optimization

Differential Calculus: From Practice to Theory covers all of the topics in a typical first course in differential calculus. Initially it focuses on using calculus as a problem solving tool (in conjunction with analytic geometry and trigonometry) by exploiting an informal understanding of differentials (infinitesimals). As much as possible large, interesting, and important historical problems (the motion of falling bodies and trajectories, the shape of hanging chains, the Witch of Agnesi) are used to develop key ideas.

A Jupyter notebook companion for a first course in Calculus, including a review of Precalculus concepts.

This is a set of lecture notes for MATH 555, Penn State's graduate Numerical Optimization course. Numerical Optimization is the study of maximizing or minimizing functions through numerical techniques. Generally, it's rare to optimize anything other than through numerical techniques (unless of course you're talking about something really simple). Numerical optimization is used every day and is built on techniques from multi-variable calculus, optimization theory (obviously) numerical linear algebra (for algorithm efficiency) and other branches of mathematics.

This is version two of a set of lecture notes for MATH 486, Penn State's undergraduate Game Theory course. Game Theory is the study of decision making under competition. The first truly mathematical study of Game Theory was initiated by Von Neumann and Morgenstern. John Nash (of A Beautiful Mind fame) added substantially to the field with his proof of the existence of equilibrium solutions for general sum games. Since then many mathematicians, economists, engineers and others have made substantial contributions to the study of games.

This is version two of set of lecture notes for MATH 485, Penn State's undergraduate Graph Theory course. Graph Theory is the study of discrete mathematical structures composed of vertices (nodes) represented by dots and edges (links) represented by lines connecting the dots. Generally speaking, Graph Theory is a branch of Combinatorics but it is closely connected to Applied Mathematics, Optimization Theory and Computer Science. In its applied form, Graph Theory is used every day by Google and Microsoft in feeding you web information.

This is a set of lecture notes for Penn State's undergraduate Linear Programming course.

The lecture notes are (roughly) based on the first 6 chapters of Bazaraa et al.'s Linear Programming and Network Flows book.  This is a reasonably good book, written primarily by and for Industrial Engineers. However, it does not present major results in the standard theorem-proof style common to mathematical discourse. This set of notes corrects this situation by presenting the material in a format for presentation to a mathematics class.

Sustainability denotes one of the main future challenges of societies and the global community. Issues of sustainability range from energy and natural resources to biodiversity loss and global climate change. Properly dealing with these issues will be crucial to future societal and economic development. This course provides the theoretical background for the discussion and analysis of sustainability issues.