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Mathamatics requirements for PhD Admission - Please URGENT- deadlines are nearer


hopethebest

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I am from Asia and do not have subjects (names) that are similar to USA. I did an Engineering degree. Please go through following (Yes it is quit long, :upset: ) list and let me know whether I am OK with following math background.

 

Mathematics (1st Year) Logic and set theory, Real Analysis (Real Number System, Real Intervals, Supremum and Infemum, Completeness Axiom, Powers on Numbers, Basic Functions: Polynomial, Exponential, Trigonometric, Hyperbolic; Their Inverses, Limit of a Function, Extended Real Number System, Continuity, Differentiability, Derivative and Higher Derivatives, Maxima and Minima, Rolle’s Theorem, Mean Value Theorem, L’ Hospital’s Rule, Sequences, Cauchy Sequences, Infinite Series, Convergence of Series: Ratio Test, Comparisons Test, Limit Comparison Test, Maclaurine’s Integral Test; Harmonic Series, Infinite Products, Power Series, Taylor’s Series, Integration of Continuous Functions, Definite and Indefinite Integrals). , Complex Numbers, Vectors, and Matrices, Basic Probability (Pigeon-Hall Principle, Permutations and Combinations, Basic Laws and Elementary Theorems in Probability, Conditional Probability, Baye’s Theorem, Integer Equations, Discrete and Continuous Random Variables. Probability and Cumulative Distribution functions, Joint Distribution Function, Integer Equations, Generating Functions for Experiments) - (Grade: A)

 

Mathematical Methods (1st Year) - Numerical Methods (Approximations by Taylor Series, Numerical Solution of System of Linear Equations: Non Iterative Methods: Gauss Elimination, LU Factorization; Iterative Methods: Gauss-Seidel and Jacobi Methods; Solution of Non-linear Equations: Bisection, Simple Iterative, Newton-Rapson; Polynomial Approximation of Functions: Lagrange Polynomials, Newton’s Divided Differences, Least Square Polynomial and Functions, Finite Differences, Interpolation and Extrapolation, Numerical Differentiation, Numerical Integration: Trapezoidal, Simpson’s Rules, Numerical Solution of Ordinary Differential Equations: Euler’s Method, Taylor Series Method.), Ordinary Differential Equations (Orthogonal Trajectories, Isoclines, First Order Ordinary Differential Equations; Variable Separable, Homogeneous, Linear and Exact; Reducible Forms, Second Order Ordinary Differential Equations, Reducible Forms), Multivariate Calculus (Multivariable Functions, Partial Differentiation, Chain Rule, Change of Variables and Jacobians, Directional Derivatives, Maxima and Minima, Lagrange Multipliers, Taylor Series Expansion, Double Integral, Triple Integral, Geodesics, Vector Functions, Introduction to Vector Calculus), and Statistics - (Grade: A)

 

Differential Equations (2nd Year) - Fourier Series approximation, Partial Differential Equations, Laplace Transform and applications, Fourier Transform and applications, Ordinary linear differential equations with variable coefficients - (Grade: C+)

 

Linear Algebra (2nd Year) - Vectors spaces, subspaces, linear combinations, spanning sets, linear independence, and bases. Column space and row space and null space of a matrix and application, linear transformation, Eigen values, Eigen vectors and related topics, Diagonalisation of matrices, Quadratic forms, Applications, Numerical Linear Algebra - (Grade: A)

 

Calculus (2nd Year) - Vector Calculus (Vector differentiation and differential operators, space curves and line integral, surface and surface integrals. Divergence theorem, Stroke’s theorem, Greens theorem in plane, Some basic applications), Complex Variables (Analytical function and Cauchy-Reimann equation, Cauchy’s integral formula and applications. Taylor and Laurent’s series, contour integration. Introduction to conformal mapping) - (Grade: A-)

 

Discrete Mathematics (2nd Year) Logic, Introduction to Graph Theory, Miscellaneous - (Grade: A)

 

Applied Statistics (3rd Year) - Discrete and continuous random variables, Statistical Inference, Use of MINITAB - (Grade: C+)

 

Operational Research (4th Year): Modeling with linear programming, geometrical solution to problems with two decision variables, the simplex method including the two phase method of a solution of problems with mixed constraints. Duality. Transpiration and Assignment problems. Theory of zero sum, two person matrix games.

