Mathematics Definition and 994 Threads

Homework Statement:: I'm looking to start learning mathematics to help me understand physics better. Relevant Equations:: N/A Hi all. For the longest time I've been talking about learning (or possibly even studying) mathematics to help me better understand physics. My biggest problem is, I'm...

Homework Statement:: What does the following quote by Mathematician Paul R. Halmos mean? "The only way to learn mathematics is to do mathematics." Relevant Equations:: What dose he mean by "doing mathematics"? Is it solving puzzles or studying theorams or reading about mathematics? Thanks

Hi, I have been studying mathematics for quite some time now, and I have an understand of what each topic constituted up unti and including graduate level mathematics. However my computations in each topic are very instructive, as if each topic carries its own instructions for calculations...

Because of having enough on my plate I don't think I would have read this book even without the negative review here, but it is the sort of thing that interests many here. https://beta.spectator.co.uk/article/let-s-leave-philosophers-to-puzzle-over-the-reality-of-numbers (The reviewer is...

Here's something that maybe should go in the list and here are the pros and cons: I was recently doing a problem which involved calculating the electromagnetic energy momentum tensor$$ T^{\mu\nu}=F^{\mu\lambda}F_{\ \ \ \lambda}^\nu-\frac{1}{4}\eta^{\mu\nu}F^{\lambda\sigma}F_{\lambda\sigma} $$In...

I will basically focus on 18th and 19th century, I got to know from the biographies of Max Planck and few other that there were no organized syllabus in Universities for studying. Students had to take classes that they could understand and it was less like a lecture and more like a private...

Since this is on the history of philosophy linked to set theory, rather than set theory itself, I presume I can't put it into the Set Theory rubrik. First, for those who are unfamiliar with the Reflection Principles of Set Theory (or more properly model theory),there are several versions, but...

Hello all, I am currently taking the first of a two semester sequence of C++ courses and I am taking the course as an Honors option and thus I will be writing an extra program to fulfill the requirements. A little about my experience, I am currently taking Calc 3 and an intro to proves...

Should i read Introduction to Calculus and Analysis by Courant? I have calculus background I want to study multivariable and single variable in rigorous way There is a lot of books in this subject like Spivak, apstoal,Courant,... . I am not sure what to choose

I'm trying to figure out this example on page 23 of the book Mathematics for the Million by Lancelot Hogben. (Here is a link to the online book: https://archive.org/details/HogbenMathematicsForTheMillion/page/n25 ) While I understand the concept that adding two and two does not always equal...

Hello, I have a few questions about mathematics as a deductive system in which mathematical statements follow as a logical consequence from axioms and other statements. In particular, consider the real number system and Euclidean geometry. Is doing arithmetic with numbers and working on...

Hi, I’m looking for video lectures on lattices in mathematics (or lattices in computer science) which might be related to number theory. Could anyone recommend some? Senmeis

or in general, is it possible to create science without mathematics? thanks

Hey PF! I'm currently studying Algebra and Trigonometry and have been looking at university level math courses. I was hoping there are some to jump into preferably before calculus like crypt analysis, number theory, or combinatorics.Are there "fun" math courses to take that don't rely on...

How did you find PF?: https://www.intmath.com/blog/learn-math/top-10-math-help-sites-5966 Hello everyone. I know that there is a group isomorphism from Z[X] to the multiplicative group of all positive rational numbers. My question is: Are Z[X] and Q isomorphic groups?

Hi, I have a particular equation in a paper, wherein the author specifies an infinite series. The author has apparently found the sum of the series and calculated the equation. Can anyone please help me in understanding how to sum such a series. I have attached part of the paper with the...

Hi all, I was wondering if I could get recommendations for texts/notes that delve deeper into the mathematics of QM as well as QM itself than what one finds in standard "Intro to QM" texts. Ideally it'd be presented in the style of Nielsen and Chuang's Quantum Computation book, but in greater...

thanks in advance

I am currently studying physics as an undergrad, and I intend to pursue a PhD in theoretical physics. My intention in obtaining a math degree is simply to enhance my mathematical capabilities and thus make me better at solving physics problems. Furthermore, I hoped having this increased mastery...

Music and the crafting and playing of musical instruments are among the earliest manifestations of science and technology in human culture not directly related to survival. Early drums used for communication also provided rhythm for dance and song. Simple reed flutes and pipes, bone whistles...

Greetings, I am a 12 year old who is vastly intrigued by the wonders of theoretical physics (experimental physics has not exactly been to my liking) as well the subtle art of mathematics. For the past six months, I have attempted to work my way up to mastering mathematical prerequisites required...

I am an incoming graduate student in Theoretical Physics at Universiteit Utrecht, and I struggle to make a choice for one of my mathematical electives. I hope someone can help me out. My main interests lie in the fields of Statistical Physics, phase transitions and collective and critical...

I have been trying to read through the following paper: https://iopscience.iop.org/article/10.1088/1367-2630/18/6/063032/pdf, but am stuck at the parts from page 6 onwards. What is the "approach/formalism" used in the following sections of the paper, and are there any gentle introductions...

Hello, as the title states, which book is better for learning Precalculus? I heard David Cohen's is much more application/computational based and is better for learning Precalculus rather than Lang's. However, Lang is also good as well because he doesn't focus on plug and chug, but rather...

Hello I am looking to find advice on the most optimal and efficient way to properly and deeply study a mathematics textbook, such that I completely understand everything and thus giving me good foundations for future study of more advanced mathematics. However, I want to change my ways of...

