As adults, we are expected to take responsibility for our decisions and our actions. At the same time, we are social beings and depend on the work done by others to carry out our own tasks. Thus, we need to trust others if we are not to re-invent the wheel all the time. However, the decision of whom we choose to trust and to what extent is our own. We need to take responsibility for such decisions.

In reverse, when people repose their trust in us, what is our responsibility towards them? Primarily, we should be clear on what is being promised. For example, in the context of providing software, it is our responsibility to put a best effort to:

• Provide specifications about how the program is supposed to work.
• Make the program work as per documentation.
• Make it possible to achieve long-term maintainability and usability.

I don't see anything there about catering to some users' desire to dump their responsibility for their own machines on software developers.

If you want to be treated like a child, there are companies that will ``parent'' you. Be warned that you may have abandonment issues later unless you use the opportunity to grow up!

Many of you seem to be confused about the role of classes/labs and examinations at IISER Mohali.¹

The above statement is based on the fact that almost all of you come for examinations and many of you miss a large number of classes/labs.

The purpose of examinations at IISER Mohali is for you to get a measure of how much you have learnt, and for the instructor to get a feedback on how much that has been taught has got across and what percentage of students have "got it". The marks and grades that result from examinations are a side effect!

To repeat, the grades that you get from examinations are not the primary purpose of the examinations.²

If you do not attend classes or labs, then there is no feedback to the instructor --- since she/he can think "Of course, the material I taught has not got across. The students are not attending."

Each faculty member at IISER has subject expertise that gives a unique perspective on the subject that is being taught. Missing their lectures is a way to ensure that you do not gain their insight. Reading the same material from a textbook is not the same thing as attending lectures. (Anyone, anywhere can do that --- even sitting at an internet cafe downloading books and courses ... and perhaps even reading them!)

So attending classes (not just being in the audience!) is an integral part of this process. Asking questions of the instructor/tutors is an equally important part.

The way the curriculum and the programme are structured, the emphasis is on learning not on grades. A student who meets the minimum CPI³ requirements is given a degree after doing all the required courses; The degree does not reflect the CPI!⁴ This means that if you tried to learn in some courses and failed to learn, but on average you learnt something substantial from many courses, you will still get a degree.

In fact, if you learn something substantial, you get a chance to show that in your final-year project which is weighted at 32 credits -- twice than the weightage of all courses in your least favourite subject in the the first two years!

In summary, take an interest in learning stuff at IISER Mohali ... the rest will follow.

Multi-Disciplinarity

The core program at IISER is multi-disciplinary. There will be courses in Physics, Mathematics, Chemistry and Biology as well as some courses in Humanties and Social Sciences and few other inter-disciplinary courses as well during the first two years.

Scholarships and Attendance

The INSPIRE and KVPY scholarships are provided by the DST as an incentive to students to take up studies in science. This means that students are expected to put in a "best effort" to learn what the program puts before them. "Scientists are those who face problems head-on rather than run away from them". In particular, students who do not put in such an effort ("bunk" labs and classes) should expect to lose their scholarship.

Duration of Program

The course structure described in the courses of study booklet, is the norm. Students are permitted to drop courses during a particular semester and take them later; this way they volunatarily create a "backlog course". However, the complete course requirement of the core and each major must be met in order to graduate. They can take up to 3 years to complete the core programme and up to 7 years to complete the whole programme.

CPI Requirement

The graduation requirement is a CPI of 5.0 after completing all the requisite courses (core, core elective, major mandatory, major elective, open elective, seminar and project courses). Completing a course means obtaining a letter grade A,B,C,D,F in the course. (Note that a CPI of 4.0 must be maintained to stay in the programme.)

Repeat Courses

In particular, there is no "repeat" requirement attached to an F grade. However, a student who is on probation is often required to repeat courses in order to raise her/his CPI above the threshold of 4.0. Only a student with an F grade can repeat a course. While registering for a repeat course during a regular semester, a student should drop some other course of similar or greater credit weightage so that the total weightage does not exceed the prescribed weightage for the given semester. At most two courses can be registered for during the summer semester.

Backlog Courses

There is no concept of "promotion" from year to year in the BS-MS programme. Students who repeat courses or drop courses or drop semesters, will find themselves "behind" their batch in terms of the number of requisite credits obtained; such students have a "backlog" of courses to complete. Students are permitted to take up to 7 years to complete the 5-year program in order to complete "backlog" courses.