Revised simplex algorithm. Dual Simplex algorithm, sensitivity analysis and parametric programming. Integer programming, Gomory’s cutting plane, branch and bound, the knapsack problem. .Dynamic programming, the inventory model. Non-linear optimization. Introduction to network algorithm including minimum connector problems: Shortest and longest path algorithms and critical path analysis. (Grade: A)

 

Note: Blue color ones are major topics followed by description

 

Thank you in advance

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I think that fulfills minimum requirements and gives you some nice extra stuff.

 

Thank you publicaffairsny

 

If you please can give me some extra knowledge on;

 

1. What are the important section when you say nice extra stuff :D

2. How do I highlight that fact in the admission process? SOP perhaps?

3. Should I submit the details of contents my math courses with the application as a separate pdf file as the subject names are different

 

Thank you. Hope I am not asking too much from you.

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The important ones are Mathematics, Mathematical Methods, Linear Algebra, and Calculus. Those seem to cover most of the material from the Calculus Sequence (plus maybe "Intro to Real Analysis") along with a standard course or maybe even two in Linear Algebra. Those are what you need to emphasize.
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The important ones are Mathematics, Mathematical Methods, Linear Algebra, and Calculus. Those seem to cover most of the material from the Calculus Sequence (plus maybe "Intro to Real Analysis") along with a standard course or maybe even two in Linear Algebra. Those are what you need to emphasize.

 

Thank you tm_member, that was helpful.

 

If anyone can give me an idea where should I give the description of math course. Like if there is a section in application then it would be ok. Otherwise, should I state those information in SOP?

 

One other thing, will that C+ in Differential Equation hurt me? I have got a A- in Signals and System subject which was heavily relied on transformation serieses in the same semester although I some how missed DE (due to the lecturer, not his bad though, but his style forced me to quit from the subject. Didn't put good effort.) Should I explain that in SOP?

 

I am planning to apply, Kentucky, Syracuse, Houston, Purdue, SUNY Buffalo, Iowa state, Missouri and couple of masters from Canada.

 

Thank you

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I think it would be a mistake to waste space in your SOP on that list. It would be inappropriate and distract from the objective of that component.

 

As has been pointed out many times on this forum as well, departments are supposed to have someone that specializes in international applications. Unless your course titles and descriptions are truly abstract compared to what you completed-in which case having a Letter writer emphasize it would probably be better anyway-I don't see any reason to go into it. Adcoms won't care. They can get it from your transcript. Letters, when they are read, are supposed to garner information that cannot be gleaned from your other sources. Tell them what they can't see otherwise.

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Thank you for all your attention and replies.

I also don't want to include these details in SOP. However, my transcript only shows names of the subjects. Website of the mathamatics department gives a detals of each subject in pdf format. Now I am wandering how to include those details in my SOP. My country is not very well known. So adcoms, may not be having good idea about names

 

thanks again for all your ideas

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I agree with the method of including it in the additional information section if there is a section, or if there isn't, putting it at the end of the CV/resume.

 

If your country is not well known I think it is safe to include the description of classes. Even if it turns out the adcom is familiar with the classes, I can't imagine it would hurt you.

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Thank you all

 

I would leave SOP then and add the details to additional material section of end of CV.

 

If anyone could please tell me, how about trying to mitigate effect of C+ on differential equation by pointing out my another subject which used the same material for which I got A-

 

For applied stat section, I got A in Econometrics class and the professor is willing to give me a LOR too. SO I think that will be OK

 

Thank again for all the people who replied

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This seems like a solid math background to me. Those C+s are going to hurt you a little, but you've covered the important subjects.

 

Thank you all

 

I would leave SOP then and add the details to additional material section of end of CV.

 

If anyone could please tell me, how about trying to mitigate effect of C+ on differential equation by pointing out my another subject which used the same material for which I got A-

 

For applied stat section, I got A in Econometrics class and the professor is willing to give me a letter of recommendation too. SO I think that will be OK

 

Thank again for all the people who replied

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