Hi everyone!
I would like to get advice concerning my math course for the spring semester.
For context, I am a Harvard freshman planning to double major in physics and mathematics with the long-term goal of doing research in high-energy theory and/or mathematical physics. I am currently...
I have developed a website aimed at bright students who are getting towards the end of high school or are in the gap before they go on to university, and who want to stretch themselves a bit and tackle some physics that goes well beyond the school curriculum but is nevertheless accessible with...
A passcode having 2 fives implies that order does not matter (5 7 5 is the same passcode as it would be if we switched the 2 fives). There are 8 available digits in total, but 5 is being used twice, so we only have 7 options for the third number in the code. There are 3 possible cases for the...
Hello Physics Forums,
I come from the math/statistics side. I have no formal Physics training beyond basic physics in university. But I do work with some hardcore nuclear medicine physicists... the kind that build their own novel PET/SPECT scanners and stuff like that. Anyway, my mathematical...
Classic text in very good condition. It is ex libris so contains the usual writing on the flyleaf, library stamps, and a card pocket in back. The spine is free of the usual white sticker of card catalog information, however, because the book was enclosed in a plastic slipcover. As a result, the...
Hello,
This month, I've solved around 700 problems in trigonometry. And, I probably went over 200 problems again to internalize a few concepts, but I still have that feeling that I'm missing something. Last week, I was practicing math in cafeteria (early in the morning) and my math professor...
Hello,
I was lying in bed the other day and an idea came to my mind. How does one actually solve a problem? Now, I know this question is impossible to answer, but I would like to know your strategies when it comes to solving problems.
I would like to make an analogy to this. Let's say that you...
In the latest edition of Scientific American, they had an opinion piece titled The Paradox of 1 – 1 + 1 – 1 + 1 – 1 + …. For those with access:
https://www.scientificamerican.com/article/1-the-paradox-of-1-1-1-1-1-1/
Scientific American, the once-venerable publication I eagerly awaited every...
hi, i love watching videos about physics and mathematics, but i have no practical knowledge, i could not make the calculations or predictions for anything ;)
Hi everyone!
I'm currently doing a bachelors in mathematics engineering. Still, there is some physics involved :) I'm looking forward to spending some time here and to interact with you guys!
I am a physics major in the second year and always have loved maths. Now that interest has grown into something bigger and I am thinking of taking some recognized distance courses in mathematics so that I will have something to show in case I decide to do a masters in mathematics.
It will be...
Hello, due to my age it's been at least 40 years since I needed to carry out in-depth calculations where I could use some support. Hopefully some of you out there can point me in the right direction when the going gets tough.
The forum attracted me due to the wide variety of discussion topics...
I have been a long proponent of beginning calculus being introduced early in math education at about grade 7 or so, and in the US (with or just after Algebra and Geometry), Calculus BC is taken in grade 10 or even earlier. It's not well known, but believe it or not, a few hundred students in...
I’ve been self studying some of the concepts related to General Relativity, by trying to model Geodesics and calculate distances on curved surfaces. I found that I seem to understand some of the concepts related to the math, but not others as when I try to make some calculations I find that my...
Hello!
As the topic suggests, atm I am a math grad student, beginning my 2nd and last year after the summer. Note that I have allmost taking more physics courses than math courses during my first year, and to me theoretical physics research seem more appealing than pure math research.
Would...
Hello,
I'm an old fart, that used to self study GR and tensor calculus. I have a BS ECE from UCD, and a MS EE from Stanford. I've since retired from my electrical engineering career which was mostly at the old HP's Stanford Park Division, and I find myself once again pondering these things. I...
Hi,
Im completly lost regarding the following exercise:
Unfortunately, I don't understand how to prove the statement using the chain rule. The chain rule is always used if there is a composition, i.e. ##f\circ g=f(g(x))## then I first have to calculate ##g(x)## and insert this result into...
My name is Feliz. I am doing a self-study of college algebra. I am not a classroom student. My student days ended in December 1993. I've always enjoyed mathematics and decided to conduct a review of material learned long ago.
I OFTEN see ridiculous math statements in the public media, usually limited to such publications as Time Magazine and others of that ilk, and even more so on the Internet, but occasionally even in more serious media such as the NASA web site and The Economist. Just ran across another one on the...
I figure one can dig around for plenty of quality problems online, but I'm hoping to skip right to the good stuff by you posting your favorite real analysis problems from college, internet, textbook, dream, imagination, etc. It would be so helpful to get some comments this time, and please don't...
The books from MIR publishers just seem so hardcore
I loved a lot of the books, most of the introductory mathematics I learnt is from Russian texts. Any recommendations y'all for cool books around the time or rare texts in general
My college has a nice library and I just want to read everything...
One of the discussion questions for my class this week was to express the condition "p is a prime number" using formal logic.
