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Angry Citizen

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**Math + Engineering = ?**

I'm an aerospace engineering major. My career will be in aerospace engineering. But recently, I've thought about doing a double major in pure math.

My main reasoning is that it would only be an extra twelve classes, and I've always been highly curious about 'proper' math. My other reasoning is that it would give me something to do while catching up on my engineering classes. As a transfer student, I've already completed all but two of my general education courses (which under a normal degree plan are interspersed throughout my college years), and will have completed all my basic, foundational science classes (intro physics, intro chem, and all three basic calculus courses). This leaves my first year entirely blank, save for two small intro engineering courses which must be completed sequentially (one in my first semester, the other in my second) before I can take any upper division engineering courses.

But I think I need a third reason. Is a pure math degree of any use in engineering? The extra classes I'd be taking are as follows:

*Foundations of Mathematics*: Foundations of mathematics including logic, set theory, combinatorics, and number theory.

*Linear Algebra I and II*: Linear equations and matrices; real vector spaces, linear transformations, change of bases, determinants, eigenvalues and eigenvectors, diagonalization, inner products (I); Eigenvalues, similarity and canonical forms, applications to differential equations and quadratic forms (II).

**Note: It is not necessary under my engineering degree plan to take linear algebra, and an 'intro' course is offered in the subject that is presumably less rigorous, but as I understand linear algebra is very useful in engineering, I think I'll be taking this even if I don't go for the math degree.**

*Advanced Calculus I and II*: Axioms of the real number system; point set theory of R1; compactness, completeness and connectedness; continuity and uniform continuity; sequences, series; theory of Riemann integration (I); Differential and integral calculus of functions defined on Rm including inverse and implicit function theorems and change of variable formulas for integration; uniform convergence (II).

*Modern Algebra I and II*: Groups, rings, fields (I, II).

*Theory of ODE's*: Existence and uniqueness of solutions to differential equations, linear systems, nonlinear equations, stability analysis, qualitative behavior of solutions, and modeling with differential equations.

*Theory of PDE's*: Formulation and solution of partial differential equations of mathematical physics; Fourier series and transform methods, complex variable methods, methods of characteristics and first order equations.

*Introduction to Topology*: Metric spaces; continuity of metric spaces; topological spaces; basic notions; separation axioms; compactness; local compactness; connectedness; basic notions in homotopy theory; quotient spaces, paracompactness and topological manifolds.

*Numerical Analysis I*: Linear systems, matrix decomposition and eigensystems, numerical integration, interpolation and numerical solution of ordinary differential equations.

*Programming in C*: Basic concepts, nomenclature and historical perspective of computers and computing; internal representation of data; software design principles and practice; structured and object-oriented programming in C; use of terminals, operation of editors and executions of student-written programs.

Taken from:

http://catalog.tamu.edu/09-10_UG_Catalog/course_descriptions/math.htm

And:

http://catalog.tamu.edu/09-10_UG_Catalog/science/math/math_bs.htm

Will any of these be useful? I understand that aerospace engineering, especially the propulsion sub-discipline, often uses differential equations, so I've tailored many of my electives around a thorough treatment of ODE's and PDE's so that I could at least be completely comfortable using them for engineering. I will, of course, be discussing this with my adviser as well, but I'd like the input of the community here before I proceed. Apologies for the somewhat long post.

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