Mathematics Definition and 995 Threads

Homework Statement I'm a student of a correspondance university in Japan. I want to learn physics and mathematics in English,but I can't find which books are suitable to study from very basic mathematics and Physics. "Very basic", I mentioned, means on a level like pupils at school in the U.K...

After using Matlab here and there whilst I was at university, I thought that although it was very powerful, its use was extremely cumbersome and slowed down what should be fairly simple processes like making 3D plots and solving ODEs, PDEs etc. That got me wondering if there were any programs...

In order to attempt to understand relativity, I thought of the following 'paradox', which I hope to resolve mathematically. An astronomer makes a terrifying observation. An asteroid is on a crash course towards Earth at almost the speed of light. An ultra advanced nuclear rocket is...

I am seeking resources that cover the Mathematics of Quantum Mechanics in order to prepare for an exam. The course is not rigorously mathematical, and as such, I am looking for materials comprehensible to the average Physics student. Websites, books, online courses/lecture notes are all...

How do I take my mathematics to the "next level?" Let me explain what I mean: I am finishing my junior year in undergraduate. I consider myself "good" at math, in the sense that I make A's in my classes. But that's not enough. I want to be a world class math student because my dream is to...

Does anybody know of online courses in mathematics. In particular I am looking for abstract algebra and real analysis or other proof based courses. I am aware of the various videos available, but I am looking for those courses in which one registers and attends online with assignments and...

Homework Statement The sum S n of the first n terms of a geometric sequence whose nth term is u n is given by 7n-an / 7n Where a > 0 Find an expression for un Find the first term and the common ratio of the sequence Consider the sum to infinity of the sequence Determine...

I really like math and I want to major in it. I want to hopefully get a masters in math. But I want to know what is it like? Do any of you here have a masters or at least have an idea of the course? I heard getting a masters is a lot of independent research. How is that different from a...

So I was wondering what mathematics I will need under my belt before starting at a brand name graduate school(MIT, UChicago, UC Berkely, CalTech, Harcard, etc...) if I were going to specialize in particle or soft-matter physics. Thank you!

This is Dr. Stephen Marquadt. http://img404.imageshack.us/img404/1373/stephenmarquardt.jpg When he was a young child, his mother was horribly disfigured in a car crash. So he eventually took the route of becoming a reconstructive plastic surgeon. As a plastic surgeon, he had to work out...

Due to personal life issues and limitations, I've been seeking other options for my B.S. and came upon Applied Mathematics. What I've been on the fence about for a while now has been which Engineering degree to pursue be it Material Science, Mechanical, or Aerospace. However, it has been...

I'm trying to write down an axiomatic development of most of mathematics, and I'm wondering whether it's logically permissible to use natural numbers as subscripts before they have been defined in terms of the Peano Axioms. For instance... the idea of function is used in the Peano axioms...

I decided to post a new thread for this. I saw the pinned thread about going into Engineering but my specific questions were not answered in that thread. I am going into Aerospace Engineering this summer. I am doing it because I love Physics, like Math, and am very interested in Spacecraft...

Hi, First of all, I am an undergraduate Chemistry student, but who is also very interested in various areas of science (most actually :P), but like many other people I am especially curious about Einstein's theory of relativity, quantum mechanics and I especially would like to be able to read...

Hey guys, I'm taking Discrete Mathematics and am having a bit of trouble with one of my proofs. If any of you has any experience with that and could tell me where I'm going wrong, I'd appreciate it! Ok, here it is: Prove each statement in 8–23 by mathematical induction: 27. A...

Could anyone tell me what is the mathematics of the 2D and 3D mesh? Thank you

When you solve an equation, how does it make you feel? Why do you open a book and solve every equation in it? After doing so what do you feel? I don't think solving maths problems can release adrenaline so how does it make you feel? Why do you guys continue to pursue maths? Do you get comfort...

