The absurdity of US college textbooks

[5v333]

sorry i meant that the exam lasted for 5.5 hours. Atleast for me...
You were alone in a classroom with a blackboard. You got three randomly selected assignments, one at a time. One computational assignment from the book
and the other two were to prepare and give a lecture on a subject like electrostatics, fields in matter, special relativity, etc... No help from books or anything but the first 5 min. Then it was you and the board for as long as you wanted.
Holding speeches is not my thang!!!

I also think it was a little bit strange. They prob want to make it clear that students have got most on EM theory because it is needed in lots of the coming courses. The entire course was hard and diffuse. "Feynmans lectures on physics" saved me a lot. I have ordered the entire box!

Wow! A´s in every course. That is impressive!!! Well done!
PDE are among the best things in life!
Did you have any strange lin alg courses?

 

[user 37518]

sorry i meant that the exam lasted for 5.5 hours. Atleast for me...
You were alone in a classroom with a blackboard. You got three randomly selected assignments, one at a time. One computational assignment from the book
and the other two were to prepare and give a lecture on a subject like electrostatics, fields in matter, special relativity, etc... No help from books or anything but the first 5 min. Then it was you and the board for as long as you wanted.
Holding speeches is not my thang!!!

I also think it was a little bit strange. They prob want to make it clear that students have got most on EM theory because it is needed in lots of the coming courses. The entire course was hard and diffuse. "Feynmans lectures on physics" saved me a lot. I have ordered the entire box!

Wow! A´s in every course. That is impressive!!! Well done!
PDE are among the best things in life!
Did you have any strange lin alg courses?

That oral exam you described sounds scary AF! 5.5h ? that is worse than my doctoral examination, were you alone in the exam or were other students also present with you? 5.5h, man, I teach college courses, I can't believe that your teacher would have the patience of being there 5.5h, he/she is at a whole different level...

Feynman's Lectures on Physics are great. TBH, I only have the volume on EM because I am not that interested on the rest. But all of them are definitely worth the read.

Yes I had a strange lin alg course, well, every course has been strange and I expect that this PDE course will be strange as well. The names of the courses give a false impression of being predictable, but they are nothing of what you would expect. For example, last semester I took a course on Ordinary Differential Equations, I was a bit bored before it began because I imagined it would be on methods of how to solve DEs, problems involving DEs, etc... Nothing whatsoever, it was basically a 100% linear algebra course focused on DEs, it was all about analysis of stability and behavior of the solutions, transforming systems of DEs into canonical matrix forms using transformation matrices, vector spaces, eigenvalues and eigenvectors, creating phase portraits and analyzing its behavior depending on initial conditions and other parameters, analysis of dynamical systems, etc... not your conventional undergraduate DE course, and every undergrad DE text I own (like Zill, etc..) proved to be useless for this course. The problems in the textbook we used were considerably hard as well, with zero solutions at the back of the book to throw you a bone in the right direction.

As a side note: I have noticed that some mathematicians sometimes like to give books names that give the false impression of being simple and dumb but are completely the opposite. For example, "Basic Mathematics" by Serge Lang, a rockstar mathematician (RIP), yes the book focuses on the basics but many parts are extremely hard and it is not for kids as the name would suggest. He also has a book simply called "Algebra", but any middle grade student would rip his eyes out with it, since it is a graduate book on Algebra. I guess that the worst is a book I have called "Elementary Theory of Equations", and let me tell you, there is nothing 'elementary' to it. I think there is a lot of pride to these sort of names, it is like their way of saying: "you think you know something? you don't know anything, not even the simplest math" or "I am so great that I can make something simple harder than you can imagine". Perhaps I am mistaken, but that is the impression that I get. But it also shows that every subject in math, like Algebra (something we take for granted), is much more deeper than one would expect.

P.S. It is probably worthless for me as an engineer, but I hope I am able to take number theory in one of the next semesters.

 

[5v333]

Thanks for sharing. Im laughing through some of this

Yeah solving equations on matrice form with eigenvalues and such is really cool.
Did you work with nilpotent matrcies and other disturbed matrices aswell?
We worked with such and innerproduct rooms in my last lin alg course
and it was too abstract most of the time actually... but very interesting.
All this is common stuff in physics ive been told.

We were alone in each class room during the exam. I think we were four students at a time. I guess after about 4 hours new
students arrived and was placed in a free rooms or something like that. The exam period elapsed during 3-4 days in total from 0900 in the morning to 1800 in the evening.
The feeling about the exam during the course hasnt exactly been contributing to low stress levels...