The answer my uni's got is (∀d∈N)[(d>=1∧p≠1)∧(d|p⇒((d=1)∨(d=p))]. My interpretation of this is all the natural number d that (satisfy d>=1 and prime number is not equal...
Hi friends, I was wondering if you could give the definition of 'closed form', with examples of closed form solutions and open? form solutions.
Foe example, is this a closed form solution?
$$\sum_{k=1}^\infty \frac{1}{2^k}$$
Or this?
$$\sum_{k=1}^5 \frac{1}{2^k}$$
Thanks.
Hi;
please see below I am trying to understand how to get to the 2 final functions. They should be the same but 6 for the first one and 2 for the second?
(I hope my writing is more clear than previously)
There is an additional question below.
thanks
martyn
I can't find a standard derivative...
A recent question about interpretations of probability nicely clarified the role of the Kolmogorov axioms:
[... some excursions into QM, negative probabilities, and quasiprobability distributions ...]
Conclusion: the Kolmogorov axioms formalize the concept of probability. They achieve this by...
Now in my understanding from text ...just to clarify with you guys; the pde is of dimension 2 as ##t## and ##x## are the indepedent variables or it may also be considered to be of dimension 1, that is if there is a clear distinction between time and space variables.
Your insight on this is...
My question; Which branch of maths is this?
Also, can you give me a clue as to where to start regards solving this. Just a hint please, not a full explanation.
I'm struggling to even guess at this one. I did think, '60 ponies, 5 of which are tagged, so, 5/60 tagged, which is 1/12
1/12 of the 60...
The rightmost position has 3 possibilities: ##x,y,z##
The remaining two letters are to be arranged in 6 spaces: ##\frac{6!}{4!}##
Now the 3 can be placed in ##\frac{4!}{3!}##
Total no of ways =$$3×\frac{6!}{3!}=12×30$$
$$OR$$
Since ##x,y,z## are three different boxes/variables, we can use the...
I read from a text: "suppose a stock with price ##S## and variance ##v## satisfies the SDE $$dS_t = u_tS_tdt+\sqrt{v_t}S_tdZ_1$$$$dv_t = \alpha dt+\eta\beta\sqrt{v_t}dZ_2$$ with $$\langle dZ_1 dZ_2\rangle = \rho dt$$ where ##\mu_t## is the drift of stock price returns, ##\eta## the volatility of...
I thought this was too easy
$$a+(b\times c)=0\implies a=-(b\times c)=(c\times b)$$
Then
$$3(c.a)=3(c.(c\times b))=0$$
Since cross product of vectors is perpendicular to both vectors and dot product of perpendicular vectors is zero.
Now here's the problem, correct answer given is 10. But how do...
DeepMind's new geometry problem-solver AlphaGeometry can solve Euclidean plane geometry questions from the International Mathematics Olympiad (IMO) almost as well as a human gold medallist.
https://deepmind.google/discover/blog/alphageometry-an-olympiad-level-ai-system-for-geometry/...
I just came across this question and the ms indicates,
Would ##31.5## be correct? ...i think it is rational as it can be expressed as ##31.5 = \dfrac{63}{2}##.
Heres how I proceeded,
Equation of line ##AC## in vector form:
$$\vec r=a+t(c-a)$$$$\vec r=(1i+4j+3k)+t(2i-6j+2k)$$
Since ##B## doesn't lie on ##AC## ##b\neq (1+2t)i +(4-6t)j+(3+2t)k##
The following equation is derived:
$$2\hat i+\alpha \hat j+4\hat k\neq (1+2t)\hat i +(4-6t)\hat j+(3+2t)\hat k...
Hello Everyone!
I created a YouTube channel (here's the link) a few years ago in which I post detailed lectures in mathematics.
I just started a series on General Topology. Following is a snapshot from a video.
I mean to deliver a comprehensive course with a lot of pictures and intuition and...
Degree in chemistry and at one point was a physics and mathematics double major, but life intervened. Never got to finish but still read and work on novel amateur theory. At least, what I would call novel and amateur.
My focus is on putting together theory on space-time and quantum field...
We have come to accept that Infinity times two is infinity. In the sense of 'size' we use to think about everyday numbers, the rules of arithmetic with infinities seem like nonsense. For example, consider the computable number
$$0.100100100100100....$$
In the decimal expansion, there are...
https://www.uni-math.gwdg.de/aufzeichnungen/klein-scans/klein/
I hope you enjoy folks. It would be nice to see an English translation somewhere. Same for his encyclopedia.
Please select up to 3 members who were most impactful in the Mathematics forums in 2023. This is a popular vote. Polls were created by weighing activity and measure of helpfulness. Everyone nominated should feel honored. Many more could be added to this poll, we can never realistically add...
Been dipping my toes into maths by examining how equations work on the most basic level, and I love encountering equations that turn out to model similar aspects in nature, for example the inverse square law is apparent in equations for gravity and for electromagnetism.
In the thumbnail of...