Mathematics Definition and 995 Threads

Hi All applications of discrete mathematics I know of seem to be in computer science. I want to know if there is somewhere discrete mathematics are applied outside of software. What can I work as if I like discrete mathematics but do not want to program? (outside of academia, of course)

I am with a query about cw complex. I was thinking if is possible exist a cw complex without being of Hausdorff space. Because i was thinking that when you do a cell decomposition of a space (without being of Hausdorff) you do not obtain a 0-cell. If can exist a cw complex with space without...

In graduate school for physics, the competition in certain fields(for example High Energy Theory) is very intense. Does anyone know how the situation is in fields of mathematics. So, which areas of mathematics are the most difficult to get into for grad school ? I would be particularly...

Hello all, I'll be going by Mathamans while I spend my time on this site. I'm currently pursuing a B.S. in both Physics and Mathematics. Afterward, if my plans don't change, I'll be pursuing a Masters in Mathematics and a PhD in Physics as I'd like to become a professor of Mathematics and/or...

I keep finding myself losing focus in the middle of doing even basic maths. I sometimes know exactly how something should be done, but make stupid mistakes doing it because I can't fully concentrate. I used to have an obsession with numbers (as a kid) and was great at mental maths. Now, I'm...

I don't know wether I should choose physics or mathematics in University. I'm very interested in theoretical physics described in those popular science books such as the string theory ,QED, relativity , and I want to become a theoretical physicist. But I'm not impressed by the physics taught in...

Hello, do you know of any books similar in style to Callahan's Advanced Calculus book(a book that explains the geometrical intuition behind the math)? This goes for any subject in mathematics(but especially for subjects like vector calculus, differential geometry, topology). Thanks in advance!

I've had a pretty poor experience going through the standardized education system in California, and now that I'm in college, I'm really fed up with how mathematics is taught (even at the college level). With this said, I thought it would be fun for me to redesign the entire math education...

Hi, I am a math major student. I am interested in the theory of computer science and I would like to go to this direction in graduate school. So I need some advice about what courses of computer science I should do, and what courses of mathematics I can ignore. My program has a lot of freedom...

Do we have any examples of physical constants appearing in topics that are focused more on abstract mathematics? For example, do the values of the physical constants ever appear in the results of papers on mathematics that are not focused on direct applications to physics? Could they do so if...

micromass submitted a new PF Insights post Omissions in Mathematics Education: Gauge Integration Continue reading the Original PF Insights Post.

I have seen some of the questions students ask in the forum and think that I may be able to help. I am missing the classroom experience, so this my be one way to recapture some of that rewarding experience.

Hello from Italy I'm switching from CS to Physics BS because i personally find it more various and interesting (and in Rome there is one of the best physics school in the world). Mathematical analysis is a common subject and my credits will be recognised but i didn't study Linear algebra yet...

Next year, I will study mathematics at university. I think I'm well prepared, I already did some linear algebra (I got some books from my brother who studies physics and the mathematicians and physicists share some courses in the first year) and with effort it seems to work out. But, are there...

Hello, I was wondering if anyone knows about the the book "The Geometry of Spacetime: An Introduction to Special and General Relativity" by Callahan and what their opinions are. Thanks!

I'm considering going after a MS in Electrical/Minor Math or Masters Math/Minor electrical. I have BS in mathematics. I am completing the background EE courses as needed. What areas of EE are the best fit for someone who had a strong interest in Analysis and continuous mathematics? I was...

Hi, I am new here and this is going to be my first post. I am pursuing an undergraduate degree in electrical engineering and I am absolutely fascinated by control engineering. I want to know whether I should take advanced math courses in order to better prepare myself for a PhD in Control...

Hello, I want to know: 1. Compiler name built especially for doing full-fledged mathematics. 2. Langauge name built especially for doing full-fledged mathematics. 3. Integrated software development environment name built especially for doing full-fledged mathematics. 4. Language, compiler and...

Dear Physics Forum friends, I am an undergraduate at US actively pursuing mathematics and microbiology. Recently, I started to evaluate my methodology of reading books in the mathematics, which raised me some concerns and worry that I want to share with you, and seek advice from you. Whenever...

Hello! I am trying to write my notes in mathematics to permanently store my knowledge, and I am trying to learn LaTeX but it is quite difficult for me...Could you recommend me some sources and books to learn LaTeX for mathematics?

I just finished my A levels in math's/physics. I decided to take a year out before I start an engineering degree. I'm looking for books to study on my work break's and any down time I get. I was looking at the 'Physics for Scientists and Engineers' by authors like Feynman and Serway. They can...

Homework Statement What is the probability that a random rearrangement of the letters in the word "mathematics" will begin with the latters "math"? Homework Equations Probability = (# of desired results) / (# of total results) The Attempt at a Solution The solution I got was (2*2*2*1) /...

micromass submitted a new PF Insights post How to self-study algebra. Part II: Abstract Algebra https://www.physicsforums.com/insights/wp-content/uploads/2016/06/aastock6.png Continue reading the Original PF Insights Post.

Hello PF community, I have a question about a choice that I need to make soon and I would like some opinions from the community. So I am double majoring in physics and applied mathematics at the moment, and I have been thinking about changing my second major to computational mathematics instead...

I was hoping someone could shed some light on a current predicament I'm having. Although I don't have the knowledge to make a real decision yet (only first year), I enjoy string theory, quantum mechanics (and quantum gravity), as well as cosmology. Based on these areas of interest, I'm unsure of...