5.5 hours was partly due to a lot of waiting
for them to come and examine each assignmnet.

 

[user 37518]

Thanks for sharing. Im laughing through some of this

Yeah solving equations on matrice form with eigenvalues and such is really cool.
Did you work with nilpotent matrcies and other disturbed matrices aswell?
We worked with such and innerproduct rooms in my last lin alg course
and it was too abstract most of the time actually... but very interesting.
All this is common stuff in physics ive been told.

We were alone in each class room during the exam. I think we were four students at a time. I guess after about 4 hours new
students arrived and was placed in a free rooms or something like that. The exam period elapsed during 3-4 days in total from 0900 in the morning to 1800 in the evening.
The feeling about the exam during the course hasnt exactly been contributing to low stress levels...

5.5 hours was partly due to a lot of waiting
for them to come and examine each assignmnet.

Since this is an applied math master's, most of the focus was spent on dynamical systems, and the variation over time of the solutions. I already knew about the eigenvalue/vector solution of systems of DE's, but this went way beyond that. A lot of time was spent on the analysis of the solution behavior, and parametric equations, and how very small variations could wreck havoc, something in the field of chaos theory, it was really interesting. The book was written by a Fields Medal recipient. You can check the textbook we used Differential Equations, Dynamical Systems, and an Introduction to Chaos. It even has some applications to Electrical Engineering

 

[5v333]

sounds cool!

and thanks for the book advice.

 

[user 37518]

Dont forget, true mathematicians say the words "If and only If" almost all the time.

I remembered your post because this was one of the first things I had to learn before proving theorems. The difference between "only if" and "if and only if" statements. I thought you might be interested in this.

It is not so much of an obnoxious way of speaking, but it rather has to do with logic, that is if two or more statements are true. The statement "only if" is used when something is true one way but not in reverse, and "if and only if" when it is true both ways. Let me illustrate with an example I got from a book. Important: The "only if" statement is equivalent to saying "if.... then...."

Statement A: A triangle with two equal sides is isoceles.
Statement B: A triangle with three equal sides is equilateral.

Which means that all equilateral triangles are also isoceles.

So we can say: "A triangle is equilateral only if it is isoceles". This is true, because if a triangle is not isoceles it can't be equilateral. That is, if two of its sides are not equal, it gets discarder right away as not being equilateral without having to check the third side. You could rephrase it and it means the same thing: "If a triangle is equilateral then it is isoceles".

But the opposite is not true, that is "A triangle is isoceles only if it is equilateral", because a triangle can be isoceles but not equilateral. So we can't say "A triangle is equilateral if and only if it is isoceles" because it is not true both ways.

However we can say "A triangle is isoceles if and only if it has two equal sides", because it is true both ways, that is: "A triangle is isoceles only if it has two equal sides" and the opposite is also true "A triangle has two equal sides only if it is isoceles" (or rephrased as "If a triangle has two equal sides then it is isoceles").

Very related to the "only if" and "if and only if" statements are the terms necessary and sufficient. So for the same example we can say "A triangle being isoceles is a necessary condition for being equilateral", because an equilateral triangle has to be isoceles to be equilateral, but it is not a sufficient condition, because just being isoceles doesn't guarantee that it is also equilateral. Likewise we could say: "A triangle being equilateral is a sufficient condition for being isoceles", because if a triangle is equilateral we already know it has two of its sides equal, but we cannot say it is a necessary condition because it is not required for a triangle to be equilateral to be isoceles. So "only if" usually means that something can be necessary or sufficient but not both.

However, we can say "A triangle having two equal sides is a necessary and sufficient condition for being isoceles". Because an isoceles triangle has to have at least two equal sides (necessary) and if it already has two equal sides that is enough (sufficient) for being considered isoceles. So "if and only if" usually means something is necessary and sufficient.

Hope this makes sense

 

[5v333]

I would love to learn, someday, how to work with proofs etc.

 

[Matador]

For those who like digital logic, A 'if and only if B' is the same as 'A XNOR B', or the result is true if both are true, or both are false.

 

[user 37518]

For those who like digital logic, A 'if and only if B' is the same as 'A XNOR B', or the result is true if both are true, or both are false.

Wouldn't it be XOR rather than XNOR, XNOR would be false if both inputs are false or true, and only true when they are different. Unless of course you consider the false output as your desired result.

