Mathematics Definition and 994 Threads

  1. Quantum55151

    Courses Math Course Advice -- Harvard freshman planning to double major in physics and mathematics

    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...
  2. F

    Insights The Many Faces of Topology

    Continue reading...
  3. philevans1745

    Extension resource for advanced high school / pre-university students

    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...
  4. M

    Probability Question: 3-Digit Combination Lock

    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...
  5. E

    Hello, non-Physicist newby here!

    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...
  6. M

    Sell Morse and Feshbach, Methods of Theoretical Physics Part 2

    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...
  7. Heisenberg7

    Studying Am I Missing the Right Approach to Studying Math?

    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...
  8. jedishrfu

    The Later Life of Alexander Grothendieck

    https://www.theguardian.com/science/article/2024/aug/31/alexander-grothendieck-huawei-ai-artificial-intelligence
  9. Heisenberg7

    Studying Advice for How to Attack Problems

    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...
  10. bhobba

    B The Paradox of 1 – 1 + 1 – 1 + 1 – 1 + …

    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...
  11. gohu

    Can I Enjoy Physics and Math Videos Without Practical Knowledge?

    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 ;)
  12. I

    Mathematics engineering student - Hello!

    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!
  13. B

    Studying Best recognized distance learning options in mathematics?

    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...
  14. Z

    Need Help with Calculations After 40 Years?

    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...
  15. bhobba

    Kumon Math and Similar Programs

    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...
  16. C

    Struggling with General Relativity Calculations?

    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...
  17. Z

    Admissions Advice about doing 1 or 2 masters during 2 yrs before doing PhD?

    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...
  18. ric peregrino

    What Are the New Methods and Notations in Differential Geometry?

    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...
  19. L

    How Do You Prove the Multivariable Chain Rule?

    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...
  20. S

    What Materials Fields are Heavy in Math?

    Hello, I'm a materials engineering undergraduate student. I would love to combine math and materials, what fields will allow me to combine these two?
  21. felizgu

    Hello From NYC!

    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.
  22. phinds

    B Innumeracy in public media today

    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...
  23. D

    I Post your favorite real analysis problem

    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...
  24. Hem

    Am Hempstone Oruko a teacher of Mathematics and physics in Kenya

    Am a graduate of Nairobi University in Bachelor of education science (Physics and Mathematics)
  25. Odin2568

    Hello all

    Hello all I'm new here hopefully I can get some help with some engineering mathematics.
  26. L

    What Questions Can You Ask About Physics, Mathematics, and Engineering?

    I've come here to ask any future questions I have regarding physics, mathematics or engineering. Thank you very much.
  27. shmwot

    Looking for Soviet era texts similar to MIR publishers

    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...
  28. L

    I Logical representation of prime numbers

    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...
  29. D

    B What is a closed form solution?

    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.
  30. M

    Partial Differentiation of this Equation in x and y

    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...
  31. gentzen

    A Concrete examples of randomness in math vs. probability theory

    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...
  32. chwala

    I Determining the dimension of a given PDE

    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...
  33. neilparker62

    Insights The Lambert W Function in Finance

    [url="https://www.physicsforums.com/insights/the-lambert-w-function-in-finance/"]Continue reading...
  34. jedishrfu

    B Maze Proof and Statistical Mechanics

    https://www.quantamagazine.org/maze-proof-establishes-a-backbone-for-statistical-mechanics-20240207/
  35. chwala

    Find the time taken by the truck to move 1 metre

    Unless i am missing something; there is an error with the textbook It ought to be , ## t= \sqrt {\dfrac{1}{0.04}}= \sqrt 25 = 5## seconds.
  36. V

    How Can a Retiree Self-Study First-Year University Math and Physics?

    Self-study mathematics and physics at first-year university level. So a freshman in retirement.
  37. paulb203

    Work out an estimate for the total number of ponies in the forest

    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...
  38. A

    Number of ways of arranging 7 characters in 7 spaces

    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...
  39. C

    A SDE valuation equation (stochastic calculus)

    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...
  40. A

    Given value of vectors a,b, b.c and a+(b×c), Find (c.a)

    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...
  41. M

    DeepMind AlphaGeometry: Is AGI just around the corner?

    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/...
  42. chwala

    Find an irrational number that satisfies the given inequality

    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}##.
  43. A

    A,B,C are 3 points with position vectors a,b,c Find length of median

    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...
  44. caffeinemachine

    I New Video Course on General Topology on YouTube

    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...
  45. walkeraj

    Just a middle-aged amateur person into physics

    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...
  46. D

    B Does Infinity Times Two Equal Infinity and Other Mathematical Paradoxes?

    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...
  47. J

    A Can You Find an English Translation of Klein's Protocols and Encyclopedia?

    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.
  48. Greg Bernhardt

    Mathematics Award

    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...
  49. S

    B More examples of equations that unexpectedly model nature in similar ways

    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...
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