Upper Division

Course Description:

• History of the development of mathematical concepts in algebra, geometry, number theory, analytical geometry, and calculus from ancient times through modern times. Theorems with historical significance will be studied as they relate to the development of modern mathematics.

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• Software and Programming

What I got out of it:

• This course provided me with essential foundations for programming through the lens of a mathematician and discussed topics outside of the scope of other mathematics classes. In particular, this course shaped my foundational knowledge of Python, which has provided me with extremely useful tools for every course I have taken since and for my senior project.

• Introduction to Mathematica, Python, Jupyter Notebooks, and Google Collab. • Final Project: Implemented code based on list structures and objects including but not limited to nodes, single linked lists, double linked list, and circularly linked list through class definitions.

MATH 191T FINAL PROJECT

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What I got out of it:

• Explored, implemented, and analyzed the numerical methods in Python. • Computer arithmetic, solutions of equations using iterative techniques, interpolation, numerical differentiation, quadrature, and numerical ordinary differential equations. Use of numerical software libraries.

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What I got out of it:

• Classical methods for solving partial differential equations including separation of variables, Green’s functions, the Riemann-Volterra method and Cauchy’s problem for elliptic, parabolic, and hyperbolic equations; applications to theoretical physics.

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What I got out of it:

• Called MATH 191T when I took it, this course explored different sub-genres of mathematics through guest speakers and post-presentation reflections.

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What I got out of it:

• Learned about analytic functions of a complex variable, contour integration, series, singularities of analytic functions, the residue theorems, conformal mappings

• Emphasis on engineering and physics applications.

• Using Fourier Analysis to solve integrals with a complex variable

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