18.330: Introduction to Numerical Analysis

Welcome to the bastard child of mathematics and computer science. Not every mathematics problem is amenable to pen and paper. Not every computer science problem reduces to sorting. This is a class about how to use calculation to do math, and how to use mathematics to understand calculations. We will bridge the gap between dt and delta-t. We will learn how to solve simultaneous equations without the matrix inverse. We will find roots without the quadratic equation. And we will do it all with precision and accuracy.

Programs: During the course of lecture I will often use MATLAB to demonstrate an idea. The programs I use for this will be available to students: program directory

News

• The grader has his own exams to study for, so he will not be able to get the latest problem set back to me until wednesday morning, giving you (and I) a good reason to come to the last lecture.
• I'm planning on doing class evaluations this wednesday.
• I have started the problem set 6 log .
• I have updated the practice exam with answers.
• A typo on problem 3 was caught and fixed. BTW it is important that the tridiagonal matrix be symmetric for the problem to make sense.
• To do problem 4 on the current homework, it is a good idea to a bit about 1-d optimization. I realized that this morning and re-ordered the syllabus a bit. It is a little messy now, but I think it has to be so you have enough material to do the homework.
• I just noticed that May 12th was missing from my list of class days on the syllabus.
• I'm going to cover the method of conjugate gradients tomorrow. There is a very nice treatment of CG and steepest descent at this link .
• Someone I know is looking to hire a UROP to implement some large scale linear algebra factorizations. This would be an excellent way to develop some practical experience with the linear algebra material we covered. If interested, read this .
• Whoops! I just noticed that I had norms/conditioning scheduled for Friday and LAPACK scheduled for Monday. I have, retroactively, changed the syllabus. I had intended to do LAPACK Friday.
• I have made up another practice exam . Remind me to add the answers in next week. I have also created another preparation guide .
• I have started the problem set 5 log .
• I have reserved our room for MAY 03's exam. It is 2-190 again.
• I have started the problem set 4 log .
• I've added reading for next week because I am going to jump about in the book for the next couple of weeks.
• I've added an 'open problem' to the problem set. I'd like to see a solution, but I don't expect everyone to try it.
• I have re-ordered some of the material and events of for the class post-break. I also want to ask the class about where the second exam should be placed.
• correction to answer 3 on the practice exam.
• I have added answers to the practise exam.
• I have started the problem set 3 log .
• Upon request, I have whipped up a practice exam .
• Let me take this opportunity to remind you that I have office hours . If you are struggling with the material this is a very good way to get yourself back on track. I'm also generally around outside of office hours.
• I have added two integrals to problem 2. Now we have 60 points.
• It has been pointed out that I am 10 points short on this problem set. I will add a couple more integrals to it later today.
• The version of problem set 3 I put out this morning has an integral on it which diverges. I've changed it to fix this.
• I have written a preparation guide for your upcoming exam. Read it, and let me know if you have questions.
• For people curious about the tanh in clisp, it turns out that a couple of students were able to get very far without even looking at the source. I have put an account of all the findings and conjectures so far in this file . Feel free to write to me with any other interesting discoveries.
• Our exam (a couple weeks from now) will be in 2-190, so we will all have some elbow room.
• I was too rushed to do Newton form and got myself turned around last lecture. I think I should do this right, so I've made a small mod to the syllabus (de-emphasizing cubic splines a bit) and removed a problem from the pset.
• I have started the problem set 2 log .
• It seems like a good idea to have a log of responses to some questions.
• Apparently my stand on canned solvers was unclear. I have added a question and my reply. I also give away some of the digits for problem 2 to help you debug.
• I've been asked about my position on the use of canned solver routines. I hope this response clarifies the issue.
• In case you were curious about MRF types of methods here is a summary of many variants which were well-known in the 70s. If you find a modern textbook treatment of any such variant, I'd be curious to know about it.
• I modified the hint on problem 2 to give more guidance.
• I added a few more examples of perl and clisp in the comments of both of those files, for those of you unfamiliar with these languages. I don't think you need to know that much order to do experiments and make reasonably convincing arguments for your answers in the problem set.
• We have a TA now. Tong Hoon Suk.
• A number of people have asked me about the book and what assigned reading there is. I figure that where the topic for the day matches closely the text of some section of the book that you should take that as a hint to read up on it. I see the book as something to supplement the lecture in case you miss something or I don't have time to prove something which is proved in the book. Around the middle of the course I will jump to sections out of order, but I will try to make this clear. Also, occassionally, I will assign problems from the book on the problem sets.
• We've fixed the room problem. Now we will meet in 2-132. We get the projector and workstation, but we lose a bit of space.
• I'm putting together the new website for 2006. Still shuffling bits.

Schedule

Class days in red , holidays in blue , reg/add/drop dates in green

Lectures

Homework assignments

Your write-up should be clear, complete and concise. There is no need to turn in pages and pages of numbers. If you find yourself writing programs more than a page long, something is wrong. You should prune and edit your work to about one page per problem, while explaining clearly your approach and reasoning.

This this is not the sort of math course most students are used to, the first problem set will be weighted less, so that it can serve more as a guide as to how future homeworks should be done.

When it comes time to writing something up or producing a program to carry out a calculation, I want each of you to struggle individually and find the heart of the matter by yourselves. I am planning on assigning few enough problems that you will be able to have these growth experiences without it taking up too much of your time.

Cheating: given the weight on problem sets in this course, there is clear incentive to cheat. Let me outline where I stand.

• Group work: For this class, I am against it. The material taught in this class is best learned by practice, which is why so much of your grade will depend on homework assignments. While students may discuss approaches and techniques applicable to a given problem, when it is time to carry out calculations or implement algorithms, this is something each student should do individually. Any exchange of numbers, formula, or software between students is forbidden .
• Use of the web and other text or software resources: I am fine with that so long as proper attributions to the sources are made, such resources are equally available to myself and your grader that we may see them as well, and such resources are not derived from any homework done in 18.330 this term or past terms. It is really for your own good that you attribute third party contributions to your problem set (see example).
• Example: I see two copies of a homework assignment in which both students make identical mistakes or both have exceedingly original solutions which are nonetheless identical, and there is no clear explanation for this. Perhaps they both got their approach from some website and neither of them attributed this -- so credit your sources. If something like this occurs, I will keep my eye out for repeat occurences of it. At the end of the semester, if I feel there is enough evidence, I will call upon such students to justify themselves. Don't do anything suspicious, and there will be no problems.

There will be 6 problem sets in all. They will be weighted mostly the same (except the first).

A link might not work if the problem set has not been assigned. If a link fails and the problem set has been assigned, then email me.