Classical algorithms: Efficient multiplication, efficient multiplication, IIIntroduction to linear programming: Introduction to linear programming. The canonical linear programming problemSymmetries and dualitiesBasic feasible and basic optimal solutions. The simplex methodAdvanced linear programming: Integer programmingInteger optimizationMulti-objective and quadratic programming. The traveling salesman problemIntroduction to stochastic linear programmingFixed point theorems: Introduction to fixed point theoremsContraction mapsSperner's lemmaBrouwer's fixed point theoremAdvanced topics: Gale-Shapley algorithmInterpolating functionsThe four colors problemThe Kepler conjectureIndexBibliography.

Optimization Theory is an active area of research with numerous applications; many of the books are designed for engineering classes, and thus have an emphasis on problems from such fields. Covering much of the same material, there is less emphasis on coding and detailed applications as the intended audience is more mathematical. There are still several important problems discussed (especially scheduling problems), but there is more emphasis on theory and less on the nuts and bolts of coding. A constant theme of the text is the "why" and the "how" in the subject. Why are we able to do a calcul.