This mathematical physics sequence explores the coordinate systems necessary for solving problems involving complex shapes, moving beyond Cartesian coordinates to General Curvilinear systems. Students derive scale factors, volume elements, and differential operators, culminating in solving Laplace's equation and understanding metric tensors.

This sequence provides a rigorous foundation in the formal mechanics of logical argumentation, distinguishing sharply between deductive certainty and inductive probability. Students move from categorical syllogisms to complex propositional logic, then transition into inductive and abductive frameworks to evaluate strength, cogency, and explanatory power in academic contexts.

This graduate-level sequence explores the pedagogical content knowledge (PCK) needed to teach mathematical sequences and limits. It traces the historical development from Zeno's paradoxes to modern rigor, equipping educators to address common student misconceptions through inquiry-based instruction.

This graduate-level sequence explores analytic combinatorics through the lens of generating functions. Students will master the transformation of discrete sequences into formal power series, solving complex recurrence relations and evaluating combinatorial identities using advanced algebraic techniques.

A graduate-level exploration of discrete dynamical systems, moving from linear growth models to the complex, chaotic behavior of the logistic map. Students apply recursive sequences to model biological and economic phenomena, emphasizing stability analysis and bifurcation theory.

A rigorous graduate-level exploration of real-valued sequences, bridging computational calculus and formal real analysis through epsilon-N proofs, Cauchy sequences, and topological theorems.

A graduate-level exploration of expected value applications in finance, covering utility theory, portfolio optimization, risk-neutral pricing, and tail risk metrics. Students transition from theoretical foundations to computational implementation using Monte Carlo methods.