Courses:

The two semesters of 6.011 presented here together display a variety of modes of interacting with the students. One version of the class gave each student the choice of including homework assignments in their final grade or not. In one of the terms, a "common room" was made available several evenings each week to assist students in completing their homework assignments. This room was used as a means for students to meet weekly with the faculty (lecture and recitation instructors), teaching assistants, and their peers, in order to work together to resolve any questions they had concerning the class material. During one of the terms, the instructor met weekly with a group of student representatives from each of the recitation sections. Students were encouraged to contact these representatives with comments and questions that would be provided as feedback to the instructor. In both semesters, occasional optional lectures on background material were offered.

Review the syllabus for the Spring 2005 version of the class.

The essential prerequisites for this course are mastery of 6.003 and 6.041 (or equivalents), and of the 18.03 material related to solving linear, time-invariant systems of first-order differential equations using eigenvalues and eigenvectors. You should certainly not plan on taking 6.011 if you got less than a C in 6.003 or 6.041. If you did get a C (and maybe even if you got a higher grade than that!), some further remedial work in the corresponding subject is important, starting immediately. If you are unsteady with 6.003, 6.041, or the relevant 18.03 material, you can be sure that 6.011 will expose that fact, sooner or later!

Do not plan on taking any other class whose meeting times have any overlap with those of 6.011.

To sign up for this course, you will need to go through the procedure, which will collect the information needed to make recitation section assignments and so on. Please do this by 5 pm on Thursday, one day after lecture 1. As backup, we also ask that you fill out the sign-up sheet and turn it in. However, recitation assignments will only be made for students who have signed up electronically, and homework will only be accepted from students who have signed up electronically. Section assignments will be available on the MIT server (On Tuesday and Thursday of the first week of classes you may attend any of the recitations since we won't yet have made recitation assignments.)

We have scheduled a couple of optional review lectures to go over essential background material that you should have seen in the prerequisite courses, but which you may be rusty or uncomfortable with. These sessions are scheduled for 11:00-12:00 (same time and place as regular lectures), on the following Fridays:

Lecture 1: Basics of Probability

Lecture 3: Exponentials as Eigenfunctions of LTI Systems, CT and DT Fourier Transforms

Lecture 7: Basic Matrix Notions, Linear Systems of Equations, Eigenvalues/Eigenvectors

If you think you might benefit from attending these sessions, mark them now in your calendars.

Attendance and participation in recitations are required (in order for you to do well in the subject! - we can't enforce attendance and participation, of course, so it's ultimately up to you). Recitations - no less than lectures - are critical to your mastering the material and doing well in the subject. They provide an opportunity for you to clarify and work with concepts and results from lecture in an informal and interactive setting, focusing on specific problems and illustrative applications chosen by the recitation instructor. It is largely between recitations and homework (and tutorials, if you decide you need them) that your understanding of the subject gets consolidated. Get to know your recitation instructor, both in recitation and open hours. (You're welcome to attend the open hours of other recitation instructors, too, and, of course, the lecturer's open hours.)

Final decisions about recitation hours and assignments will be made after all the sign-up information is tallied. We will accommodate your first or second choices of recitation hour, according to the preferences you indicate when you sign up on the MIT server (and on the attached sheet). After the initial assignments are made, we will consider further changes only if these do not significantly unbalance the different sections, because such imbalances would not be fair to your classmates or to the recitation instructors. For all such change requests, contact the TA.

You are given two options regarding the weekly tutorial sessions: you may choose to make the commitment to attend tutorials every week, in which case you will have a regular, weekly time reserved for you; or, you may sign up for an available tutorial slot via the Web and on a week-by-week basis.

If you elect to be assigned to a regular, weekly tutorial session, you are expected to attend that tutorial each week. If you miss your assigned tutorial, you will lose your reserved time for the remainder of the term, but will, of course, retain the option of signing up for a tutorial session on a weekly basis.

To select the option of a reserved, regular, weekly tutorial time, please complete and sign the tutorial sign-up sheet. You may request a reserved tutorial time now, or at any time during the term.