Bachelors In Mathematics and PhD In Physics Hello, As of now, I am maneuvering through undergraduate work, with the intention of gaining a bachelors in mathematics and (someday) a PhD in physics. For my mathematics courses I have taken, I have done all three calculi, discrete mathematics...

Hello, I am a senior in high school wondering if I should major in mathematics. I am developing a strong interest in the subject and am currently enjoying and doing well in my AB AP Calculus course. The problem, however, is that I have read in many places (such as on these fantastic forums) that...

I saw somewhere that mathematics can be divided into 10 sections, i quote: "1-Arithmetic 2-Basic Logic and Set Theory: proof techniques and reasoning, Sets, operations on sets, mappings, binary relations (you'll need that if you expect to go anywhere beyond arithmetic..)...

I'm currently taking a course on Boolean algebra. It's officially named "Mathematical Logic", but I really don't see much resemblance between what I'm doing and other courses of mathematical logic that are taught in the US. It has only been a couple of weeks, but to let you have an inkling of...

I am currently studying in 12th standard in India. My subjects are English, Bengali, Maths, Physics, Chemistry and Computer Science. I am quite good in mathematics. I would like to study maths and physics in Germany. Please give me some detailed information about the maths ans physics curricula...

Hi. I would like to learn the mathematics from Gravitation by MTW, but i find the book hard to follow mainly due to its style. Many other authors seem to work mainly with components and do not employ the exterior derivative etc. Does anyone know some text which treats GR similarly to MTW, but...

Problem Given: Scientists estimate that the flow southward of the North Atlantic deep-water current is 10 Sverdrups. (A Sverdrup is 1 million meters3 per second) If the volume of the Atlantic Ocean is 3.24 X 1017 meters3, how many years would be required for the entire Atlantic Ocean to...

I have received some admissions decisions from the graduate programs that I have applied to, and I am stuck with a tough decision to make. I am hoping to hear from those who may have found themselves in a similar situation or someone who may have relevant industry experience who can shed some...

Hello folks, I was wondering if anybody could give me some suggestions on which mathematics courses will be of the most use for theoretical physics. I am a sophomore at Wayne State university and am taking intro to quantum mechanics and a first course in optics this semester. I am taking...

Hello all I am a new member here. I've found this forum today by chance. My question is, which theory or field of math deals with tables, meta data and table functions? Is it group theory? Regards Tunc

All the relevant information about the problem is in the attachment. I just have a problem with the first step, my question it: How is b true? I would have thought that the second part of the exponential function would be taken outside of the integral as well as A since you're taking the...

This question was posed by algorithmshark and not yet solved on math.stackexchange.com: He has posted some thoughts on his question: real analysis - Evaluating $\sqrt{1 + \sqrt{2 + \sqrt{4 + \sqrt{8 + \ldots}}}}$ - Mathematics Various members (including myself) have shown this expression...

I am curious about the note taking strategies implemented by others on this board. I am referring to notes taken while reading (as opposed to notes taken during a lecture). As I progress further in my studies, I am noticing that I learn the material best when my notes become somewhat of a...

Here is my situation: I am currently finishing my undergraduate physics program and thinking of doing graduate studies. My only concern is that the knowledge of mathematics is fairly weak. My program offers little mathematics, its very general physica. I am interested in doing theoretical...

mathematics - Q 8 -- Forming Differential Equations

Homework Statement I have not been doing Lyapunov for a while and when doing an ordinary Lyapunov problem the other day, I ran into a funny situation. The correct way of doing it: \begin{align} \dot{e} &= \frac{1}{L}(u - R(e + x_{ref})) \\ V(e) &= \frac{1}{2}Le^2 \\ \dot{V} &= Le\dot{e} = Le...

Hi everyone, I've set up my schedule through the next three years so that I will be able to graduate with a double major in mathematics, and economics (both bachelor of science). I was just wondering if anyone knew the job outlook on these two degrees. I have a strong interest in both...

