# Math for Life and Social Sciences.

York University, 2013-14

## >news.

• 1 May, 2014 - Marks are finally posted! I ended up curving all four segments of the overall mark (Webwork, quizzes, midterm, and final) by computing the mean and the number of standard deviations of each individual score from the mean. This is called a z-score. I then applied a 'bump' to everyone's z-scores to improve the class average and ensure that at least one person had an A+ in each category. (In other words, your grades are a bit higher than they would be under a completely unbiased curve.) For example, for the webwork, if your z-score was higher than 0, it was multiplied by 1.67 to deal with the heavy clustering of the class near the maximum possible number of points. The class average on the final was 100.4 points, which was actually the highest for any of the 1505 sections if I understand correctly. So good work team. I'll set an 'office day' for Tuesday, May 6th in case anyone wants to see their exams. I'll be around my office from 9-4, minus lunch hours.
• 5 Apr, 2014 - A bit of a change to office hours for tomorrow: I'll be around my office to answer questions from 10:30-12:30 and from about 3-5 on Monday.
• 31 Mar, 2014 - Here's some brief solutions for the midterm.
• 5 Mar, 2014 - The final exam will be held on April 8th, at 7pm.
• 26 Feb, 2014 - Abd has kindly set up a Facebook group for the page; you can find it here.
• 13 Jan, 2014 - There's a survey about the class available here. If you have a few minutes, please fill it out. Your responses will be completely anonymous; the class rep is collecting the data and delivering it to me with the student id numbers removed.
• 8 Jan, 2014 - Welcome back! First quiz of the second half of the course is on 15 January, then every other week after that. There's also new WebWork up, due next Tuesday at midnight. Finally, here's a link to problems from the book for the rest of the year.
• 10 Dec, 2013 - Practice midterm solutions. Page 1, 2, 3.
• 8 Dec, 2013 - A couple things: I'll be in my office Tuesday from 10am to noon to answer questions. Second, after thinking a bit about putting up WebWork problems, I think it's probably more productive to study the problems from the book, which are common to all the sections of 1505.
• 30 Nov, 2013 - There's a practice midterm here. (Updated on Wednesday Dec 4th to include a linear algebra problem.)
• 26 Oct, 2013 - We didn't quite get started on derivatives last week, which were in the WebWork, so I've extended Set 5 by a week, and have not put up a new set for this week.
• 9 Oct, 2013 - There's a free 'background' class being offered by Bethune, if you feel you're having trouble with the course.
• 7 Oct, 2013 - There is a quiz coming up on Wednesday, October 9th. Finally, I'll be on the road on Friday, so we'll have a substitute on that day.
• 26 Sept, 2013 - I wrote some short notes about the applications I talked about in class on Wednesday. This won't be on any tests or quizzes, but gives some nice exmaple of different ways of thinking about matrices, in a way that comes up very often in applications.
• 20 Sept, 2013 - I've added information about tutorials and PASS in the 'essential data' section. I've also put up some more webwork about linear systems. This isn't due until October 2nd, but could be useful practice for the quiz on Wednesday the 25th.

## >essential data.

• Course Number: Math 1505, Section G
• Lecturer: tom denton
• Email: sdenton4 at gmail dot com
• Office: TEL 2026
• Class Time: MWF, 9.30-10.30am
• Office Hours: MW, 10.30-11.30am
• Book: Neuhauser, either the full book or the (cheaper!) York-specific edition

Tutorials:

• Wedneday 10:30am-12:30pm, HNES 034
• Friday 2:30-3:30pm, Ross S133

Class Reps:

There is also a Math Lab in S525 Ross, open from 10:30a-3:30p, Monday through Friday. It's a good place to work and have people on hand to talk to and get help from.

More help is available from PASS, Peer-Assisted Study Sessions, given through Bethune. These are free, and happen on Tuesday from 5:30-6:30pm, and Friday 4-5pm. Bethune also has peer tutoring sessions every day of the week for 1505. All of the services are given by previous students who have previously scored at least an A in the class, so the advice should be helpful!

## >homework.

Graded homework for the class will be given via the WebWork system, starting during the second week of classes. WebWork problem will account for 10% of your final grade. The problem sets will open on Wednesday and be due each Tuesday at 11:59pm, unless otherwise noted.

WebWork

If you have problems with logging in or other issues with webwork, you should start by asking either of our two WebWork TA's: Haohan or Farid.

For additional problems to work on, there are many problems in the book. Odd-numbered exercises have solutions in the back that you can check against. Here is a list of practice problems for the sections we'll be covering this year.

## >philosophy.

Calculus is the mathematical study of change. The world is constantly changing around us; calculus is useful for helping us understanding and predicting the way that things change, and has numerous applications in all branches of science, from astrophysics to zoology. It also has applications that aren't obviously problems about 'change,' such as in optimization. Our goal is to learn the basics of calculus, understand the underlying concepts and to learn to use some of the techniques of calculus.

I generally approach life as a big sequence of games with rules that I might or might not understand. But we play the games anyway, and do our best. And when we start playing a new game, we tend to do badly or ok, but as we play more and more, we develop strategies, optimize our approaches, and figure out systematic ways of approaching the game. And then spreadsheets get involved, which essentially means that we're tracking data and using some kind of math to help improve our strategies.