The tutorial sessions are optional and are strictly limited to five students at a time. For students without a reserved weekly time, one may sign up via the MIT server. Please sign up for one slot at a time each week; if you want to sign up for a second slot in any given week, please, wait until you have attended the tutorial session for the first slot you reserved before you sign up for the second. If you do sign up for a tutorial slot, then you will be expected to attend. If, after signing up, you find you will be unable to attend for whatever reason, please let the appropriate TA know at least a day in advance, so that the slot can be cleared for someone else (repeated failure to do this will not be viewed kindly!). If all posted slots fill up, we will try to schedule additional ones, so send mail to the TA and check back later.

The tutorials will, in effect, function as the TAs' primary office hours, so bring your questions to them. Don't necessarily expect the TAs to have prepared questions and problems for you - the burden will be largely on you to articulate what you are having trouble with, and to give examples of the kinds of things you are getting stuck on. You should expect to go to the board and help work things out alongside your TA or fellow students. The tutorials are not intended to be mini-lectures or mini-recitations.

Although tutorial sessions are optional, all students are encouraged to attend and participate. At the end of each term, several students invariably suggest that tutorials should have been required rather than optional, either because they benefited greatly from them, or because they recognize (too late!) that they would have benefited from them. Do the smart thing, and sign up for tutorials if you're having the least bit of trouble with the course! If your quiz and exam scores are poor and your attendance at (recitations and) tutorials has been poor too, then you should not expect to be given the benefit of the doubt in our final discussions of course grades.

We urge you to use the time that the staff makes available as open hours, so bring in your questions or comments. The staff wants to see you! If you're stuck on something that does not seem to yield to your efforts, ask for help - that will be seen as a sign of involvement and interest in the course, rather than as an admission of failure or incompetence.

There will be two evening quizzes: Quiz 1, after lecture 12, and Quiz 2, after lecture 20. Each will be designed as a one-hour quiz but you will have two hours to do it: 7:30pm-9:30pm. A three-hour Final Exam will be held during exam week. The quizzes and exams will all be closed-book, but you will be allowed a specific number of sheets of notes for each of them (details will be announced closer to test dates.)

Homework will generally be handed out in lecture on Mondays, and be due in recitation on Tuesday of the following week. Solutions will generally be handed out in the lecture following the submission date. Some parts of the homework will involve MATLAB® exercises. It is assumed that you already have some familiarity with MATLAB® from 6.003.

As described in the handout titled Homework Contract (PDF), you are asked to choose between two options, Option 1 in which you do not hand in homework and it is not graded, and Option 2 in which your homework is graded. If you do not explicitly choose Option 2 by signing the Homework Contract, it will be assumed that you have chosen Option 1. Late homeworks will be accepted only for the most compelling reasons, and only if the TA assigned to your section is informed on at least the day the homework is due. A homework turned in after the solutions are posted runs the risk of just being recorded as "submitted", with no grading or scoring (again, occasional exceptions may be made at the discretion of the TA or recitation instructor).

Your solutions for each problem set will be given a score of:

• 0, if there is little evidence of any original thought or work - e.g. if a solution is quite clearly lifted from solutions distributed in an earlier term!
• 1, for some attempt, but with significant gaps;
• 2, for good effort, but with some deficiencies in understanding; or
• 3, for a solid effort, demonstrating good understanding.

Additional comments on questions or solutions related to homework should be solicited from the staff, after you have studied the solutions that we will be handing out for each problem set. Don't leave your comparison and study of our solutions and yours till the night before a quiz!, make sure this is a weekly effort. To facilitate this effort, you may want to make yourself a copy of your homework solutions before you turn them in!! This will allow you to begin comparing your solutions with ours as soon as you pick up ours, rather than waiting till your solutions are returned a week later (by which time we will be into other things). This copy will also be valuable in those instances in which homeworks go astray somewhere along the way after you submit them (though rare, this has happened in the past, and those students who haven't kept a copy have generally regretted not doing so).

