Consider the two following important results in complex analysis (stated imprecisely of course):
1) The integral of a function over a closed curve is determined only by its behavior at the interior singularities. (Cauchy's Integral Formula)
2) A function takes on every value (except possibly...
I don't know how useful it is in "doing" physics, but I think learning complex analysis deeply fills a hole that every human being has in their heart after taking just real calculus, whether they know it or not. It's like standing in front of the Louvre and deciding whether to go in: it's not a...
I'm not really worried about the heaviness, I'm sure I can handle SICP after having dealt with the abstraction of real analysis. But signerror, why do you say that SICP is not about functional programming?
Molu
Wow, thanks signerror and Coin, really helpful replies. It seems to me from your examples that a lot of Python's power (apart from the convenient syntactical sugars) comes from it allowing a functional programming approach. So I think I'll start learning Python after I pick up a little purely...
Hi,
I've been programming for some time now, and I've learned the so-called industrial languages, like C, C++ and Java. Now I want to pick up a scripting language, but I'm getting confused by the variety. Even if I take the most well-known options, there are Perl, Python, Ruby and PHP. Which...
Hi,
I'm a 2nd semester student in the Indian Institute of Technology, Kanpur. My fields of interest are AI, particularly machine learning, pattern recognition etc. I have done a project on pattern recognition in the Indian Statistical Institute, Kolkata.
I've some ideas about constructing...
Ah, that's what I was looking for. Though irrationality measure seems a very difficult thing to wrap your mind around, so I don't know if we can effectively explain that in a short time period, but let's see. Incidentally, is there any particularly intuitive reason for e having the irrationality...
Ok, we could talk about that, but that's rather too basic for a 2nd sem undergrad class. Most of the students have already encountered that material in high-school, they would appreciate something slightly more challenging.
Hi,
I'm presenting a proof that e is transcendental, but I want to spice up the presentation a bit by exploring some interesting perspectives, such as connections to topology, abstract algebra etc. I've already selected the Lindemann–Weierstrass theorem as a possible candidate. Can you suggest...
Hi,
I'm looking for video lectures for the classic MIT course Structure and Interpretation of Computer Programs. While MIT OCW doesn't have any videos for this course, on the internet there seems to be at least two different sets of videos claiming to be of this course. It seems that one is...
I don't know why no one has mentioned this, but Crosson's writing has a strange quality, distant and dream-like, at once alluring yet alienating. He seems in exquisite command of the language without ever dominating it.
turbo, since you were writing code long before the computer scene took its...
Evolution bibliography [Urgent]
Hi,
I'm writing an article for my college magazine. As always, I'm already behind the deadline. I need to include a very basic bibliography on evolutionary theory. I've included Richard Dawkins's The Selfish Gene and The Extended Phenotype as introductory...
Evolutionary computing bibliography [Deadline-urgent]
Hi,
For my college magazine I'm writing an introductory article on Evolutionary computing, with the focus being on drawing parallels between Evolutionary computing vs the traditional paradigm and Lamarckism vs Darwinism. The problem is...
The allotment results are out, I've been allotted Mathematics and Scientific Computing in IIT Kanpur. I can specialise in CS, which means I'll have a very mathematically rigorous foundation in theoretical CS. That suits me very well. Thanks to everyone for their input.
Hi,
I used to take private tutions in chemistry from a researcher in inorganic reaction mechanism (55 years old). What do you think will be a suitable inexpensive parting gift to give to him? Last year I gave him Clayden, Greeves, Warren and Warthous's Organic Chemistry. Thanks for your help...
40 years down, I want to look back and say I've done something of some small significance, like developing an algorithm with important uses. What I don't want is looking back and realising that my only achievement has been attending lots of meetings, making lots of deals and bossing around lots...
Finally, a ray of light! I think I see this now. The rotational matrix does not describe the rotation of one specific vector, but the entire vector space, which introduces an extra DoF. Right? Thanks a lot. It feels great when the necker cube suddenly falls into place.
Molu
PhD without Masters? How does that work out? How much time is required? Does doing a PhD have any effect on a non-academic career? Also, what is the availability of R&D jobs and do they pay as much as managerial jobs? Thanks.
Molu
If I study CS, what I would like to do is do my Masters from somewhere like MIT, Berkley, CalTech, ETH Zurich etc and then take a R&D oriented private sector job that will require theoretical work.
Molu
How I wish I could do that! In India there is no option to double major (heck, very very few institutes allow you to minor, and not many allow for electives). A double major, even at the cost of an extra year, would be very desirable because of the greater variety of options available, including...
A question I've also dwelt on :redface: I gave up after learning that none of the fields I'm interested in has a significant number of girls, let alone pretty ones. For example in IIT Kharagpur, the B.Tech in CS has a total of one girl in its four years!
Actually, I don't like the engineering way of thinking (ie, throwing rigor and abstraction out of the window). But CS is more theoretically oriented than other engineering branches, where you can actually prove theorems. I also like programming, so I think I would enjoy CS.
In fundamental...
Physics or Computer Science? [Urgent]
Hi,
I just received my ranks in IITJEE and AIEEE (Indian entrance exams for technical education). As it stands, I have the option of pursuing an Integrated M.Sc. in Physics from an IIT (Indian Institute of Technology, Kharagpur probably) or B.Tech. in...
I understand that it's due to Pauli's exclusion principle. But how does that fit in with the Standard Model, where all forces can be classified as due to one of the four fundamental interactions? I mean, if a star is resisting a compressive force, that means an opposite force is acting. To which...
I was wondering something, a collection of fermions can resist compressing forces due to what is termed degeneracy pressure. I was wondering, which of the four fundamental interactions is this due to? Thanks.
Molu
I've thought long and hard but I really don't get this. How can the rotation of a vector *not* be described by 2 independent parameters? If I specify the change in angle with the z axis and the change in angle with the x-axis of the projection on the x-y plane, I've completely specified the new...
But aren't you talking about rotation of rigid bodies? A vector is characterised by three coordinates. If we take, for example, the spherical polar coordinate system, there is one scale coordinate and two angle coordinates. That means a pure rotation can be described completely by giving the...
Hi,
After obtaining the 2D rotation matrix (as a function of rotation angle) once by geometry and once by complex algebra, I tried to obtain it by invariance of the Euclidean metric. By this approach, the four elements of the 2D rotation matrix can be determined in terms of a single...
Hi,
I'm now in 12th grade and studying Physics, Chemistry, Math and Statistics. I'm in a dilemma over whether a B. Tech in computer science will be right for me. My other interest is physics, so if I do study comp, I'll like to work in the theoretical part, like AI and machine learning etc...
So, when the momentum imparted to the second magnet has a counterpart, but instead of being on an object it is being carried away by the propagating field?
Incidentally, Griffiths writes that it's possible to formulate classical electrodynamics as an action at a distance theory rather than a...
Hi,
I was wondering, is Newton's third law true? Let's say I've an electromagnet turned on at a constant intensity for a sufficiently long time for the field to have reached a point some distance away. At that point is another electromagnet, but turned off. Now I turn on the second...