up the stairs to the second floor. As I pushed open the fire door to the stairwell, we collided with Angus. He was a student who had taken Calculus I with me two years previous and had somehow managed to pass the class, just barely. For some unknown reason, that had convinced him to be a math major.
"What's going on?" he asked. He used to ask that a lot in class, too. "I heard the fire alarm and a lot of screaming."
"We don't know exactly, but people are acting crazy," I replied.
"Very crazy," added Marsha.
From down the hall, I saw a head poke out an office door. It was Jessie, a professor in the Biology Department with a strong mathematical bent. She had been my wife's best friend, and my wife had helped her through a difficult divorce. When my wife was diagnosed with breast cancer, Jessie was there for us through the entire two-year ordeal, which culminated in my wife's death five years ago. After that, Jessie did her best to console me and help with my kids, and that led very quickly to an ill-conceived attempt at a relationship. But it had been much too soon for me. The relationship disintegrated quickly and after that we had avoided each other. But under the circumstances, these personal issues seemed suddenly peripheral.
"Craig, get down here," she called. With Angus and me helping Hoyle, we made it down the hall. Jessie locked the door once we were inside. Sitting in Jessie's office chair was Oscar Gunderson.
"Hello, Williams," he said. Those were the first words he had spoken to me in eight years.
Gunderson was tall and thin, with a shaved head and thick-rimmed, stylish, chunky, black glasses that looked out of place on his long face. He sported the carefully trimmed stubble that always looked to be much more trouble than the careless attitude it was supposed to project. His clothes always conformed to whatever Men's Style announced as the latest fashion.
Gunderson had arrived at Roberts College three years before me. As the hot young applied mathematician with a National Science Foundation grant to support his research and invitations to speak all over the world, he had cruised through the tenure process. Then, three years later, when I came up for tenure, I barely scraped by, as I was to learn afterward. I had plenty of papers, both single author and with my students. But Gunderson had been on my tenure review committee. He argued that my chosen field of low dimensional topology was dead, and that it would be a big mistake to tenure someone in an area that would soon cease to exist. He also argued that the fact I was publishing papers with students meant it couldn't be good work. Lucky for me, there had been other senior faculty in the department who believed in me, and I had received tenure in spite of his best efforts. Two years later, Perelman proved the Poincaré Conjecture using some of my work on Ricci flow. So my supporters were vindicated and I had plenty to work on for the next half century. I ignored Gunderson as we lowered Hoyle into a chair.
"Jessie, do you know what the hell is going on?" I asked. She motioned to her window, which gave a good view of the science quad.
Excerpted from Zombies & Calculus by Colin Adams. Copyright © 2014 Princeton University Press. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Table of Contents
CHAPTER 1 Hour 6 3
CHAPTER 2 Hour 7 19
CHAPTER 3 Hour 7 1/2 32
CHAPTER 4 Hour 7 3/4 48
CHAPTER 5 Hour 8 63
CHAPTER 6 Hour 9 80
CHAPTER 7 Hour 10 95
CHAPTER 8 Hour 18 111
CHAPTER 9 Hour 24 137
APPENDIX A Continuing the Conversations 155
APPENDIX B A Brief Review of Calculus as Explained to Connor by Ellie 191
What People are Saying About This
"If you're dying to read a novel treatment of calculus, then you should run (don't walk!) to buy Zombies and Calculus by Colin Adams. You'll see calculus come alive in a way that could save your life someday."Arthur Benjamin, Harvey Mudd College"Before Zombies and Calculus, math was quick to kill my appetite. In fact, math damn near killed me altogether throughout most of college (it is of course a cliché to say that as a math student I was pretty much a zombie). If I had only had this book then . . . at least now I can stomach derivatives as well as a zombie outbreak. That's no small accomplishment! Read Zombies and Calculusyou'll laugh . . . you'll cry . . . you'll multiply."Steven C. Schlozman, M.D., author of The Zombie Autopsies"Using a fictional, tongue-in-cheek account of an outbreak of a zombie virus at a small liberal arts college, Adams discusses mathematical subjects such as the spread of a disease in a population, differential equations, and tangent vectors. He succeeds in conveying the idea that calculus is useful in numerous aspects of lifeincluding surviving a zombie apocalypse. The book is one of a kind."Joel Hass, University of California, Davis"Zombies and Calculus shows how calculus can be used to understand many different real-world phenomena, from population growth to Newton's law of cooling. The fast-paced narrative propels readers forward, and Adams's style is humorous and compelling. I laughed out loud, in public, several times while reading this book. I had a hard time putting it down."Amy N. Myers, Bryn Mawr College"Zombies and Calculus is unlike just about anything I've ever read. It is both an introduction to assorted math concepts and an action-packed adventure story about escaping a zombie invasion. It's also laugh-out-loud funny in many places."Meredith L. Greer, Bates College