It should be evident from our grading policy that we do not intend the homeworks as tests, but as vehicles for learning. We will therefore not hesitate to use problems from previous terms again. Relying on "bibles" to get you through the homeworks - rather than on your own thinking and understanding - will undoubtedly cause you difficulties on the tests. You can expect that every test will include problems of the same flavor and difficulty as those encountered on the homework, but sufficiently modified to test your thinking and understanding, rather than your ability to "pattern match".

Solutions to problems labeled as "Optional'' on the homework do not need to be turned in. However, we select these problems with the same care as the assigned problems. They will give you valuable practice and/or bring up important issues, so you're likely to find them helpful to do as time permits, either along with the other problems or in reviewing for the exams.

We expect each of you to put in enough time alone to understand the specific difficulties and issues raised by each problem. Moderate collaboration on homework problems with one or two of your classmates may be useful for some of you. Discussions with the staff are encouraged, especially since this is the best way for the staff to get to know you. (When grades are assigned at the end of the term, comments from staff who know a student often push up a borderline grade, and rarely pull down a borderline grade.) There is no harm in seeking minor assistance from others who are knowledgeable but not involved in the class, although we would much prefer that your discussions be with those in the class. We expect you to independently write up the actual solutions that you turn in, and to note on your solutions the name of anyone you have collaborated with or obtained help from, and citations of all reference materials you have used in any significant way.

The final grade in the course will be based on our best assessment of your understanding of the material and your participation in the course. The relative weighting given to the written components of the course in arriving at a preliminary grade will be:

Factors such as your interaction with the staff and your participation in recitations can also affect the final grade, particularly if your preliminary grade falls near a borderline.

The process of assigning a final grade involves considerable discussion among the staff, and very often involves a careful review of the final exam to look behind the numbers and understand better the kinds of mistakes that were made. We know that the final grade is important to you, and we take the process seriously.

The essential prerequisites for this course are mastery of 6.003 and 6.041 (or equivalents), and of the 18.03 material related to solving linear, time-invariant systems of first-order differential equations using eigenvalues and eigenvectors. You should certainly not plan on taking 6.011 if you got less than a C in 6.003 or 6.041. If you did get a C (and maybe even if you got a higher grade than that!), some further remedial work in the corresponding subject is important, starting immediately. If you are unsteady with 6.003, 6.041, or the relevant 18.03 material, you can be sure that 6.011 will expose that fact, sooner or later!

Do not plan on taking any other class whose meeting times have any overlap with those of 6.011.

The lectures, recitations and homework in 6.011 will teach you more about signals, systems and probabilistic models. We will also explore prototype problems and applications from communication, control and signal processing that involve deterministic and/or random signals and systems in discrete and/or continuous time (DT, CT). The problems we tackle will involve aspects of analysis, synthesis and optimization. The ideas, approaches and methods you learn here will significantly expand the range of engineering applications that you will be able to understand and work with at some level.

What will be new relative to 6.003 and 6.041? The list includes most of the following (we won't necessarily hit them all this term): new kinds of signals (e.g., random processes); new signal properties (e.g., energy/power spectral densities, correlations); new kinds of systems (e.g., for CT communication of DT signals); new system descriptions (e.g., state-space models for causal systems); new system properties (e.g., group delay, reachability/observability); new signal processing tasks (e.g., multirate processing, optimal estimation); new communication tasks (e.g., optimal detection); new control tasks (e.g., state estimation, observer-based controller design); and more intimate mixing of DT and CT in several applications.

These topics do not fall on a linear path from 6.003/6.041 to some hypothetical next stage in your study of this area. Rather, we will be expanding out in a spiral, sampling the many routes that lead out from 6.003/6.041, coming back to some of them one or two times. At the end you may be surprised to find how much territory you have covered without moving all that far away from the basics in 6.003 and 6.041.

Mondays and Wednesdays at 11:00 - 12:00. For missed handouts, see your TAs.

