Mathematics Definition and 994 Threads

I want to review early mathematics to cover the gaps in my knowledge, yet I'm struggling with where to start, or more precisely, how? Should I just go into Lang's book and start developing a sense for proofs and mathematical rigour while also understanding the topics that I missed in school? Or...

Are there any practical applications of Laplace transform? I would not use Laplace transforms to solve first, second-order ordinary differential equations as it is much easier by other methods even if it has a pulse forcing function. How can Laplace transforms be introduced so that students are...

In the late 80’s and early 90’s there was the idea of ‘calculus reform’ and some emphasis and syllabus changed. The order of doing things in calculus also changed with the advantage of technology. Similarly in linear algebra, there was a linear algebra curriculum study group that produced some...

Considering the definition of supersymmetry as a set of operators that extend the transformations of Poincare group, I wonder if they are of some value for mathematics, particularly for differential geometry. Most of the formalism I can find relate to "superspace", which does not seem a natural...

I am studying mathematics as bachelor in my second year. At the moment I am taking abstract algebra, analysis (measure and integration theory) and probability course. I don't know exactly what I want to do with maths but the applications in physics always have fascinated me. The next term I have...

The mathematician and mathematical physicist Alain Connes has expressed in many occasions that he is a Platonism and he thinks that mathematics itself does exist in the same level (or even in a "stronger" level) as physical reality. This is very similar to Max Tegmark's hypothesis of the...

Is it worthwhile to read the book Course of Higher Mathematics by Smirnov?It is a serie so may be it easy to read because there are not gaps when reading process occur(?) for self-study mathematics for physics?

In Nielsen and Chuang p.223 we have the following situation: $$\frac{1}{2^t} \sum\limits_{k,l=0}^{2^t-1} e^{\frac{-2\pi i k l}{2^t}} e^{2 \pi i \varphi k} |l\rangle$$ Which results from applying the inverse quantum Fourier transform to state ##\frac{1}{2^{t/2}} \sum\limits_{k=0}^{2^t-1}...

Summary:: I need to learn the deepest information I just started computer science. I have to learn computer basics and then what maths should I learn? What math should I learn after I've learned basic math?

Hello,I am trying to teach myself mathematics by starting with Euclid and going up to today. My only background is college algebra and high school algebra and geometry. I am 44 years old. I've read Euclid and Apollonius. I understood everything except he Appendix in the Conics book (Green Lion...

I had seen some online information many years ago or some literature that I did not track saying that Introductory Algebra and Geometry such as the two courses at the high school level are "Foundational Mathematics Courses". I wonder if what I read was misstated, or if these Foundational...

I've no political agenda. This is strictly a math question about optimization. Those addressing it should do so strictly from a mathematical perspective. Thank you! If the world simply had one global currency, like Bitcoin, and everyone had an account, then the sum total of all accounts...

I have calculated the height of the segment using the Pythagorean Theorem and that's currently where I am right now. I don't seem to find any equations that can help me. Though I might be not trying hard enough or using the wrong words because I'm not really fluent in mathematical terms as you...

Homework Statement:: Mathematics to understand Quantum Scattering Theory Relevant Equations:: Suitable math book to understand Quantum Scattering Theory I need to study Scattering theory from Introduction to Quantum Mechanics by David Griffith. But I think I need to study mathematics first...

I've been reading a brief history of mathematics, from the ancient civilisations onwards and found the following striking quotation from Roger Bacon (1214-94): Mathematics reveals every genuine truth, for it knows every hidden secret and bears the key to every subtlety. Whoever then has the...

The other day I found a fascinating video on geometric algebra: At 34:50, after showing how to rotate a vector in three dimensions, he says, "wait a minute, this looks like a spinor from quantum mechanics. The way that spinors rotate is always said to be a part of so-called 'quantum...

Hi PF Don't you think that natural logarithm is not that natural, and complex numbers are not that complex? Words are absolutely necessary, but are so imprecise... For example, to write this post, and make this message clear, as I'm not native, I've had to look at Cambridge Dictionary online...

I can understand that we can have limitations on physics, as we are trying to describe nature and so constraints can naturally occur - even meta-constraints that limit our ability to model nature to an arbitrary degree. However, why does that applies to a synthetic system such as mathematics as...

Hi everyone, Has anyone tried to model Radiative Transfer equation on comsol? I am stuck at defining the integral term which includes scattering. Also , how do i make my functions have 3 variable dependence as RTE has dependence on position, time and direction vector

I mean, as a simple example, vector analysis involves the study of higher-dimensional objects in Euclidean space, objects that are downright impossible to visualize using simply pencil and paper. When my professor taught it, he often explained the topics using analogies that tied into vector...

Hello, everybody: I am translating La leçon de Platon, by Dom Néroman (La Bégude de Mazenc, Arma Artis, 2002), which deals with music theory and mathematics in the works of Plato. The problem which brings me here is not about translation, but about mathematics, although a proper understanding of...

Hello everyone, I don't know if that's the correct place to ask this (didn't want to pollute the science and math textbooks recommendations), sorry if it is not. I have undergraduate physics and mathematics textbooks that I am trying to sell. I live in Belgium and I bought textbooks...

Hey guys, so I was on this thread on tips for self studding physics as a high schooler with the aim to become a theoretical (quantum) physicist in the future. I myself am a 15 year old who wants to become a theoretical physicist in the future. A lot of people in the thread were saying that...

This playlist on YouTube contains mathematics reviews and exam preparations for school and university mathematics. It's useful for people preparing for exams or reviewing mathematics from previous years. Topics include: Prealgebra, Algebra 1, Geometry, Algebra 2, Trigonometry, Precalculus, SAT...

