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    Proof of the Lindemann-Weierstrass Theorem

    I am wanting to find a good proof of the Lindemann-Weierstrass Theorem. Most importantly I need the part that states that eα is transcendental where α ≠ 0 is algebraic. What are good online resources or books for the proof? Thank-you.
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    Determining a formula for a (sub)sequence

    I currently have the first 125,256 terms of a sequence of natural numbers. I need to find a formula for any non-finite sub-sequence. Are there any good methods for obtaining such a formula? I can already say that it isn't a linear distribution, and I highly doubt it being polynomial (although...
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    Principal root of a complex number

    Homework Statement I am doing a problem of a contour integral where the f(z) is z1/2. I can do most of it, but it asks specifically for the principal root. I have been having troubles finding definitively what the principal root is. Anyplace it appears online it is vague, my book doesn't...
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    Verify that the Stokes' theorem is true for the given vector field

    This is a problem from an old final exam in my Calc 3 class. My book is very bad at having examples for these types of problems, and my instructor only went over one or two. Help would be much appreciated. Homework Statement Verify that the Stokes' theorem is true for the vector field...
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    Need help understanding Lagrange multipliers at a more fundamental level.

    I understand that for Lagrange multipliers, ∇f = λ∇g And that you can use this to solve for extreme values. I have a set of questions because I don't understand these on a basic level. 1. How do you determine whether it is a max, min, or saddle point, especially when you only get one...
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    Use Lagrange multipliers to find the max & min

    Homework Statement Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x,y) = exy; g(x,y) = x3 + y3 = 16 Homework Equations ∇f(x,y) = λ∇g(x,y) fx = λgx fy = λgy The Attempt at a Solution ∇f(x,y) = < yexy, xexy > ∇g(x,y) = <...
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    Programs What can one specialize in for a MS/PhD in Mathematics?

    What is a list of areas of focus for Masters/PhD pursuers for Mathematics? What has the best future prospect for careers?
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    Genetic Modification of a Live Organism Is it Possible?

    *** I know this is of questionable ethics, but I am asking a hypothetical *** If we had a human of adult age, let's say, age 20-30. Would it be possible to genetically modify all cells in the body and make the changes take effect in a realistic manner? If so what would be the limits and steps...
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    Converting an Integral to a Rieman Sum

    I know I should know this, but how would one convert a typical integral into a Rieman Sum? ∫0n sinx + x dx for whatever n. for example.
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    Find symmetric equations for the line of intersection of the planes

    Homework Statement Find symmetric equations for the line of intersection of the planes The planes: 5x - 2y - 2z = 1 4x + y + z = 6 Homework Equations r = r0 + tv x = x0 + at y = y0 + bt z = z0 + ct The Attempt at a Solution I have attempted this in many different manners and would like...
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    Programs Math & Computer Science Double Major - What Graduate Degree?

    I am heading into my Freshman year in college. I know it's going to be far in the future, but I want to start brainstorming what my 5-10 year goal is. Any help is appreciated. With these majors, I'm planning on getting a masters in Computer Science, but what should I do with the math degree...
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    Math What to do after obtaining my undergraduate degrees - Math and CIS

    I am currently attending IUPUI for a double major in Pure Mathematics and Computer & Information Science with a double minor in German and Physics. Overall this will take me 4 1/2 years and give me $38,000-$45,000 of debt. 1. I am wondering, which masters degree should I go for first? Math or...
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    Determinants of matrices greater than 3x3

    I am wondering how one would find a the determinant of a 4x4 or greater. This isn't an urgent question, just a curiosity.
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    Vectors - Boat & Stream problem

    Homework Statement A boatman wants to cross a canal that is 3 km wide and wants to land at a point 2 km upstream from his starting point. The current in the canal flows at 3.5 km/h and the speed of his boat is 13 km/h. (a) In what direction should he steer? (b) How long will the trip take...
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    Where to begin assembly?

    I've been programming c/c++ for a month or two, I have experience with Expression 2 (an in game programming language in Garrys Mod which is similar to VBasic), and 7 years experience with web development. What I'm wanting to do now is begin learning Assembly language and how to compile it...
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    Programs What degree should I get?

    I'm planning on going into Physics and Mathematics. Should I get a double major in: 1. Physics & Applied Mathematics 2. Physics & Pure Mathematics - How would Applied/Pure affect my career? What minor should I get?: 1. Computer Science 2. Chemistry 3. Other? I am planning on...
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    Issue with stringoperator[]

    #include <iostream> #include <string> using namespace std; void str2hex(string str) { int strlen = str.length(); // Assign the length of input/str to strlen string hex[strlen]; // Initialize the Array hex with the length of the string for (int x = 0; x <...
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    Programs What Double Major Should I Get?

    I am currently thinking about getting a double major with a combination of any of the following degrees: Physics Mathematics Chemistry German And possibly (With less consideration): Biochemistry Molecular Chemistry Software Engineering Most recently I have thought about doubling...
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    Converting between bases without base 10 mid-step

    I am currently trying to go between any two bases which are between and including base 2 to base 10. (i.e, base 10 to base 3, base 4 to base 6, etc...). Is there an equation or set of formulas for a one-step transition between the bases (or one-way method, rather than converting to base-10 then...
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    The Basics

    I am a high school senior who is new to these forums. So far, I have found them intriguing, but I do have a question that I have asked many of my teachers, but sadly, had no real response. What are the basics of quantum physics? Basic concepts, theories, equations for example. I haven't been...
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    Orbits of planets

    As my state (Indiana) has removed Astronomy from the curriculum, my school no longer offers it. I have taken AP Physics B and that is my best knowledge provided by the modern school system, so I apologize ahead of time for any low-level or simple questions. I am wanting to know the equations...