Summer Courses

In order to assist such students in completing their program in time, summer courses are sometimes offered by faculty members during a specified 8 week period in summer. The offering of such courses is voluntary on the part of the faculty and enrollment by students in such courses is also voluntary on the part of the students. Moreover, only students with an F grade in a course may register for a summer course.

Registration for Electives and Projects

The course structure has a number of electives and a final-year project in two parts. Students must register for such courses by choosing an elective and providing their choice of possible project supervisors. However, such registration is subject to approval. The instructor of an elective course may ask a student to provide proof that they are capable of handling the course contents. This may include questions about courses they have already done. A faculty member may similarly ask searching questions of a student wishing to do a final-year project with her/him. Students may want to keep this in mind while acquiring F grades or dropping courses or semesters.

An Extreme Example

As an extreme example, suppose a to-be brilliant Mathematical Physicist joins the programme and gets A in all Math and Physics (non-lab) courses and an 'F' in all other courses. Let us calculate her CPI/SPI from semester to semester.

Semester I

            BIO101:F, BIO111:F, CHM101:F, CHM111:F, PHY101:A, PHY111:F,
            MTH101:A, IDC101:A, HSS101:F
            CPI=SPI= 80/19 = 4.2

            (IDC101 is programming which is mathematical enough!)

            (Loses scholarship as CPI < 6.0.)

Semester II

            BIO102:F, BIO112:F, CHM102:F, CHM112:F, PHY102:A, PHY112:F,
            MTH102:A, IDC102:F, HSS102:F
            SPI= 60/19 = 3.2; CPI = 140/38 = 3.7

            (Gets a warning and is put on probation.)

Semester III

            BIO201:F, BIO111:F, CHM201:F, CHM211:F, PHY201:A, PHY211:F,
            MTH201:A, IDC201:A, IDC211:F
            SPI= 80/18 = 4.4; CPI = 220/56 = 3.9

            (IDC201 is Astronomy/Astrophysics which is math/physics enough!)

            (Gets a termination letter and (say!) is allowed to continue
            on probation.)

Semester IV

            BIO202:F, BIO212:F, CHM202:F, CHM212:F, PHY202:A, PHY212:F,
            MTH202:A, IDC204:A, HSS202:F
            SPI= 80/19 = 4.2; CPI = 300/75 = 4.0

            (IDC204 is Theory of Computation which is math enough!)

            (Survives in the program (only just!) and chooses Math Major)

Semester V

            MTH301:A, MTH302:A, MTH303:A, MTH304:A, PHY302: A, IDC351:A
            SPI= 210/21 = 10.0; CPI = 510/96 = 5.3

Semester VI

            MTH305:A, MTH306:A, MTH307:A, MTH308:A, IDC402: A, IDC352:A
            SPI= 210/21 = 10.0; CPI = 720/117 = 6.2

            (IDC402 is Non-linear dynamics which is math/phys enough!)

            (Scholarship is restored as CPI has crossed 6.0!)

Semester VII

            MTH401:A, MTH402:A, MTH416:A, MTH411:A, PHY622:A, PHY301:A
            SPI= 250/25 = 10.0; CPI = 970/142 = 6.8

Semester VIII

            MTH406:A, MTH407:A, MTH408:A, MTH410:A, PHY635:A,
            SPI= 210/21 = 10.0; CPI = 1180/163 = 7.2

Semester IX

            PRJ501:A, HSS302:F
            SPI= 160/20 = 8.0; CPI = 1340/183 = 7.3

Semester X

            PRJ502:A, HSS304:F
            SPI= 160/20 = 8.0; CPI = 1500/203 = 7.4

The student graduates with Mathematics Major and enough Physics courses as well! (Note that the student has a total of 27 F grades!)

Can it be done with Mathematics Courses only? In other words, all the PHY/IDC open electives to be replaced by MTH electives and get F in PHY theory core as well. In that case, the CPI = (1500-4310-2*10)/203 = 6.7 (since the IDC201 course is ``too much physics'') which is enough to graduate. However, she won't escape the core years with successive CPI's of 50/19 = 2.6, 80/38 = 2.1 110/56 = 2.0, 160/75 = 2.1!

Numbers play multiple roles:

• As a way of counting. (Cardinals)
• As a way of ranking. (Ordinals)

For natural (finite) numbers, these different senses of the use of numbers coincide. (Though one can have some doubts when the numbers are really large!)

In the same way, mathematical objects can be considered in different ways:

• "Pure" set-theory. (Axiomatic set theory)
• Sets with some sort of structure. (Category theory)

Even for finite sets, these notions do not coincide! For example, there are many different finite groups of the same size.

