Hello everyone,
I'm currently doing some research about feedback systems in engineering and right now I'm playing around with special types of feedback matrices. In the process, I stumbled upon a potentially interesting polynomial, which is actually the characteristic polynomial of the system...
Hello everyone,
My question for this thread concerns the application of (mainly) mathematical analysis to fields such as signal processing and machine learning. More specifically, I was wondering if you happen to know of some interesting application of things like measure theory or functional...
My father and his brother are real Dylan freaks so I've been indoctrinated with his music from an early age. He is one of the reasons I learned how to play the guitar and to sing :) He ages like a good wine, too; his raspy voice from his later albums such as "Time Out of Mind" and "Modern Times"...
Thanks a lot for recommending problems Micromass, I recently started studying from this book and have so far worked through all of your recommended problems (plus some more of the interesting problems in the book of course!) in the first three chapters.
I'm now working through the problem set...
If you want something complementary to the textbook you're using you can always try to find video lectures of the subject you're studying, online. MIT OCW has some nice lecture series on linear algebra and calculus, I think. However, they seem to follow the "required" textbook for the course...
Thanks for the answer and the book suggestion. So Thomas' book doesn't contain both single variable and multivariable calculus in the earlier editions (it seems to do in later editions)? Do you perhaps have the table of contents for the 3rd edition (can't seem to find it)?
Hi guys,
I have a question about the book "Calculus: An Intuitive and Physical Approach" by Morris Kline. I was wondering if it includes a sufficient coverage of multivariable calculus as well as single variable? I am about to take a course in calculus of several variables and I am a bit...
Gelfand's Algebra book is awesome, I learned tremendous amounts of mathematics doing the problems. However, the problems can be very hard (at least for me) and if you haven't done math for a long time, it's probably going to be a tough start. I would recommend a slightly "softer" book like...
Tyler, when I did high school math I learned a lot of stuff outside the curriculum by self studying. I used textbooks that other more experienced learner of mathematics (even mathematicians) recommended to others, and I worked them through page by page (mostly). If you want som good advice on...
Cool, and thanks for your kind words epenguin. :smile: And thank you so much for your help, Dick and epenguin, I am grateful to you for you took the time and effort to help me with this!
Ah! I see now the mistake I made (I accidently wrote 6192 instead of 6912...). The third equation in #11 should be 4928 = A + 256D -16E - 16F + 256G (I used the values 1, 4, -4 for the roots). Can't believe I messed up with the numbers twice - I thought I was sooo cautious...
Sorry guys! I have been too lazy to write down the solution here. :redface: Anyways, here is the full solution I wrote down in my papers (I also remind you that English is not my native so have forgiveness for any language errors):
When we expand the expression Δ = (x1 - x2)2(x2 - x3)2(x3 -...
I don't think I understand. On what basis do you exclude the possibility of a p6 term? You say that when expanding the expression we get aijkƩx1ix2jx3k where aijk is a coefficient (integer) and i+j+k = 6. But that doesn't exclude the possibility of the case where i=6, j=0, k=0?
Ah, this makes sense! I honestly think that I reasoned like this for a minute buth dismissed the argument because I argued something like this: sometimes when you factor an expression you rewrite it by adding and subtracting terms - what says you won't add any terms where the variables have...
Very interesting, thank you for the link! This looks like quite profound mathematical theory above my level and my brain is going berserk trying to read it haha... But it's nice to know that there is a theorem that supports my assumption although I don't understand it yet.
I have tried it twice and have deduced the five equations further down by the following method:
1. Construct a polynomial of degree 3 and compute its discriminant Δ. (I have constructed polynomials where P=-1 in every polynomial.)
2. Set Δ=Ap6 - 4q3 - 27r2 + Dpqr + Ep3r + Fp4q + Gp2q2.
3...
This is really interersting epenguin. My textbook doesn't seem to cover the idea of symmetry - or it doesn't mention anything about it explicitly I should say because when I think about it, I have definitely encountered some symmetrical expressions earlier in the book. (Perhaps it wants the...
Yes, but it's more or less assumed in the problem statement. The author of the textbook has written: "Find (x1 - x2)2(x2 - x3)2(x3 - x1)2 as an expression containing p, q, r." I think it implies that I may assume that there is such an expression.
Perhaps it's not very elegant then but I still...
Well, I gave the argument that in terms of p, q, r, the listed terms are the only possible terms in the expression. So if there is an expression in p, q, r, it must consist of some collection of one or more of those terms. Isn't that enough?
1. Background/theory
We know that if the equation x3+px2+qx+r=0 has solutions x1, x2, x3 then
x1 + x2 + x3 = -p
x1x2 + x2x3 + x3x1 = q
x1x2x3 = -r
2. Problem statement
Find (x1 - x2)2(x2 - x3)2(x3 - x1)2 as an expression containing p,q,r.