 

[user 37518]

Update: That course in Cryptography that I'm taking is really beating my ass, I will be lucky if I get a C as a final grade. It is full of theorems, modular math, group theory, rings, abstract algebra, and lots and lots of proving stuff.....

It is extremely interesting though. Basically, most cryptographic systems are based on the difficulty of solving something called the Discrete Logarithm Problem. As an example, you raise an integer to an exponent (another integer) using modular arithmetic, and you transmit that number over the internet, but computing the logarithm (to get the exponent back, that is, the reverse operation of exponentiating) in modular math is extremely difficult, especially when large numbers are involved. That exponent that you used originally is basically used to encrypt and decrypt a message, so if someone knows the exponent, he or she can easily decode the message, but finding the value of the exponent by brute force is insanely difficult (that is what is called solving the Discrete Logarithm Problem), you basically need a computer to try out many many numbers to see which one produces the desired result, the security of the algorithm is based on the assumption that the current state of computing technology would take millennia to solve it by trial and error, so they use massive numbers to insure that no computer will find the solution in a reasonable amount of time. Quantum Computing seems to be causing a headache to cryptography scientists, since it could be used to solve these sort of problems much faster.

Of course everything I said is an over simplification and there is a lot more to it, but that is the gist of it.

 

[john12ax7]

I took cryptography with a renowned professor in the field, his real world stories made it quite entertaining. I might have some notes and papers if you think they would be useful.

 

[user 37518]

I took cryptography with a renowned professor in the field, his real world stories made it quite entertaining. I might have some notes and papers if you think they would be useful.

Thanks! Sure, whatever you have is useful. Do you have a degree in Math or Computer Science?

 

[john12ax7]

Actual degree(s) are EE. But took a whole bunch of classes in various fields for "fun".

 

[user 37518]

Update: if anyone cares, I was miraculously able to barely score an A in Cryptography. It was one of the most demanding courses I've taken so far. It required a good basis (which I didn't have) on Abstract Algebra and Number Theory, as well as proof writing skills (which I lack). Overall, it was very interesting learning how this stuff works, and trying to break the codes. I programmed stuff in MATLAB using parallel computing to break the simplest of Elliptic Curve encryption and RSA keys (which are used by most Internet companies like Facebook and such), small 5-6 digit numbers took like 5 minutes to break with all my CPU cores working at the same time, the current RSA uses 4096-bit keys, so it is practically impossible to break by brute force.

Anyway, 5v333, what about you? How did QM treat you?

 

[john12ax7]

That's interesting, was the matlab part of the course or something you did on your own? When I took it (two courses) was all pen and paper theoretical stuff, no computers involved. Would have preferred to have some practical real world implementations.

 

[user 37518]

That's interesting, was the matlab part of the course or something you did on your own? When I took it (two courses) was all pen and paper theoretical stuff, no computers involved. Would have preferred to have some practical real world implementations.

Part of it required implementing algorithms, wasn't strictly MATLAB, some used Python, the parallel computing stuff arised more from a necessity rather than a requirement. Solving the discrete logarithm on an elliptic curve field to break a code took more time than I was willing to accept, which is why used parallel fors and similar stuff.
I also had to develop several codes for many things, testing the primality of a number, verifying a digital signature, summing or multiplying points on an elliptic curve field, and so on. I believe I enjoyed the algorithmic side much more than the theoretical side. Some theory problems were really hard, and involved a lot of proofs, but the other stuff was much more enjoyable.

 

[5v333]

Well done!
If QM = quantum mechanics then
It whent great. Turned out i liked alot about it and the mathematics. I have got heisenberg on my mind most of the time...

Subatomic though is a different story.
Look up fermis golden rule for ex

We have three labs and rapport to do at the same time while the book and lectures are as dry as it gets...
Not my subject...


Scored high on QM, Mathematical physics and analytic functions/transform theory.

 

[user 37518]

Well done!
If QM = quantum mechanics then
It whent great. Turned out i liked alot about it and the mathematics. I have got heisenberg on my mind most of the time...

Subatomic though is a different story.
Look up fermis golden rule for ex

We have three labs and rapport to do at the same time while the book and lectures are as dry as it gets...
Not my subject...


Scored high on QM, Mathematical physics and analytic functions/transform theory.

Nice to hear that. Yes, I meant Quantum Mechanics.

