Math 2041 - Symbolic Computation Lab I Professor: Mike Zabrocki email: Meetings: Tues 11:30-1:30 :: Thurs 11:30-12:30pm Gauss Lab Ross S110 Office hours: TEL 2028 - Monday 1-3pm, Thursday 4-5pm This model was designed by one of my students and printed out on a 3d printer

Course description:

Calendar copy: An introduction to symbolic computing in the Maple environment. Topics from single-variable differential and integral calculus, including simple ordinary differential equations, are covered. Both mathematical understanding and applications are emphasized. Three lecture hours, open laboratory hours. One term. Three credits. Prerequisites: SC/CSE 1540 3.00 (formerly COSC) or equivalent computing experience; SC/MATH 1010 3.00 or SC/MATH 1014 3.00 or SC/MATH 1310 3.00.

Many of the technological advances that come from scientific innovation depend on efficient means of computation and analysis of large amounts of data. Before digital computers became widely available, these sorts of computations were largely done by hand or with the aid of mechanical calculation tools or tables. However, for every computation tool that we have available, there are always mathematical problems that are beyond the limits of our computational power. For example, the ability to factor an 800 digit integer which is the product of two primes or find the determinant of a large matrix is out of the reach of our current computational tools.

This course will use the program Maple to answer numerical and discrete computation questions which would otherwise be too difficult to do by hand or the use of a simple calculator. Maple is an example of a Computer Algebra System (CAS) but other examples such as Sage, Mathematica and Matlab are similarly capable of doing a wide range of computations and other many specialized programs (such as R, GAP and Macaulay) are particularly efficient at certain types of computations.

Your assignments will be to complete worksheets and computation tasks and the grade for the class will also include the results of in class tests and quizzes.

There will be four components to this class: assignments (35%), quizzes (30%), a midterm (15%) and a final (20%).
assignments - will be given usually once per class when there are not quizzes (some may take more than one class period). You are encouraged to work together with other students to get the answer, but each person should follow along on a different computer and hand in their own work and hand in/upload their own answer. Each assignment will have its own instructions for what you need to do to complete the assignment.
quizzes, midterm - a short assignment (the midterm will be slightly longer) that you will be expected to do within the class period and hand in DURING THE CLASS TIME. There are 5 quizzes scheduled. You may drop one.
final - this will be held during the final exam period and will be similar to the assignments and quizzes but longer.

To be clear: SHARING FILES IN THIS CLASS IS A DEFINITE 'NO!' Failure to follow this instruction will result in immediate F on the assignment (for all parties involved) followed by referral to the dean of FSE.

### Course schedule

 Lecture dates Topic/sections in text 1 Sept 6, Thurs Maple is a calculator; main goal today: get set up, some problems to get started 2 Sept 11, Tues Go over all the different ways to solve assignment 1, assignment #2 - manipulating strings 3 Sept 13, Thurs assignment #2 4 Sept 18, Tues assignment #3 5 Sept 20, Thurs Quiz #1 6 Sept 25, Tues Go over assignments #2 and #3, assignment #4 7 Sept 27, Thurs assignment #4 8 Oct 2, Tues Complex numbers, taylor series, assignment #5 9 Oct 4, Thurs Quiz #2 10 Oct 9, Tues assignment #5, talk about functions and assignment #6 11 Oct 11, Thurs class cancelled, continue to work on assignment #6 12 Oct 16, Tues assignment #6, assignment #7 13 Oct 18, Thurs continue to work on assignment #7 14 Oct 23, Tues Midterm 15 Oct 25, Thurs assignment #8 16 Oct 30, Tues assignment #9 15 Nov 1, Thurs No class 17 Nov 6, Tues Quiz #3 18 Nov 8, Thurs assignment #10 19 Nov 13, Tues assignment #11 20 Nov 15, Thurs Quiz #4 21 Nov 20, Tues assignment #12 22 Nov 22, Thurs assignment #13 23 Nov 27, Tues Finish up all assignments 24 Nov 29, Thurs Quiz #5

### Announcements:

(Tuesday, September 6, 2012) - There is a lot of information needed to get started.
You will need to get a key card for access to this lab. Here are the instructions.
You will need to activate your AML account for the lab. We will try to do this in class today.
I am not going to recommend a book for this class. We will mostly use the online help system. Some people like to have a textbook to follow along with, but the goal here will be to complete some tasks and learn how Maple (and other Computer Algebra Systems) can be used as a calculator.

