Based on a paper written by Prof. Dr. Marcel Oliver and Prof. Oliver Bühler, this paper examines the efficiency of computation of transparent boundary conditions for waves traveling in shear flow, represented as grid points on a truncated lattice. An improved Gradient-Penalty method is suggested over the QR decomposition, what, in the particular linear system whose matrix is similar to a unitary matrix, significantly reduces the computational costs. Theoretical comparison of computational costs and a pseudocode for implementing the Gradient-Penalty method are provided.

The paper, presented in a graduate Mathematics class, derives the Black-Scholes partial differential equation from the underlying stock price stochastic differential equation. It is subsequently transformed into a form of Heat equation. The well-known solution to the latter is then used to solve the Black-Scholes PDE and derive the European call pricing formula.

The paper gradually introduces all major concepts needed to prove the Fundamental Theorem of Algebra. One of numerous available proofs is provided in detail (for other proofs, please refer to V. Tikhomirov's paper in the references list). A few famous corrolaries are proven.

This paper introduces a reader to combinatorial Game Theory. Nimbers game is used as an example of an impartial game. A winning strategy of this particular game is stated and proven. Other interesting theorems are stated.