Classes Definition and 592 Threads

(X,\rho) is a pseudometric space Define: x~y if and only if ρ(x,y)=0 (It is shown that x~y is an equivalence relation) Ques: If X^{*} is a set of equivalence classes under this relation, then \rho(x,y) depends only on the equivalence classes of x and y and \rho induces a metric on...

I am not in the honors program at my University but I really want to get good at math so I was thinking about perhaps enrolling in an honors section for the Discrete math and Linear Algebra classes I'll be taking next fall. It seemed like the greater depth that these classes go would be really...

Homework Statement R is a relation on the integers, xRy if x^2=y^2. Determine the distinct equivalence classes. Homework Equations [x]={yεZ}|yRx} Where Z is the set of integers The Attempt at a Solution [n]={-n, n} where n is an integer is this correct?

I have worked in the field of wildlife biology for years and have recently switched professions to teaching. One of my biggest concerns with the current biology curriculum is that it seems way too obsessed with it's molecular aspects. I think this over-focus can be extremely harmful to the...

I am new to astronomy and astrophysics, can anyone point to a great free online place to learn scientific notation? I am quite obsessed with learning the math, but unfortunately have not the funds to attend a proper school. Unfortunately I work for a cheap employer who doesn't even pay for work...

Hello guys, I was wondering if you all, who are more experienced than I, could perhaps offer a bit of advice about something I'm struggling with. I'm starting to feel very, very stupid. I'm a third year math/finance major who's struggling with upper level courses. For some reason my...

Hi PhysicsForum! Fall 2012 semester will be my last semester as an undergrad in Math and Statistics and I was planning on taking a handful of graduate level classes. I'm planning on applying to grad school in Applied Math and concentrating on differential equations, fluid dynamics, or...

Find the smallest positive integer which when divided by 12, by 17, by 45 or by 70 gives a remainder of 4 in each case. I know I can approach this problem by writing the equivalence classes. x=4mod12 x=4mod17 x=4mod45 or x=4mod70 I also know I can find x by multiplying 12*17*45 + 4...

Hi all, first post, please bear with me! I am trying to understand Lagrange's Theorem by working through some exercises relating to the Orbit-Stabilizer Theorem (which I also do not fully understand.) I think essentially I'm needing to learn how to show cosets are equivalent to other things or...

Hi, I need help to prove this for my professor this is called "Distribution of power congruence classes" or something like that With all n∈NiS∈N correct 1) n ≡Qs(n)(mod 10s-1) 2) n ≡Qs(n)(mod 10s+1) http://img546.imageshack.us/img546/8341/withall.png

please help! it's very important!

The two classes would happen during the same summer session which lasts six weeks. The lectures would be 2 hours long each every Monday through Thursday. I would have the month of June to look ahead (if that helps at all) in my Calculus book since we use the same book for the entire Calculus...

Alright, so a few years back I was one of those "Am I too old...?" people. Well, I've stuck with school part-time at the local CC and this upcoming fall I will finally be in a position where I can attend school full-time, so I am in the process of sending out applications to some 4-year...

Homework Statement class Person(object): """Defines a person with dob (date-of-birth, string), gender (two-value string), name (string) and age (integer).""" def __init__(self, dob, gender, name): assert (isinstance(dob,str) and dob.isdigit() and len(dob) == 8), 'dob is...

Hey guys, i'll be a sophomore next year, and I was wondering about what classes you could recommend me taking then, as well as advice for future coursework. Which 4 of the following would be (the most) useful for theoretical physics? -Differential Geometry -PDEs -Fourier analysis -Complex...

Hey guys, I'm a second semester sophomore who goes to a school that's not terribly well known for math. As such, I'll have taken most of the math classes I want to take by senior year (we don't have a very strong graduate program, so not a lot of good grad courses except for applied...

Hi guys, I'm just wondering if there's supposed to be a big jump between my foundational calculus and physics classes versus the technical ECE classes... I found the calculus and physics to be super easy, and I could basically follow the professor's train of thought during the lecture...