One example from my own life is bicycling. I used to race bikes a bit, and still love going on long bike rides. When I got started, I would go on long rides with friends, go fast down and up hills, wander the backroads of Oregon for days or weeks at a time, sleeping on the side of roads beneath the innumerable stars. And eventually I joined the UC Davis bike team and started training pretty seriously. At this point, I started getting a bit obsessive about things like my average velocity under different conditions like going up or down hills, heart rate, pedalling cadence, and so on. I ended up with lots of equipment to measure these sorts of things, and a spreadsheet keeping track of all kinds of different variables. And this is the broad story of applied science: you get kind of obsessive about something, start collecting data, and then use some combination of math and reasoning to figure out new things from all of this data.

This class is about the math.

Calculus broadly falls into three big ideas:

1. Limits. What happens when a tortoise bicycles halfway to the finish line, then halves the distance again, and again, and again, and so on to infinity? Does he actually get there, or does he get stuck in this never-ending sequence of "halfway-there"s? This is called Zeno's paradox, and it was a problem for the Greeks because they didn't like the concept of infinity. Zeno made it clear that infinities are all around us, if we look closely, and that if there is to be math in the world, the math will have to be able to deal with these sorts of problems. Limits are how we deal with Zeno's paradox, and a host of other spinning infinities.

2. Derivatives. Derivatives are for exactly measuring rates of change. For example, if I'm bicycling at twenty-three kilometers an hour, that's the rate at which my position is changing with respect to time. But what if my velocity is changing with time, perhaps because of the hills and headwinds I encounter along the way? How do I measure the rate at which my position along the road is changing?

3. Integrals. Integration is about the accumulation of things over time. If I am able to track my velocity - the rate at which my position is changing - I can use that information to determine how far I've travelled. Add up changes over time, and you get the total accumulation.

Over the course of the year, we'll make these ideas precise and learn mathematical tools for approaching these kinds of problems. In the end, we'll also look at some basic probability, which is vitally important for understanding the only-somewhat-predictable world we live in.

One last note: Increasingly, we-the-scientists-of-the-world use computers to do the kinds of computations you'll encounter in this class. All of the computations we will do are trivial to do by computer, but completely reasonable to do by hand. We learn how to do some computations because it helps us better understand the concepts, and gives us an idea of what we're doing when we use a computer for mathematics. (In fact, blind computation is often worse than no computation at all.) As such, what matters are the concepts of the course: only knowing how to do the computations is actually useless.

## >structure.

This is a year-long course, one of eight sections being offered. We'll have a shared midterm with the other sections during the December testing period, and a shared final during the April testing period. These will count for 30% and 50% of your total grade, respectively. The final 20% will come from a combination of in-class quizzes and online homework. Details for the online homework will be made available by the second week of the class.

## >ground rules.

A few things to keep in mind.

1. Commit to Learn. Math can be difficult, but should be approached like mountain climbing. It takes some endurance, but you get some amazing views once you get to where you're going. But actually getting there means sucking up some pain along the way, and pushing through things that might not seem very fun or interesting on a day-to-day basis. And you won't get there unless you really commit to doing what it takes to get through.

2. Work (almost) Every Day. Cramming doesn't work. Period. No, really, cramming doesn't work. Cramming means maaaybe getting through the test, and then forgetting everything shortly thereafter. You'll get the most out of the class by doing a bit of work every day; you'll internalize concepts by seeing them every day.

3. Don't Be a Flake. Show up to tests. Do the assigned work. Don't make excuses. There won't be make-up assignments or extended deadlines in this class, so you need to keep on top of things. It is a very large class.

4. If You Do Flake, Own It. I don't want to waste time sorting out good excuses from bad excuses. I prefer to hear that you missed a deadline and are doing X to keep it from happening again, than to hear that your grandmother's dog died of tuberculosis. Which leads nicely to...

5. Prioritize Your Life. Are you here to go to classes or to do your extracurriculars? Structure your time accordingly. As someone who is involved in a great variety of things outside of mathematics, I know it's possible to achieve a good balance. But be ready to decide what comes first when a choice has to be made.

## >frequently asked questions.

• What calculator can/should we buy/use?
For in-class quizzes, no calculators will be allowed. Problems will be structured so as not to require calculators. To that end, it's better to leave answers in exact rather than decimal form: write "sqrt(2)" instead of "1.414....", for example. Answers should be moderately simplified: cancel things that obviously cancel, and don't bother doing long multiplication problems. I prefer to see something like "1091*245" than to have you waste five minutes actually getting the number 267295.
• Which edition of the book can/should we buy/use?
There are many possible choices. The recommended version if you're buying a new book is the York-specific softcover, which is a bit cheaper and has all the material we'll be covering in the course. If you're buying used, there is also a hardcover version available; the second and third editions are both fine.

## >resources.

We live in the future! There are piles of great resources for learning calculus freely available on the interwebs. Often, the best way to learn something is to have a central text (our course textbook and class notes), and then to branch out to other resources if something doesn't click; often hearing something explained in different ways helps us build understanding. So here are a few other resources to consult when you're stuck.

1. MIT Open Calculus Text: An excellent and very extensive set of calculus notes.  Note the Equation List, and that there are notes (not necessarily in the same order) for most or all topics to be discussed in class.

2. Khan Academy: Calculus The Khan Academy has short, topical videos on many, many topics in mathematics, including calculus.  If you're unclear on a concept or stuck on a homework problem, it is a good idea to try watching the Khan Academy video to achieve a better understanding.

3. Jason Grout's webpage has links to a number of free calculus textbooks and other resources.