Attendance and participation in recitations are required (in order for you to do well in the subject! - we can't enforce attendance and participation, or course, so it's ultimately up to you). Recitations - no less than lectures - are critical to your mastering the material. They provide an opportunity for you to clarify and work with concepts and results from lecture in an informal and interactive setting, focusing on specific problems and illustrative applications chosen by the recitation instructor. It is largely between recitations and homework (and tutorials, if you decide you need them) that your understanding of the subject gets consolidated. Get to know your recitation instructor, both in recitation and in office hours. (You are welcome to attend the office hours of the other recitation instructor too.)

Final decisions about recitation hours and assignments will be made after all the sign-up information is tallied. We will try to accommodate your first or second choice of recitation hour, according to the preferences you indicate when you sign up on the attached sheet. After the initial assignments are made, we will consider further changes only if these do not significantly unbalance the different sections, because such imbalances would not be fair to your classmates or to the recitation instructors.

The optional tutorials will be run by the TAs on a sign-up basis, strictly limited to five students at a time. Sign-ups are done on the MIT server. Please only sign up for one slot at a time each week; if you want to go to a second slot in any given week, wait till you've attended the first before you sign up for the second. If you do sign up for a tutorial slot, you will be expected to attend. If, after signing up, you are unable to attend for some reason, please let the appropriate TA know at least a day in advance, so that the slot can be cleared for someone else (repeated failure to do this will not be viewed kindly!). If all posted slots fill up, we will try to schedule additional ones.

The tutorials will in effect function as the TAs' primary office hours, so bring your questions to them. Don't necessarily expect the TAs to have prepared questions and problems for you - the burden will be largely on you to articulate what you are having trouble with, and to give examples of the kinds of things you are getting stuck on. You should expect to go to the board and help work things out alongside your TA or fellow students. The tutorials are not intended to be mini-lectures or mini-recitations.

Although tutorials are optional, all students are encouraged to attend and participate. At the end of each term, several students invariably suggest that tutorials should have been required rather than optional, either because they benefited greatly from them, or because they recognize (too late!) that they would have benefited from them. Do the smart thing, and sign up for tutorials if you're having the least bit of trouble with the course! If your quiz and exam scores are poor and your attendance at (recitations and) tutorials has been poor too, then you should not expect to be given the benefit of the doubt in our final discussions of course grades.

We have reserved a room from 6:30pm onwards on MTW each week (the three days preceding the Thursday that homework is due), for you to drop by if you'd like to work on homework, reading, etc., alongside other 6.011 students. We'll aim to have at least one staff member there for a good part of 6:30-8:00pm each of those three nights. These hours will serve as the primary "open hours" for the staff, with other hours being available by appointment.

We urge you to use the time that the staff makes available as open hours, to bring in your questions or comments. The staff wants to see you! If you're stuck on something that does not seem to yield to your efforts, ask for help - that will be seen as a sign of involvement and interest in the course, rather than as an admission of failure or incompetence.

There will be two two-hour evening quizzes, at 7:30-9:30pm:

• Quiz 1: Six days after lecture 12
• Quiz 2: On the day of lecture 20. (Note: This is apparently the same day as the 6.012 midterm, so let Prof. Verghese know early if you are taking 6.012, so some arrangement can be worked out).

The quizzes will be designed as challenging one-hour exams, but you will have two hours to do them.

A three-hour Final Exam will be held during exam week.

The quizzes and exam will all be closed-book, but you will be allowed a specified number of sheets of notes for each of them (details will be announced closer to test dates).

The final grade in the course will be based on our best assessment of your understanding of the material and your participation in the course. The relative weighting given to the written components of the course in arriving at a preliminary grade will be:

For anyone who is interested in doing a term paper that develops some portion of the subject in an interesting way, perhaps connecting it to an application, we offer a term-paper option. Submit a one-page proposal to Prof. Verghese in the last lecture before spring break, in lecture 13. You are welcome to have some prior discussion with him on your choice of topic, and he may suggest topics from time to time during lectures. If your proposal is accepted, a rough draft of the paper will be due by lecture 21, and a final version (10-15 pages should be fine) by two days after lecture 24. The term paper will count for 10% of the grade, and the weight on the final exam will be reduced to 25%.

