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    Books for Reviewing Undergraduate Mathematics Before Grad School

    Hi, I will be starting my graduate study in mathematics in August 2011, and I was thinking of reviewing mathematics that I have learned while I was an undergraduate as soon as my summer vacation begins in June. The topics that I am considering to review include algebra (abstract and...
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    Should I apply to my undergrad institution's graduate program?

    I am almost done with applying to graduate schools in mathematics. My new question now is whether to apply my undergraduate institution's graduate program. First of all, all the professors that I have talked to told me that I should go somewhere else for graduate school. And I strongly agree...
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    Schools Am I really competent enough for grad school in math?

    First of all, I apologize you guys for posting another thread like this; I know there are millions of threads that ask something like this already, but it would be great if you can read and respond to another one. I am applying to 11 graduate schools in mathematics. I have enjoyed studying...
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    Schools Math Grad Schools in Canada?

    I am a senior math major in the US who would like to go to a graduate school in mathematics. I am still in a process of finding where to apply. Most of the schools that I have been looking so far are in the U.S., but recently I realized there are some decent schools in Canada as well (U British...
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    Isomorphisms of graphs

    Hi, I didn't know where graph theory falls into, so I decided to post this question on here; please let me know if there is another thread where this post is more appropriate. I am working on The Princeton Review's "Cracking the GRE Math Subject Test", and there was one problem about graph...
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    Graduate-level analysis vs. second-year physics

    Hi, I am a math major who will be a senior in my undergraduate career. I will be applying to graduate schools in mathematics. I still have not decided which courses to take in my senior year. So far, I have taken most of the undergraduate math courses, including real analysis, complex...
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    Schools I want to go to grad school in math, but

    I just finished my junior year at my university, and I am currently interested in going to graduate school in mathematics. But from reading some of the posts on here, I am starting to feel maybe I'm not really a desired candidate for graduate study in mathematics. I will post some information...
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    Text for Analysis Review

    I just finished taking a year-long undergraduate analysis sequence. The texts I used for this sequence were the first eight chapters of Rudin's PMA (everything before multivariable calculus) and Spivak's Calculus on Manifolds, as well as a little bit of my professor's lecture notes on...
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    Any good book to review abstract algebra?

    Hi, I am a junior and a math major, and I am almost done with my year-long abstract algebra sequence for undergraduates. While I found the materials interesting, I feel like I got lost at some places in this course, and I would like to review (or in some topics, relearn) the materials that I...
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    Foreign Language over the summer?

    I am a math major who is about to finish his junior year. I am still not so sure what I want to do over the summer (besides starting on my senior thesis project), and since there aren't that many summer courses that might be interesting for me to take, I was wondering if it would be good idea to...
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    Programs Quantum Mechanics for a math major

    Hi, I will be a senior next year, and I am thinking of taking a physics class that deals with quantum mechanics. I am a math major, and have taken variety of math courses (e.g. real analysis, abstract algebra, complex variables, advanced linear algebra, and etc.) as well as first-year physics...
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    Complex Analysis (Practice Exam)

    Homework Statement This question is in my exam review problem from my complex analysis class. Compute f(100)(0)/100!, where f(z) = 1/(1+i-sqrt(2)z). (f(100)(0) means the 100th derivative of f evaluated at 0.) Homework Equations Cauchy's integral formula might be helpful. The answer to this...
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    Got rejected by REUs now what should I do?

    Hi, I am a junior and a math major, and I applied for 8 REU programs, and it looks like I will be rejected by all of them (I'm already rejected by 7, and I'm still waiting to hear back from UW, but the chance of getting in there seems very low). Now I have no idea what to do over this...
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    Differentiation on Euclidean Space (Calculus on Manifolds)

    Homework Statement This is from Spivak's Calculus on Manifolds, problem 2-12(a). Prove that if f:Rn \times Rm \rightarrow Rp is bilinear, then lim(h, k) --> 0 \frac{|f(h, k)|}{|(h, k)|} = 0 Homework Equations The definition of bilinear function in this case: If for x, x1, x2...
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    I want to get A's in analysis and abstract algebra

    I just finished my first quarter of analysis (Text: Rudin's PMA) and abstract algebra (Text: Beachy and Blair) courses. I must say I really enjoyed these courses, and I feel like I learned a lot from them. However, I still ended up getting B+'s from both of these courses. While I'm not...
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    Math REU - summer 2010

    I am a math major and a junior, and I'm interested in doing REU during next summer. I've been looking through some of the REU programs for math, and while most of them still show the summer 2009 information, a lot of them sound pretty interesting. So what are some tips to get accepted to this...
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    Abstract Algebra & Computer Science

    Hi, I have heard a few times that it is beneficial to study abstract algebra if I want to study computer science at advanced level (i.e. upper class, grad school, etc.), but is this true? If so, why would it be so? Thanks
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    Any thoughts on Introduction to Mathematical Statistics by Hogg, Craig, and McKean?