(Tuesday, September 6, 2012) - While I will be teaching this course around Maple, I myself use Sage which is an open source programming language centered around the python programming language. It is more advanced and not supported on the lab computers. If you know a little bit of Maple already, have your own laptop, and want to graduate on to something a little more challenging please talk to me.

(Tuesday, September 6, 2012) - There will be an additional site for this course called a Moodle where you can log in an submit your assignments but typically I will post all announcements here.

(Tuesday, September 6, 2012) The course Moodle is up. You should be able to sign in. If you are unable to log into this web site please follow the instructions here.

(Saturday, September 8, 2012) The first day we got set up on the computers and played around with Maple. I gave you a few exercises to get started with Maple. The exercise was not graded, but it is important that you know how to answer similar questions for quizzes and tests. You will need to learn how to learn to succeed in this class. You should check in with me if you did not during this first class.

(Saturday, September 8, 2012) You can access Maple from home with an internet connection. You will need to download a client. The instructions for doing this are here. I have also found that you can access Maple 6 (text version) if you ssh to unix.aml.yorku.ca and then at the unix prompt type "maple".

(Thursday, September 13, 2012) A handful of people have finished assignment #2. We aren't going to do something new in class today so if you are finished so you are off the hook until Tuesday. Turn your assignment in on the Moodle.

(Thursday, September 27, 2012) Just a reminder about collaborating.... I really like it when you work together in groups to solve these problems. In case you haven't noticed that there isn't quite enough of me to go around to answer all questions. Some of you have lots of questions and don't get the kind of attention that I would like to give you. While I want you to ask your neighbor and get help solving the question, I DRAW THE LINE AT SHARING FILES. It is easy to see when this happens and I will refer cases to the department or the Dean and there is an automatic penalty of 0 for everyone involved. On the quizzes I am very explicit and I would like you to work alone on those problems.

(Thursday September 27, 2012) As you found on the first question of assignment 4 that the sequence that we were looking at is not in the OEIS database. Sad. Someone should add it (hint, hint, although make sure you start at $n=0$). If you want a formula for it I was able to figure it out after class. Let $g(x) = \frac{1}{(1-x)^2}$ and let $\zeta = e^{2\pi i/3}$. $\zeta$ is called a third root of unity because $\zeta^3 = 1$. Let $f(x) = (g(x) + g(\zeta x) + g(\zeta^2 x))g(x)/3$, then if you take the taylor expansion of $f(x)$ you will find $f(x) = 1 + 2x + 3x^2 + 8x^3 + \cdots~.$ Try out the command f:=(1/(1-x)^2+1/(1-exp(2*Pi*I/3)*x)^2+1/(1-exp(4*Pi*I/3)*x)^2)/(1-x)^2/3; and then map(expand,taylor(f,x,16)); and you should see the sequence from this problem. If you want to know why this is (a) come ask me at my office some time (b) take my fourth year course Math 4160.

(Monday October 22, 2012) I've posted two more solutions to the assignments 5 and 6. Unless someone asks for a solution to assignment 4, I wasn't planning to do that one.

(Monday, October 29, 2012) Since classes aren't being held on Thursday, I won't be holding my office hours Thursday afternoon either. If you need to see me then, please either schedule an appointment for another time (I can make Tuesday at 4pm this week).

(Tuesday, October 30, 2012) Do you want to see the interaction of mathematics and computers in action? York is hosting a conference on the programming language APL (A Programming Language) this Thursday. The event is called APL@50 http://www.cse.yorku.ca/museum/apl50/. This is a great opportunity to meet people in industry and computer science.

(Tuesday November 20, 2012) We will have a final in this class and it will be on the computer. It will be a similar format to the rest of the class and closer to the midterm than the assignments and quizzes.