Coming to the problem of "infinity". The simplest notions of infinity are:

• The set of natural numbers. (Cardinal aleph_0)
• The ordered set of natural numbers. (Ordinal small omega)
• Asymptotic points or points at infinity. (For example, the point (1:0:0) in projective geometry)

Each of the above have associated arithmetic and algebraic operations. For example, with counting numbers we have addition and as a consequence multiplication. With ordinal numbers we have the notion of a successor which can be used to define a notion of addition. The corresponding structure in sets is that of Boolean or sigma algebra of sets. Category theory also has its own notion of algebra called ``universal algebra'', which is like (but not quite the same as) the sigma algebra of sets (infinite sums and products need to be defined and may not exist!).

So to re-phrase the question, we are asking if the ordinary notion of arithmetic and algebraic operations extends to infinity.

At first glance it does. We can certainly perform Boolean operations with infinite sets. The problem is that the usual statements about these operations are sometimes no longer true and our intuition about algebraic identities would fail us.

For example, it is usual to say that multiplication is the operation of repeated addition. When the number of additions is infinite, it is not very evident what this means. We define the product of sets AxB which clearly explains what this operation (multiplication) is for sets.

Similarly, it is natural to think of addition as repeated successor operations, but it is not always clear what this means for the infinite successor operation. Again, ordinal succession is defined in a way that such an operation is meaningful through the notion of limit ordinals.

However, in each case some "obvious" results from the finite case are no longer valid.

It is worthwhile to extend notions from the finite to the infinite when this is useful in giving us expectations regarding questions (about finite sets!) that we could not have arrived at otherwise. (For an interesting example, have a look at the Goodstein sequence.)

As an addendum, I would like to add the naive re-statement of Skolem-Lowenheim.

Since language consists of countably many sentences, we can only hope to define countably many things and from a practical point of view we can only define finitely many things.

Thus, infinity is a notion that mathematicians handle with care, limiting the roles that it can take, so that playing around with infinity gives meaningful (and correct!) results about the finitely many things that we will actually encounter! Mastering this way of handling infinity with care is what a lot of mathematical training is about.

An important aspect of science is to look for patterns in the data and use that to grasp some simple underlying principles on the basis of which that data can be organised, studied, etc. Such a search for patterns is what mathematics (in its broadest form) is! Hence, it is no surprise that I would like to underline its importance.

Note that we are looking for simple principles. How does one understand simplicity? Is "simplicity" in the eye of the beholder? Indeed it often is! By the time we reach our teens we are looking at the world through thick layers of glasses of preconceived ideas --- some of them put there by our teachers --- and sometimes simplicity involves removing some of these filters/lenses.

The purpose of teaching is also simplification. Some may say that our purpose is to pass on the accumulated knowledge suitably distilled. However, "distillation" is insufficient to arrive at a learning time exponential lower than the time taken to collect the knowledge (note that what we teach in 12-15 years is based on 3000 years of data collection), unless this distillation involves simplification in a central way.

In other words, one of the functions of a teacher is to simplify what the teacher already knows --- and one measure of simplicity is that it should take the learner less time than it took the teacher to learn the same thing!

The bottom line for teaching-researchers is this: Do not tell your students that they need to spend years to learn something since it took you that long --- instead, do some research and try to simplify the material! [*]

What if everyone believed that law-abiding citizens should use postcards for their mail? If a nonconformist tried to assert his privacy by using an envelope for his mail, it would draw suspicion. Perhaps the authorities would open his mail to see what he's hiding. Fortunately, we don't live in that kind of world, because everyone protects most of their mail with envelopes. So no one draws suspicion by asserting their privacy with an envelope. There's safety in numbers. Analogously, it would be nice if everyone routinely used encryption for all their email, innocent or not, so that no one drew suspicion by asserting their email privacy with encryption. Think of it as a form of solidarity.

In other words, encrypting mail is a form of solidarity with the person who needs to say something private and confidential. It is also a form of insurance for the time when you are that person.

Twenty years on, this is not as commonplace as Phil Zimmerman imagined. The primary reason is that the public key infrastructure (the web-of-trust) that the authors of PGP thought would lead to an exponential spread of the use of PGP (or tools like it) has failed to grow in the manner envisaged.

The (to my mind) no-so-important reasons cited for the lack of encrpyted mail are the lack of computational power and the lack of security of mail contents. It is true that encryption creates a small overhead. It is also true that encrypted mail does not ensure security in any absolute sense. (Absolute security is absolutely impossible!)

So I find it amazing that, in institutions where this infrastructure is already in place, there are sensible people who argue that we should not do it.