What Connections Are There Between Number Theory And Partial Differential Equations?

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• THEORY OF EQUATIONS :1 ) A)Find the number of real roots to the following equation ? OR?

  B) Factorise the given equation to TWO CUBIC FACTORS or ONE LINEAR FACTOR and "FOURH DEGREE FACTOR". x^6 - 5x^4 + 16x^2 - 72x + 9= 0,,,, Can some given me a solution which not consume a lot of time ? 2nd QUESTION : A)Find all possible roots...

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  1/ A The second derivative is 6*5 x^4 - 5*4*3 x^2 + 16*2. Since the discriminant is < 0, the graph...

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• What would be a roadmap to learning Sheaf Theory and Topos Theory for a mathematics graduate?

  I am trying to acquire some basic mastery of the mathematics of sheaf theory and also topos theory. To achieve this, what would be a good reading list and road map for self-study? I have an undergraduate degree in mathematics from a long time ago, and...

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  To be perfectly honest, first enter math graduate school and get a good foundation in graduate level...

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• Which do you think would be a more difficult elective, Number Theory or Graph Theory?

  Number Theory: Properties of the natural numbers, congruences, diophantine equations, and elementary arithmetical functions. -Prerequisites: CALC3 & MAT300 (Intro to Proofs). -Textbook: Kenneth H. Rosen; Elementary Number Theory and Its Applications...

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  I personally thought that number theory was more difficult than graph theory, but that might have been...

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• Norse mythology number 9 ?

  I have recently (re)read the poetic Edda of Norse mythology and another book which has prose retellings of the myths, in which the number 9 appears repeatedly (the nine worlds, Odin hangs on Yggdrasil for nine days and nights, etc). The author of one...

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  That is doubtful. The Norse were great at navigating by the stars, but there is next to no evidence...

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• What does it look like to solve an undergraduate physics problem with string theory?

  How do you get from the equations of string theory and what they describe to something like the static electric field of a charged rod? I would love to see someone show which limits you take and how it stops being quantum mechanical as you get Maxwell...

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  The type of questions that string theory tries to answer are very different in nature than the ones...

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• Should I take Combinatorics or Number Theory in 5th semester?

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  Can you take both? I would take Combinatorics this semester. Then Number Theory later. But choosing...

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• Which math does have the most abstract algebra calculus 3, differential equations, discrete math, euclidean geometry, linear algebra, algebraic structures or number theory?

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  With the topics you've listed, linear algebra will usually be a prerequisite for abstract algebra but...

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• Why are higher mathematics like number theory, combinatronics, topology, manifolds, and even secondary or tertiary courses in linear algebra so difficult to learn?

  I have studied mathematics up to and including ordinary differential equations, statistics, and elementary linear algebra and would love to advance my (theoretical) skills set but after surveying the subject matter of higher courses it just looks too...

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  You just have to train your brain to stop assuming things.  The first time I encountered the difficulty...

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• I have a year to take any course I want at my university.  Which of these course will best prepare me for graduate study in machine learning or analytics?

  Background: I have one year (3 quarters at my school) to take any course I want.  My long term goal is to be able to apply machine learning techniques effectively to business problems/ work in startups.  My knowledge at the time of embarking on this...

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  In my opinion the three classes you cannot pass up are Numerical Analysis, Linear Algebra and Advanced...

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