    Any thoughts on "Introduction to Mathematical Statistics" by Hogg, Craig, and McKean? Dear PF members, I was looking for a textbook for my mathematical statistics course, and it turns out that Introduction to Mathematical Statics by Hogg, Craig, and McKean will be the book for the course...
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    Courses Yet another which math course to take? thread

    Yet another "which math course to take?" thread Dear PF members, First, I would like to apologize in advance for asking this type of question repeatedly. I just haven't made my mind yet, and I just think getting another advice from PF members might be helpful. So, I'm going to be a...
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    Prerequisites for Electromagnetism?

    Hi, Just out of curiosity, what should I know if I am going to take upper-division electromagnetism course. The text for the course is Griffiths' Introduction to Electrodynamics. I am not a physics major (I am a math major), but I have taken the first-year, calc-based physics sequence...
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    Question from a theorem in Baby Rudin (Re: Least-Upper-Bound Property)

    Hi, I am reading Baby Rudin on my own to get prepared for the analysis class that I will be taking in the fall. I got up to this theorem, and I was wondering if someone can clarify me the proof of this (i.e. Thm 1.11, the first theorem). 1.11 Theorem: Suppose S is an ordered set with the lub...
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    How can I explain math to someone who doesn't know math?

    Hi, So I am an undergraduate math major who goes to a state university, and often time I get into conversations like the following: My friend: "What are you taking this summer?" Me: "I'll be taking (abstract) linear algebra." Case 1: My friend: "Hmm... 'linear' and 'algebra'? That...
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    Pure and Applied Math

    Dear PF members, I am about to begin my junior year as a math major, and I feel like I made one observation. That is, if I want to study math at advanced level, I need to choose either pure or applied mathematics. I have also noticed that if I get a title of "mathematician," that implicitly...
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    Programs [Undergrad Math Major Advice] What should be my next step?

    Hi all, I have just finished my second year at my university as a math major, and I am wondering what math classes to take next year. I will list my preferences and options so that you can give me some kind of advice. Where I am now: I mentioned here a few times that I did not do so well in...
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    Real Analysis vs. Topology

    Hi, I am currently a sophomore and a math major with thinking of adding computer science as either minor or second major. I get to register for my classes for Fall Quarter in a week, and I am thinking of taking 2 math classes: One will be numerical analysis, and the other is not yet...
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    How do I learn pure math?

    Hi all, The title is kind of straight forward, but let me add you a few background. I am majoring in mathematics and minoring (or possibly double majoring) in undecided (i.e. I'm still looking for the second concentration... right now I'm thinking of either physics or computer science)...
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    Math and Neuroscience

    Hi all, Back when I was in high school, I was in this group where we competed with other school on a Jeopardy-style quiz competition where all the questions are related to basic neuroscience. Ever since then, I was fascinated by neuroscience. Right now, I'm a sophomore at a university and...
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    Basic Algebra by Knapp

    Hi, I wonder if I'm posting my question at a right place, but does anybody know if this is a good textbook for abstract algebra, especially for someone who's taking a "serious" math course for the first time? BASIC ALGEBRA by Anthony W. Knapp...
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    How useful is nonlinear ODE (stability, periodic solutions, etc)?

    Hi, I have a choice of taking this advanced ODE course, and I am wondering if this is worth studying. The course will cover mainly chapter 9 of Boyce/DiPrima textbook after we cover existence and uniqueness theorem. Chapter 9 is called "Nonlinear Differential Equations", and covers topics...
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    Real Analysis vs. Intro to CS

    Hi all, I'm starting my second year at my uni pretty soon, and I'm trying to make a final decision about the classes that I'm going to take. I still haven't figured out what I want to do in future yet, but I'm thinking of along either academics (not necessarily math, but math is one of my...
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