For a mathematician, how is rotation defined in the most general sense? Question arose to me because it occurred to me that an essential property of the rotation matrix is that it preserves lengths. Is this the only mapping (if not please give me a counterexample) that has this property...

Author: Ronald Graham, Donald Knuth, Oren Patashnik Title: Concrete Mathematics: A Foundation for Computer Science Amazon link: https://www.amazon.com/dp/0201558025/?tag=pfamazon01-20 Prerequisities: Calculus Level: Undergrad

Iam a High school Student starting grade 11 this year . I want to learn all undergrad physics chapters like Classical Mechanics , Optics , Statistical Mechanics , Thermodynamics , Electromagnetism , Quantum Mechanics , Solid State physics , Nuclear Physics , Plasma Physics , Relativity etc . I...

As I've been looking at universities this year, a lot of them offer a joint bachelors and masters in math for undergrads, and I'm unsure if this is a good idea. I'm afraid that I won't get a thorough, well-rounded education if I rush through things, but on the other hand it could be helpful get...

Abstract Algebra Aluffi - Algebra: Chapter 0 Artin - Algebra Dummit, Foote - Abstract Algebra https://www.physicsforums.com/showthread.php?t=704700 https://www.physicsforums.com/showthread.php?t=704865 https://www.physicsforums.com/showthread.php?t=672385 Herstein - Topics in Algebra...

Author: Chris Tsokos Title: Probability for Engineering, Mathematics, and Sciences Amazon Link: https://www.amazon.com/dp/1111430276/?tag=pfamazon01-20

Author: Douglas Smith, Maurice Eggen, Richard St. Andre Title: A Transition to Advanced Mathematics Amazon Link: https://www.amazon.com/dp/0495562025/?tag=pfamazon01-20 Level: Undergrad Table of Contents: Preface Preface to the Student Logic and Proofs Propositions and Connectives...

In (Shannon) information theory, information is said to be the log of the inverse of the probability - what is the information content of 1+1=2? Or for that matter any fundamental axiom.

Can one tell me about the Mathematical Equivalent to Landau & Lifgarbagez. or any other set that deal with all Graduate Level Mathematics. There is a Series by Springer, Springer Graduate Texts in Mathematics but they contains too many books. It would be great if they contain Max. 20 books...

See a picture that represents the relations of the two triangles what is a "?" 3?3=3 3?3=4 3?3=5 3?3=6 3?3=7 3?3=8 3?3=9 3?3=10 3?3=12

Author: What Is Mathematics? An Elementary Approach to Ideas and Methods Title: Richard Courant Amazon Link: https://www.amazon.com/dp/0195105192/?tag=pfamazon01-20 Table of Contents: Preface How to use the book What is mathematics? The natural numbers Introduction Calculations with...

There is a book out there called Mathematics and Go (or the other way around, I am not sure). This book talks about an ancient game called Go (or in Chinese 围棋*wéiqì*） and the application of math to it, I think it can be done better since it does deal with surreal numbers and those do not really...

Author: Serge Lang Title: Basic Mathematics Amazon Link: https://www.amazon.com/dp/0387967877/?tag=pfamazon01-20 Prerequisities: Mathematics before high school Level: Motivated high-school students, college students Contents: Real numbers, solving equations, logic, geometry, trigonometry...

Say, I make some modifications to the basic assumptions and concepts to the existing Mathematics framework. How would the Mathematics community decides if it makes sense or not. Say, in my variation of Mathematics, I allow arithmetics between infinity. I understand infinity is a concept...

Hello! The following question was asked in a Soviet Union mathematics Olympiad about 2-3 decades ago. A friend brought it up a few days ago and it has been bugging us since then. The problem goes along the lines of: "There are 10 ammo boxes each containing 10 bullets, and each bullet...

I've come to these forums a lot, but I don't think I've ever really posted--so here goes number one. I am a freshman in a large public university, and I just recently switched over to mathematics/economics as my majors. I was originally an engineering major, but I abandoned ship because it...