I am recreationally self studying physics and math with the ultimate goal of understanding theoretical/mathematical framework of classical mechanics, general relativity, and quantum mechanics (in addition to the actual physics). The question I have is how deep in the realm of pure math does one...

Please help me understand the RSA encryption. I understand part of it, then I don't understand. Definitions: M=plain text message C=encrypted message N=public key E=encoding key D=decoding key P,Q are prime factors on N I get that P x Q = N (where P and Q are primes). I get that Φ(N) =...

Summary:: The problem with Mathematics in Physics The problem with Mathematics in Physics: Consider the equation x = y x z What does it tell us about Physics? Pretty much nothing, I am sure you would agree. Now consider F = m x a That's a lot better, it tells us how much force is required to...

Hi all, I'm partaking in a PT Astronomy degree and I'm curious about self-teaching myself maths for Physics/Astrophysics. I'm currently working through the Foundation section in Stroud's Engineering Mathematics. I am of course familiar with the usual recommendations of Riley's and Boas's...

Dear Everyone, I am wondering how to deal with the self-doubt in proof-writing in general situation like on exam or homework question. Suppose I want to prove Theorem B. I assume the hypothesis. Then I apply the right mathematics definition. I am hesitant on the next step; I have the feeling...

When the proof justifies the theorem, by a growing alphabet, then is it possible to talk about the complexity of the theorem via the growing alphabet of the theorems proof? In as short as possible, would it be possible to entertain the notion that complexity in non-congruent mathematics is...

Hello everyone, so for my math IA, I will be exploring the principals of flight. Does any of you know a book that explains the drag/lift and other principals of flight in a detailed mathematical way ? ( It would be also preferable for it to mention the flight characteristics of an Airbus A-320...

I will be taking intermediate mechanics next semester, and am a bit concerned about potential gaps in my mathematical knowledge. Long story short, I used to be a physics major, switched to electrical engineering, and then decided to double major after a semester in EE. The issue is that, as a...

Hello, I was watching a video lecture from MIT 8.04 (Allan Adams)– lecture #24 (around the 38 minute mark give or take) The topic is quantum computing, Dr. Adams is deriving / explaining how to get various computing operations. For the “NOT” operation he explains that the operator $$ U_{Not}...

I have a B.S in Mathematics, but wish to pursue Theoretical Physics. I still have a great deal of undergraduate Physics coursework to take before I can apply to graduate programs. My question has to do with the Mathematics that is crucial in order to do Theoretical Physics. Is the mathematics...

Summary:: How can I get mathematics modeling for these tree systems? First of all, my mother tongue is not English, so my expression could be ambiguous. I want to get mathematics modeling for these three system above, like this form. First one is b -> (b1+b2), right? but I'm not sure...

Does anyone have experience with using these books for learning mathematics? I'm particularly looking at the one on linear algebra. The fact that there are countless practice problems with solutions is a selling point. Also, this book in particular sells for like 1/4 of the price of a proper...

I came across a rather strange thing in an introductory class I still don't understand. There was a statement that $$lim_n (2+ \sqrt(2))^n $$ is an integer. I recalled that I never understood this and just recently tried to take the limit but just get that the expression diverge? Which I think...

Sort of like the one by Morris Kline titled "Calculus: An Intuitive and Physical Approach". However this one barely scratches the surface as far as ODE and multivariable calculus go. In short I'm looking for a sequel.

After i read about RSA encoding, it looks like as if one need an alternate history universe to justify that in the not so far (cyberpunk) future the coded message of an important person involved in shady business can be cracked in reasonable time, let alone during a single night. I read that...

Hi there. I'd like to ask you, educated folk, a question. I'm graduating from university next summer. My major is the law. Although, all the time I keep some kind of passion for physics. Even though I am not a techie. I realize that I graduated as a dummy in math, physics, and chemistry due to...

What I am going to outline should not be seen as a recommendation for most. Probably only a minority would benefit from it. One possibility to learn the necessary maths to study physics, from a "mathematical physics" point of view is to first study a degree in maths (and maybe also a Master...

Hello everyone! I finished a masters in integrative neuroscience about a year back, which was supposed to have a very strong mathematics tilt. Despite this, and the two semesters of mathematics, I feel that it did not help me out much. I ended up doing my masters thesis in a lab of physicists...

How does the process of collaboration in math work ? Do mathematicians like to share their problems ? Can I do this by e-mail ? How to ask mathematicians if they want to collaborate in a math project ? I'm still learning more advanced math but these are questions I had in mind and didn't know...

Summary:: What is (are) the best book(s) to understand the mathematics of Feynman diagram? Hello, Can anyone recommend some books for the mathematics of Feynman diagram? (I don't mind if they also include the physics; in fact it may be better). Ideally I would need books that are very...

Our forums are full of physics and mathematics. One cannot talk about the former without getting into calculations and mathematics sooner or later: Hilbert spaces, differential operators and linear algebra all over the place. Students of both faculties have normally a similar motivation...

Hello, I am a retired Marine that has decided to pursue an undergraduate degree in programming and am currently working on paper that discusses the future of Mobile Computing. In this paper I am introducing a hypothetical process that assists in forecasting the future of mobile computing. To do...

Part (i) *Pink represents mark scheme method Part 2 However I am still confused on the diagram.

I suspect many here are published within their fields. What is your general advice for writing academic papers in mathematics, physics or any other "hard" science discipline?Were there any resources that helped you?What have you found to be the most successful aspects of your approach to...

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