To be honest, Quantum Mechanics seems to me like a good exercise of mental gymnastics, fantasy and mathematics. Honestly, I've taken quantum mechanics before, but mostly oriented towards semiconductor physics. And, really, the stuff really doesn't work as they want you to believe, or rather, it kinda works. I mean, the stuff at the microscopic level does work, but when they start talking about what the electron does at the atomic level, we are now in fantasy land. Scientist will arrive at equations that don't work, which they have to fudge by adding "empirical constants" or terms (which is their way of making reality fit their theory, rather than the theory fit reality) and attribute the differences to "second-order effects", which is their way of saying "we don't know what the hell is going on". In the end, semiconductor caracterization is made by behavioral analysis and modeling, which is a fancy way of saying trial and error, and curve fitting to experimental data.

The statistical distributions do not work universally, you have to use Fermi-Dirac when Maxwell-Boltzman fails miserably for certain application, but you have to return to the latter in other applications because the former fails. In my opinion, QM 'kinda' explains some things, but it has lots and lots of patches to make it work. I still believe that the probabilistic nature of it is not completely true, and that is not my own opinion, some Nobel laureates agree with me (or rather I agree with them). To give an example, and I think I have already have mentioned this anecdote before, a colleague of mine (with apparently has some time to spare) was once messing around in an Excel spread sheet, he had a circle enclosed by a square, and he was adding random points at the figure. I don't remember exactly how the process worked, but, for example, if you averaged the points that lied outside the circle but inside the square and divide it by something (again, I don't remember the exact process) you would get the value of pi. In any case, both he and I thought it was very interesting that you could derive pi from a random probabilistic process, however, it would be a mistake to assume that the relationship between the circumference and the diameter of a circle (pi) has a probabilistic nature. I think the same thing happens in QM, the probabilistic approach kinda works (just like in the circle) but it doesn't mean that reality is like that. [/rant]

 

[5v333]

Mental gymnastics, fantasy and mathematics.
Sounds like physics!

I actuly did a matlab script in the begining of my program that simulated the thing with the square and the circle.

The sceptical physician you are thinking of might be Einstein.

 

[user 37518]

Mental gymnastics, fantasy and mathematics.
Sounds like physics!

I actuly did a matlab script in the begining of my program that simulated the thing with the square and the circle.

The sceptical physician you are thinking of might be Einstein.

Yes, Einstein was very vocal about it, but some modern and current physicists are still claiming the good old "God doesn't play dice" originally pronounced by Einstein.

The circle and square stuff seems like one of the least objectionable ways to waste some time these days

 

[5v333]

from wiki

Einstein was gracious in his defeat. The following September, Einstein nominated Heisenberg and Schroedinger for the Nobel Prize, stating, "I am convinced that this theory undoubtedly contains a part of the ultimate truth."

 

[user 37518]

from wiki

Einstein was gracious in his defeat. The following September, Einstein nominated Heisenberg and Schroedinger for the Nobel Prize, stating, "I am convinced that this theory undoubtedly contains a part of the ultimate truth."

Nevertheless it's not the whole story

 

[user 37518]

During the summer semester I will be taking a course on something regarding applications of linear algebra, plus another course on regression analysis. This last one sounds very interesting, apparently, it involves using a software called STATA to handle huge data sets and create regression analysis out of it, plust other stuff, I have to check the syllabus more carefully. I guess it might have some Data Science orientation, which is like a very hot topic today in many industries. I honestly have zero interest on learning anything regarding machine learning or AI.

What about you, what is up in store for next semester?

 

[user 37518]

Well done!
If QM = quantum mechanics then
It whent great. Turned out i liked alot about it and the mathematics. I have got heisenberg on my mind most of the time...

Subatomic though is a different story.
Look up fermis golden rule for ex

We have three labs and rapport to do at the same time while the book and lectures are as dry as it gets...
Not my subject...


Scored high on QM, Mathematical physics and analytic functions/transform theory.

During the summer semester I will be taking a course on something regarding applications of linear algebra, plus another course on regression analysis. This last one sounds very interesting, apparently, it involves using a software called STATA to handle huge data sets and create regression analysis out of it, plus other stuff, I have to check the syllabus more carefully. I guess it might have some Data Science orientation, which is like a very hot topic today in many industries. I honestly have zero interest on learning anything regarding machine learning or AI.

I might be able to finish the entire degree during the fall semester, but I would have to take an extra course at a time, I don't know if it is wise because it is a capstone course, which are usually harder. I am thinking about doing something regarding Network Synthesis using some numerical methods (e.g., the Simplified Real-Frequency Technique) for the capstone course, but let's see how it goes.

What about you, what is up in store for next semester?