YoungEconomist

02-23-2008, 10:49 PM

I will definitely take the following courses:

Calculus with Analytic Geometry I

First quarter in calculus of functions of a single variable. Emphasizes differential calculus. Emphasizes applications and problem solving using the tools of calculus.

Calculus with Analytic Geometry II

Second quarter in the calculus of functions of a single variable. Emphasizes integral calculus. Emphasizes applications and problem solving using the tools of calculus.

Calculus with Analytic Geometry III

Third quarter in calculus sequence. Sequences, series, Taylor expansions, and an introduction to multivariable differential calculus.

Advanced Multivariable Calculus I

Topics include the chain rule, Lagrange multipliers, double and triple integrals, vector fields, line and surface integrals. Culminates in the theorems of Green and Stokes, along with the Divergence Theorem.

Introduction to Differential Equations

Introductory course in ordinary differential equations. Includes first- and second-order equations and Laplace transform.

Matrix Algebra with Applications

Systems of linear equations, vector spaces, matrices, subspaces, orthogonality, least squares, eigenvalues, eigenvectors, applications. For students in engineering, mathematics, and the sciences.

Introduction to Mathematical Reasoning

Mathematical arguments and the writing of proofs in an elementary setting. Elementary set theory, elementary examples of functions and operations on functions, the principle of induction, counting, elementary number theory, elementary combinatorics, recurrence relations.

Probability I

Sample spaces; basic axioms of probability; combinatorial probability; conditional probability and independence; binomial, Poisson, and normal distributions.

My question is: What will be the marginal benefit of adding the courses below in terms of being prepared to succeed in a PhD program? (just for the record, I am not worried about the signaling benefit of the following courses, because they won't be on my transcript anyway because I would be taking them around the time I get admits/rejects) Also, out of the courses below, which ones are most crucial? Are any of them more important than some of the classes I've listed above which I plan on taking for sure?

Advanced Multivariable Calculus II

Elementary topology, general theorems on partial differentiation, maxima and minima, differentials, Lagrange multipliers, implicit function theorem, inverse function theorem and transformations, change of variables formula.

Probability II

Random variables; expectation and variance; laws of large numbers; normal approximation and other limit theorems; multidimensional distributions and transformations.

Introductory Real Analysis I

Limits and continuity of functions, sequences, series tests, absolute convergence, uniform convergence. Power series, improper integrals, uniform continuity, fundamental theorems on continuous functions, theory of the Riemann integral.

In case it matters for the advice, I don't aspire to top 10 programs (in fact, I won't be applying anywhere in the top 10, and possibly not even in the top 20). The overwhelming majority of programs I'll be applying to are in the range of 20 - 40 (according to US News Rankings).

Calculus with Analytic Geometry I

First quarter in calculus of functions of a single variable. Emphasizes differential calculus. Emphasizes applications and problem solving using the tools of calculus.

Calculus with Analytic Geometry II

Second quarter in the calculus of functions of a single variable. Emphasizes integral calculus. Emphasizes applications and problem solving using the tools of calculus.

Calculus with Analytic Geometry III

Third quarter in calculus sequence. Sequences, series, Taylor expansions, and an introduction to multivariable differential calculus.

Advanced Multivariable Calculus I

Topics include the chain rule, Lagrange multipliers, double and triple integrals, vector fields, line and surface integrals. Culminates in the theorems of Green and Stokes, along with the Divergence Theorem.

Introduction to Differential Equations

Introductory course in ordinary differential equations. Includes first- and second-order equations and Laplace transform.

Matrix Algebra with Applications

Systems of linear equations, vector spaces, matrices, subspaces, orthogonality, least squares, eigenvalues, eigenvectors, applications. For students in engineering, mathematics, and the sciences.

Introduction to Mathematical Reasoning

Mathematical arguments and the writing of proofs in an elementary setting. Elementary set theory, elementary examples of functions and operations on functions, the principle of induction, counting, elementary number theory, elementary combinatorics, recurrence relations.

Probability I

Sample spaces; basic axioms of probability; combinatorial probability; conditional probability and independence; binomial, Poisson, and normal distributions.

My question is: What will be the marginal benefit of adding the courses below in terms of being prepared to succeed in a PhD program? (just for the record, I am not worried about the signaling benefit of the following courses, because they won't be on my transcript anyway because I would be taking them around the time I get admits/rejects) Also, out of the courses below, which ones are most crucial? Are any of them more important than some of the classes I've listed above which I plan on taking for sure?

Advanced Multivariable Calculus II

Elementary topology, general theorems on partial differentiation, maxima and minima, differentials, Lagrange multipliers, implicit function theorem, inverse function theorem and transformations, change of variables formula.

Probability II

Random variables; expectation and variance; laws of large numbers; normal approximation and other limit theorems; multidimensional distributions and transformations.

Introductory Real Analysis I

Limits and continuity of functions, sequences, series tests, absolute convergence, uniform convergence. Power series, improper integrals, uniform continuity, fundamental theorems on continuous functions, theory of the Riemann integral.

In case it matters for the advice, I don't aspire to top 10 programs (in fact, I won't be applying anywhere in the top 10, and possibly not even in the top 20). The overwhelming majority of programs I'll be applying to are in the range of 20 - 40 (according to US News Rankings).