Last semester I took a combined course of Diffy Q and Linear Algebra. I feel I know the basics of LA and want to explore things a bit further. After talking to some professors at my school they told me that the next linear algebra class is a graduate class.. After looking at the course notes for...

I am wondering, after one has created a bunch of header and implementation files for a bunch of related classes, what do you do with them? How can they be organized so that I do not have to #include " " an unreasonable amount of headers in different programs? I am googling this, but I am not...

A metric space of equivalent Cauchy sequence classes (Z, rho) is defined using a metric of the sequence elements in the space (X,d), where d is from XX to R (real numbers). The metric of the sequence classes is rho = lim d(S, T), where S and T are the elements of the respective sequences. To...

I am interested in taking Calculus and an introductory Chemistry class online over the summer. Does anyone know where I can do this? I am currently a high school junior. Any answers are appreciated.

Hey everyone, I'm currently a junior in high school and I'm wondering if it would be possible to take a class or two at a community college without a high school diploma. I would like to be able to simply pay for some classes, take them, and leave. I don't want to stay at a community college...

Approximately how many hours a day do you spend doing your homework and/or studying? How many hours do you spend daily (approximately, of course) on physics homework alone, math homework alone, studying for physics, studying for maths, studying/doing homeworking for the rest of your class...

Hey I was hoping some of the established engineers on here could help me out. I have my B.S. in Physics, I work as an electrical engineer, and I'm starting my second semester for my M.S. in Nuclear Engineering. I am not currently employed in the nuclear field but I'm looking to move into it in...

I am at the University of Maryland and just successfully enrolled in the double degree program with physics as my second degree to mechanical engineering. Here are the requirements for physics: http://umdphysics.umd.edu/images/pdfs/ugrad/physprofreqs.pdf. I am wondering what further classes I...

Spring 2012 Freshmen E@M Fall 2012 Waves, Optic and Thermo Modern Physics Spring 2013 Quantum Waves Anayltical mechanics Fall 2013 Junior E@M semester 1 Junior Quantum semester 1 Spring 2014 Junior E@M Semester 2 Junior Quantum semester 2 Reading in Particle Physics Fall 2015...

Hey I'm currently a freshman math major and just registered for my spring classes. When I went to my adviser, she thought I was insane for taking three math classes at one time. Am I insane? Schedule: -College Calculus 3 -Introduction to Differential Equations -Introduction to Linear...

I'm currently in high school and I'm deciding whether or not to take a computer course such as Computer Science. The thing is, it seems like a dull subject (sorry to those who like it, this is just my opinion) involving basic mathematics. My friends have told me it's helpful for university...

Homework Statement Define a relation ~ on ℝ by a~b if and only if a-b∈Q. i) Show that ~ is an equivalence relation. ii) Show that [a]+=[a+b] is a well-defined addition on the set of equivalence classes. Homework Equations Q represents the set of rational numbers. An Equivalence...

I am currently getting a physics BS. was going to double major in math but am going down to just a minor due to the huge work load the latter would be. the class i can't get rid of is an introductory proofs class. and i then have a choice between advanced calc (calc proofs), abstract algebra, or...

Hi all, I am an EE major and planning on transferring to a different school next year and noticed that instead of stand alone Linear and Diff Eq classes they have an amalgamated EE math class that teaches you all the math fundamental to EE. I was reading the reviews of this course and everyone...

I'm almost done with my electrical engineering Bachelor's Degree. I have 1.5 semesters left, and I'm heavily considering grad. school in control systems (probably just a master's). I've focused on areas such as signal processing, control systems, circuit design, some electromagnetics, and...

Hi all, I have really enjoyed this forum and I appreciate all the interaction. I am planning to transfer to a different EE program (Great reputation, and a lot closer) and I am trying to plan my courses for next semester. Just wanted to see if anyone had any input. I am definitely taking...