My attempted solutions was, for example let's say we have 4 atoms, and if i ask the oracle about any two atoms that are connected by edge, i can narrow done some possibilities to two atoms. I'm still not sure where i am going with my solution, but if any of you can think this through and come up...

Hi guys, I am in desperate need for help with my assignment in advanced maths. In my assignment, I am required to use geogebra to support in answering the given questions. If someone can help me, that will be greatly appreciated.

My background is BS Math with Physics minor (3.5) and MA Math (3.7) from the University of Houston. My current plan is to explore the necessary background for doing research in finite element analysis. Over the next few semesters, I plan to take Numerical Methods for PDEs, Statistical Computing...

Hi, I recently have rekindled my love for mathematics while in University for Political Science. I have reviewed all of my old pre cal books, but now I want to start learning Calculus eventually on to more difficult things like PDEs and things of that nature. I like having a series of textbooks...

I am an undergrad in physics and math (pure). I want to do msc in Applied mathematics . There are few things that worry me : 1. Topology, complex analysis, differential equations, calculus, Probability, 3 Analysis and 3 Algebra - these are roughly my courses. I didn’t take any “applied” kind of...

I have attached a word document demonstrating the working out cos i was too lazy to learn how Latex primer works and writing it like I did above would've been too hard too read. I tried to make it as understandable as possible, presenting fractions as ' a ' instead of ' a / b ' . ------ b

I have Thomas and Finney's book on Calculus for reference. Am I prepared for Feynman's Lectures? I've studied physics for two years in high school.

I want to produce a resource that has a narrative and includes the following topics: Sets, logic and proofs, numbers (irrational, integers, rational, …), binomial theorem, geometric series, inequalities, define things like identity, polynomial, symmetry, sigma and product notation. It is in aid...

I'm talking about "Mathematical Tools for Physics by James Nearing". https://www.amazon.com/dp/048648212X/?tag=pfamazon01-20 it seems it cover lots of math... but it feels like it's just a reference book.. will it be enough? or should i get more specialized books to learn each subject thoroughly?

Homework Statement A cyclist traveling east at 8 km/hr finds that the wind appears to blow directly from the north. On doubling his speed it appears to blow from the north-east.. Find the actual velocity of the wind.[/B]Homework Equations Wind(relative) = Wind(Actual) - Velocity(cyclist)...

Physics, Economists, Biologists, Astronomers and my brother all love the word "Random", as that allows allows them to get out of clockwork processes and allow for variations due to unknowns or whatever else. But, how does a Mathematician reconcile itself with the idea of random? There's no...

I found this interesting article https://blogs.ams.org/matheducation/2019/02/14/mathematics-gatekeeper-or-gateway written by Mark Saul So the question is: What is mathematics: A necessary evil or the universal language physics is written with? If you tune in on a random tv quiz show and wait...

Can an expanding balloon be considered a control volume?

Greg Bernhardt submitted a new blog post Lie Algebras: A Walkthrough The Representations Continue reading the Original Blog Post.

Good day to you all, dear dedicated scientists! My name is Daniel and I'm in my last semester of undergraduate mathematics studies, in Universidad de los Andes, Colombia. Although I'm always eager to discuss math and science, I'm also very interested in discussing the non-scientific aspects...

I found this interesting article about the balance between mathematical creativity and necessary content. https://blogs.ams.org/matheducation/2019/01/15/reflections-on-teaching-for-mathematical-creativity/ I don't want to make the discussion exclusively a pedagogic one, which is why I posted...

Greg Bernhardt submitted a new blog post Lie Algebras: A Walkthrough The Structures Continue reading the Original Blog Post.

This is perhaps the single most important mathematical physics papers I have ever read; I think everyone - especially (theoretical) physicists - interested in theoretical physics should read it. In fact, read it now before reading the rest of the thread: Klainerman 2010, PDE as a Unified Subject...

Greg Bernhardt submitted a new blog post Lie Algebras: A Walkthrough the Basics Continue reading the Original Blog Post.

Hello, I am a Belgian master in physics and astronomy with a couple of years of working experience under his belt, who recently decided to obtain a second master in statistics. Normally I should graduate in 2020. My goal is to become a data scientist, but preferably within a scientific context...

Having read many times about normalizing quantum mechanics to agree with classical equations, can you please give an explanation or an example of the mathematics involved? I have looked in Wikipedia, but was unable to find anything. Maybe I am using the wrong keywords. Is there an article or an...

Let S = {1,2,5,6 } Define a relation R on S of at least four order pairs, as (a,b)  R iff a*b is even (i.e. a multiply by b is even)

When The denominator is checked, the poles seem to be at Sin(πz²)=0, Which means πz²=nπ ⇒z=√n for (n=0,±1,±2...) but in the solution of this problem, it says that, for n=0 it would be simple pole since in the Laurent expansion of (z∕Sin(πz²)) about z=0 contains the highest negative power to be...

I am Baibhab Bose, from India. I have just completed Masters in Physics from University of Delhi. I hope to delve into deeper insightful discussions on physics and mathematics and would like that there would be no 'Poles' of any order in the space of my understandings which is inside the...

Imagine two smooth scalar functions defined on the surface of a sphere. Is it possible to find a smooth coordinate translation that slides the values of the first function over the sphere, until it becomes equal to the second function everywhere? It seems reasonable that if the number of...