Advanced Calculus II

• Riemann Integrals
• Riemann Integrals, Riemann Sums, and Lebesgue Measure
• Fundamental Theorem of Calculus
• Absolute & Conditional Convergence and Square Summable Sequences

Advanced Mathematical Programming (using Optimization in Operations Research by Ronald L. Rardin)

• Knights, Knaves, & Werewolves and EMS Location Problem
• Dijkstra’s Algorithm, Uncapacitated Facility Location, and Completeness
• Unconstrained NLPs and Taylor Approximations
• Integer Programming, Knapsack Problem, and Branch & Bound Algorithm
• KKT Conditions and Langrangian Function

Design of Experiments

Discrete Optimization

• Integer Programs and Linear Relaxations
• Branch and Bound
• Discrete Improving Searches
• Simulated Annealing

Linear Programming

Modern Algebra (using Visual Group Theory by Nathan Carter)

• What is a group?

Network Optimization

• Strong Induction Proofs
• Dijkstra’s Algorithm

Sample Optimization Case Study

• MTBE Sample Case Study
• MTBE Sample Case Study Presentation

Stochastic Optimization

• Farmer’s Problem, News Vendor Problem, and Financial Problem