Hello! I'm completing my IB Physics IA and after collecting my data and plotting the raw graph my graph seems to be a negative parabola. In order to linearize it I though one had to square the x-axis data; however I simply get the same graph shape. What am I supposed to do? Only when I plot the...

I am trying to prove that the above is true when performing the change of variable shown. Here is my attempt: What I am not quite understanding is why they choose to isolate the partial derivative of ##z## on the right side (as opposed to the left) that I have in my last line. This ultimately...

I'm starting my 1st year of Physics at university in September. Although I've learned a lot of single variable Calculus and various topics of Physics this year, I'd like to get a general overview of the topics touched in a 1st Physics course at uni. I just wonder if there's an equivalent to...

Hello, i want to get a mathematics book for physicists, and i have stumbled across some good books, but as i have not read them yet, i can't really decide which one to buy. So, which one do you prefer and why? Also, do you have any other book to recommend? Thanks!

My son is a college freshman at an Ivy League college. He is currently taking classes in Applied Math and Physics but will have to choose a major by the end of sophomore year. He is interested in going to graduate school but is not entirely certain where he would like to work. He is not...

Hello, PF! I had been meaning for some time already to start a thread like this, in which we can share our personal, technical (math, physics, engineering) library (as a list or in pictures too), and also recommend your favorite textbooks or handbooks. Here is my collection so far, as a junior...

I have been reading a lot of books on deliberate practise like Grit - Angela Duckworth, Talent is Overrated - Colvin and Peak - Ericsson and Pool and I'd like to implement the principles in my training to become a good mathematician. There isn't much advice on how to apply these principles to...

Humans created that tool, that language, that consists of axioms and their implications. Mathematics do a good job of communicating the behavior of physical phenomena. In some instances, pure mathematical areas have been found to describe some aspect of reality, only years after having been...

Good, bad or indifferent? Any ideas or suggestions? Gimblestitch

micromass submitted a new PF Insights post Problems with Self-Studying Continue reading the Original PF Insights Post.

Hi there, I'm currently a second year chemistry student in the UK. Since starting my degree I've found myself interested in theoretical/quantum chemistry. I would like to apply for a PhD programme in theoretical chemistry, which follows courses in quantum mechanics/statistical thermodynamics. I...

Hi Everyone, I have completed high school mathematics which has: 1.) Algebra 2.) Trigonometry 3.) Co-ordinate geometry rectangular co-ordinates 4.) Basic Vectors and 3D geometry 5.)Calculus:- Functions Limits Continuity Differentiability Functional Eqns...

Hello everyone! So, I'm currently double majoring in Math and Physics at my University. My end goal is to hopefully go onto graduate school to earn a PhD in Astronomy, the specific areas of Astronomy I'm interested in are Observational Astronomy, Instrumentation and Planetary Science. Here are...

Are there "things" mathematics describes that can't exist in the real world; things mathematics says can exist but are actually impossible to ever exist in the world we live in? Also, are there things that do exist in our world that mathematics says can't exist? The obvious answer to me is no...

I've seen a few threads discussing a topic similar to this, and I've been making some serious considerations and thinking about things. I'm currently debating switching over from a Physics major to a Math major and minoring in Physics. There are a few various reasons to do this, one being it...

Homework Statement Reading Feynman The Principle of Least Action out of The Feynman Lectures on Physics, Vol 2. Link to text http://www.feynmanlectures.caltech.edu/II_19.html So I'm having a problem proving that, section 19-2 5th paragraf, that "Now the mean square of something that deviates...

I'm currently building a PC and I want to buy components that will be able to support whatever programs/software I will be using while getting my degree. I'm going to be starting the physics program at my university this fall so I don't really know what my professors will be having me...

micromass submitted a new PF Insights post How to self-study analysis. Part II: intermediate analysis Continue reading the Original PF Insights Post.

To what extent is the term infinity used in the physical world. When talking in terms of mathematics we can have a set of all natural numbers called an infinity, then we can have a value that comes after this set of infinity (lets call it 'a'). After 'a' comes 'a+1' then after this set of...

How to self-study mathematics https://www.physicsforums.com/insights/how-to-study-mathematics/ How to self-study basic high school mathematics https://www.physicsforums.com/insights/self-study-basic-high-school-mathematics/ How to self-study calculus...

I'm currently a first year MathPhys student, and next year I have to decide my stream. I can pick a combination (pure) Mathematics, Applied & Computationtal. Mathematics, Statistics, MathSci, Physics, Theoretical Physics or Physics with Astronomy & Space. Naturally there are restrictions, and I...

What are the mathematics behind multiple dimensions? Does mathematics allow for the existence of more than four dimensions? What allows the ability to possesses more that four dimensions, if there is already proof? I looked around, but I didn't find much by way of the answer I was looking for.

Or basically anything that isn't a positive integer. So I can prove quite easily by induction that for any integer n>0, De Moivre's Theorem (below) holds. If ##\DeclareMathOperator\cis{cis} z = r\cis\theta, z^n= r^n\cis(n\theta)## My proof below: However I struggle to do this with...

I have a big choice to make which is not letting me sleep or study properly. For the last few years I have been attending community college. For financial reasons I left school during the 9th grade. Both of my parents were terminally ill. My father passed away, my mother still lives. I placed...

What is the most motivating way to introduce group theory to first year undergraduate students? I am looking for some real life motivation or something which has a real impact.