Factors such as your interaction with the staff and your participation in recitations/tutorials can also affect the final grade, particularly if your preliminary grade falls just below a borderline.

The process of assigning a final grade involves considerable discussion among the staff, and very often involves a careful review of the final exam to look behind the numbers and understand better the kinds of mistakes that were made. We know that the final grade is important to you, and we take the process seriously.

Homework will generally be handed out in the Wednesday lecture or sent you by email sometime by Friday of a given week, and will be due in recitation Thursday of the following week. Solutions will generally be posted on the MIT server by 9pm on the submission day, and paper copies of the solutions will be made available on the shelves outside the TA offices at 5pm that day. Late homeworks will be accepted only for the most compelling reasons, and only if the TA assigned to your section is informed on at least the day the homework is due. A homework turned in after the solutions are posted will most likely be just recorded as submitted, with no grading or scoring (again, rare exceptions may be made at the discretion of your TA).

Make for yourself a copy of your homework solutions before you turn them in, so that you can begin comparing your solutions with ours as soon as you pick up ours. If you don't do this comparison soon after you turn in the homework, you are unlikely to do it till the night before a quiz, and by then it will be WA-A-A-Y too late! Again, make for yourself a copy of your homework solutions before you turn them in! This copy will also be valuable in those instances in which homeworks go astray somewhere along the way after you submit them (though rare, this has happened in the past, and those students who haven't kept a copy have generally regretted not doing so).

Some parts of the homework will involve MATLAB® exercises. If you have never worked with MATLAB®, you should start getting familiar with it right away. The time you invest in learning it will assuredly be worthwhile in the long run at MIT and quite likely in your career beyond as well.

Your solutions for each problem set will be given a score of:

• 0, if there is little evidence of any original thought or work. Caution: We are good at detecting when a solution is simply lifted from one distributed in an earlier term, or copied from a classmate's. Any instances of such mindless copying will result in disciplinary action. If the term gets hectic and you find yourself tempted to take such shortcuts, resist the temptation! - you will gain little, if anything, and you may lose a LOT! Instead, take this temptation as a signal that you need to re-balance your time; either give 6.011 the time it needs, or drop it.
• 1, for some attempt, but with significant gaps;
• 2, for good effort, but with some deficiencies in understanding; or
• 3, for a solid effort, demonstrating good understanding.

If you're following the course well and doing the homeworks attentively, you should expect to be getting 2's and 3's on your homeworks.

Additional feedback on questions related to homework should be solicited from the staff, after you have studied the solutions that we hand out. Once more: don't leave your comparison and study of our solutions and yours till the night before a quiz! - make sure this is a weekly effort.

The above grading policy should make clear that we do not intend the homeworks as tests, but as vehicles for learning. We will therefore not hesitate to use problems from previous terms again. Relying on "bibles" to get you through the homeworks - rather than on your own thinking and understanding - will undoubtedly cause you difficulties on the tests. You can expect that every test will include problems of the same flavor and difficulty as those encountered on the homework, but sufficiently modified to test your thinking and understanding, rather than your ability to "pattern match".

Solutions to problems labeled as Optional on the homework do not need to be turned in. However, we select these problems with the same care as the assigned problems. They will give you valuable practice and/or bring up important issues, so you are likely to find them helpful to do as time permits, either along with the other problems or in reviewing for the exams.

We expect each of you to put in enough time alone to understand the specific difficulties and issues raised by each problem. Moderate collaboration on homework problems with one or two of your classmates may be useful for some of you. Discussions with the staff are encouraged, especially since this is the best way for the staff to get to know you. (When grades are assigned at the end of the term, comments from staff who know a student often push up a borderline grade, and rarely pull down a borderline grade.) There is no harm in seeking minor assistance from others who are knowledgeable but not involved in the class, although we would much prefer that your discussions be with those in the class. We expect you to independently write up the solutions that you turn in, and to note on your solutions the name of anyone you have collaborated with or obtained help from, and citations of all reference materials you have used in any significant way.