That is, I'm supposed to find the discriminant of...
From reading the first pages of this thread I kinda got the impression that engineering studies is mostly for those who have some sort of passion in knowing how things works technically. Is that the case? I'm probably majoring in engineering, starting next semester, and in my entire life I've...
I have no idea what the approach is in Thompson's book but I studied elementary geometry from Harold Jacob's "Geometry" (1st edition). It was really a great book that taught me a lot. It can come across as a bit too easy sometimes and the author doesn't let you prove many theorems completely by...
Thank you, mathwonk! I have this book accessible for free at the local library so if the lack of set theory won't handicapp me for further math studies, I will give it a try since I liked what I've read in the book so far.
And out of pure interest, mathwonk, have you ever taught calculus from...
How is the exposition of the calculus in this book compared to moore modern treatments of the subject? I'm about to study calculus rigorously later (self-study) and I don't really know what a good calculus book should contain. For instance, there seems to be a lack of set theory in this book?
In my country, it's mandatory to learn some calculus in high school if you want to major in science or engineering. We also study calculus based physics parallel with the mathematics which I think enhance the intuition of the subject. All is done in a very intuitive and computational way. Then...
I have used Lang's "A first course in calculus" a little bit for my high school class (we are going through derivatives and integration right now) and the presentation of the mathematics so far is excellent. The first edition, "Short Calculus", only has about 270 pages, so If you could get your...
This one has some good reviews on Amazon: https://www.amazon.com/dp/3540761780/?tag=pfamazon01-20
Don't know what level it is on, though. Maybe i'ts more suitable for talented high school students and beginners at the university?
Thank you for that Algebra-list! I have worked through the algebra part in Basic Mathematics by Lang and I am halfway through Algebra by Gelfand. However, I feel that I lack som basic skills that I want to have from elementary algebra, such as standard techniques of factoring polynomials amongst...
Well, maybe there are enough exercises then. I guess I just got a little suspicious of the fact that there are no "Questions for Practice" after several topics. I probably have to take a deeper look into the material.
RJinkies, thanks for posting. A related topic might be the approach some...
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I like Euler's writing style and his exposition of the subject. I also think Elements of Algebra contains a lot of interesting stuff that standard textbooks in Algebra does not contain. However, if one's purpose is to study and learn mathematical substance/skills from the...
Oops, I meant "Elementary GEOMETRY", not Algebra! I aksed earlier in this thread about the importance of learning euclidean geometry thouroughly and I got some mixed answers, but I finally decided to give it a try (can't hurt and one can always make some extra sparetime for mathematics right :))...
Thank you, ovael! Chapters 1,3,4,5 looks very interesting!
I was actually thinking of buying it, because I've heard such good things about here on PF. But I'm currently doing "Basic Mathematics" (Serge Lang), "Elementary Algebra" (Harold Jacobs) and "Algebra" (Gelfand) at the same time, and...
I'm interested of the content in "Principles of Mathematics"; I have googled for a detailed table of contents, but can't seem to find any. I would love to read a more in-depth review of the book as well. So if anyone know of any, I would love it if you shared! :)
Also, "Fundamentals of Freshman...
I think it to a large degree is a matter of psychological satisfaction, which can vary between individuals; some people ask the question "Why?" more often than others. Eventually, you'll hit a wall where you feel satisfied with the mathematical theory "behind" things. Personally, I'm using...
I meant in high school (in general). It would be interesting to know what the high school curriculums in other countries generally put their emphasize on.
Applied mathematics vs. "pure" mathematics in high school?
I've just started working through "Basic Mathematics" by Serge Lang. It immediately struck me, when I skimmed through the pages, that there is a large emphasize on proving things and manipulating expressions, and very little exercises...
Hm, can you post a link to some kind of study plan or maybe describe what's included? In Sweden (which is where I'm from) Engineering Physics is a 5 year degree programme, where the first 3 years basically is a mix of pure/theoretical physics and mathematics, along with a few typical...
Because it's largely based on libertarian principles. The principles of classical liberalism, that goes back to John Locke and more or less all the way back to the middle ages holds just as true today, according to them. The thing is, the essence of libertarianism is just the individual rights...
@ mathwonk, RJinkies
Hi guys, thanks for the responses. Out of pure curiosity, what's so important about euclidean geometry? The mentioned book seems to go very deep, and I suspect there's much unnecessary drilling with profoundly derived techniques, if you know what I mean.
BTW: When I come...
I don't want to start a new topic for this question, so i post it here:
How important is (euclidean) geometry in the higher (that is at the university) mathematics education? I'm currently in high school and feel that I've barely touched the subject, only simple computations with area...