Homework Statement If f ∈ C(R) with f(0) ≠ 0, show that there exisits a g ∈ C(R) such that [fg] = [1], where [1] denotes the equivalence class containing the constant function 1. Homework Equations The Attempt at a Solution Let f ∈ C(R) such that f:R → R is defined as f(x) = 1/x...

Homework Statement Define a relation on R as follows. For a,b ∈ R, a ∼ b if a−b ∈ Z. Prove that this is an equivalence relation. Can you identify the set of equivalence classes with the unit circle in a natural way? Homework Equations The Attempt at a Solution I have already proven that this...

Hello, I am a first year student majoring in chemistry. I really like it and I'm very interested in the subject, but I am worried about my math skills. I am taking calculus 0 right now and I really struggled on my first exam. What kind of math is in the upper-level chemistry courses? Right now...

I am a 3rd-4th year student planning to try and get into graduate school in my field of study. But I got some terrible marks in my first year in courses relating to my program (science and math courses), and in a non-related course. Since some universities specifically require an undergraduate...

Hello Physicsforums, i am a computer science student and i am just wondering what would be some good classes to supplement my CS degree with. i have some free electives from AP courses and i don't really want to waste them. I was thinking of taking a Number Theory class and an upper level...

Homework Statement Prove: If E1, · · · , Ek are the disjoint equivalence classes determined by an equivalence relation R over a set X, then (a) X = union of disjoint equivalence classes Ej (b) R = union of disjoint (Ej x Ej) Homework Equations R is a subset of X x X The Attempt at a Solution...

I'm not sure if I did these 2 questions correctly, so would someone please check my work for any missing ideas or errors? Question 1: Homework Statement Prove: For every x belongs to X, TR∩S(x) = TR(x) ∩ TS(x) Homework Equations The Attempt at a Solution TR(x) = {x belongs to X such that...

Anyone taking either of these this October or plan on taking them soon? Questions, comments...etc. Always an interesting conversation...

My professor assigned a project that has the user enter information for an Object called Student which is derived from Person. The information is a name, an id number, two scores, an average, and the letter grade equivalent of the average. I'm having trouble sorting the student's according to...

Hello all, I am wondering if I could get some advice from people who have done MHD/Plasma Physics (or even better, went to do something like 'MSc in Fusion Energy' which is offered by York University). Ideally I would like to work somewhere with fusion energy (although it is vastly dominated...

I'm a senior in HS. Took AP Physics B last year had a 93 avg and got a 5 on the AP. Taking Ap Physics C this year. Started reading "The Fabric of the Cosmos" by Brian Greene and learning about astronomy over the summer. I really like this kind of stuff but the actual class, Physics B and C...

Hi, If we change coefficients in Homology, we can use the universal coefficient theorem to find the change in the homology group. Still, is there a way of knowing what happens to _individual classes_ under this change of coefficients? I am just thinking of cases where there is a...

If I take 2 more classes I'll have a my minor in mathematics. I am curious about which ones would be most beneficial to me….Probability Theory, Number Theory, Complex Analysis…other? Any suggestions? (Physics Major)

Hello Physics Forums! I am new to this forum but have definitely been browsing through here for a while now. I am just wondering how hard is it to get an A in physics? I am talking about the beginning general physics with calculus. From what I have seen, students at my school seem to have a...

Hi everyone, I may be being a bit dramatic about this but I feel extremely cruddy right now. I am (technically) a junior in college at the moment. I say technically because my first year was at community college where I not only didn't take 12 hours each semester (full time) but some of those...

I'll be taking a first course in quantum field theory and general relativity this fall at the masters level and I have a few weeks until I start. I was wondering if anybody had some advice on what to brush up or even self-teach before I'm neck deep in them (on top of other classes) so I can be a...

So I graduated in undergrad in May 2008 with a BS in EE. I went directly into a PhD program with full funding. I put in a year and did decent in my classes and my research. But I didn't enjoy my research and I wasn't doing as well in my classes as I had hoped. I decided to take a leave of...