(Thursday November 29, 2012) The FINAL EXAM will be in the Gauss Lab Thursday, December 13 2012 at 2pm-5pm.

(Thursday November 29, 2012) For this class I can tell you a few things that you should be able to do in Maple for the final : manipulate lists and strings, loop through a set of values and count the number of times some condition is true, find the area between two curves (polar, rectangular), find the length of the curve (polar, rectangular), find the minimum/maximum of a function in an interval, find the minimum/maximum of a surface or equation subject to a constraint equation, plot all types of functions, take the real and imaginary parts of complex numbers, write functions and procedures which return values, compute sequences of integers which are defined recursively, solve equations or determine when two graphs of functions intersect, convert between rectangular and polar coordinates, compute tangent vectors and normal vectors.

(Thursday November 29, 2012) I'm sorry that I haven't got the grading done for this class. I've been trying to tackle it but I haven't had a lot of time this term. I expect to make progress on it next week.

(Thursday, November 29, 2012) The undergraduate office reminded us that the number of students filling out course evaluations is quite low. Please fill out a course evaluation for this class at http://courseevaluations.yorku.ca.

(Thursday, November 29, 2012) I will try to post some practice problems for the final for this class here at least a week before the exam. Check back soon.

(Thursday, November 30, 2012) I will have office hours December 4 from 12-1:30pm. I will also be available Wednesday December 5 from 10am-12pm.

(Monday, December 10, 2012) Some practice problems for the final is posted below. We have done problems like these all term. They make take a while do to, but you should know how to do similar calculations.

(Wednesday, December 13, 2012) The following email message was sent to everyone on the class list.

This is an announcement about the Math 2041 exam that will take place December 13, 2012 from 2-5pm.
* bring a piece of photo identification
* do not log into the computers before the start of the exam
* access to the lab will be restricted to our class
* The internet will be disabled during this time except for access to the Moodle
* you will *not* have access to the computer file system
* You will have access to Maple and the Maple help pages
* You may bring a USB stick with your files
* You may bring a (single) reference book if you feel it is necessary, but the the scope of the exam does not extend beyond what we have encountered in the assignments in this class so it is probably not necessary.
* additional instructions will include the obvious: no phone or other communication device, do not look at your neighbors work
If you have any questions, email me.
-Mike Zabrocki

(Thursday, January 3, 2012) grades have been posted to the university system. The grade on the moodle is a flat average and not weight to the distribution described above (assignments 35%- quizzes(best 4 of 5) 30%-midterm 15%-final 20%).

### Handouts:

(September 8, 2012) assignment 1
(September 11, 2012) assignment 2
(September 13, 2012) Solution to first assignment problem #1 in html
(September 13, 2012) Solution to first assignment problem #1 in maple worksheet
(September 13, 2012) Solution to first assignment problem #2 in html
(September 13, 2012) Solution to first assignment problem #2 in maple worksheet
(September 18, 2012) assignment 3
(September 25, 2012) Quiz 1
(September 25, 2012) assignment 4
(September 27, 2012) Solution to assignment 2 maple worksheet (right click and save)
(September 27, 2012) Solution to assignment 3 maple worksheet (right click and save)
(October 2, 2012) assignment 5
(October 4, 2012) Quiz 2
(October 8, 2012) assignment 6
(October 16, 2012) assignment 7
(October 22, 2012) Solution to assignment 5 Question 1 maple worksheet (right click and save)
(October 22, 2012) Solution to assignment 5 Question 2 maple worksheet (right click and save)
(October 22, 2012) Solution to assignment 6 maple worksheet (right click and save)
(October 23, 2012) Midterm
(October 25, 2012) assignment 8
(October 28, 2012) assignment 9
(October 29, 2012) Solution to assignment 7 maple worksheet (right click and save)
(November 6, 2012) Quiz 3
(November 8, 2012) assignment 10
(November 13, 2012) assignment 11
(November 13, 2012) Quiz 4
(November 20, 2012) assignment 12
(November 23, 2012) assignment 13
(November 29, 2012) Quiz 5
(December 10, 2012) Practice for the final