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This text provides a practical, hands-on introduction to the fundamental concepts of mathematical programming and network science. Particular emphasis is placed on linear programming, mathematical modelling and case studies, the implementation of the Simplex Method in Python, and classical techniques from nonlinear convex programming. The text also features a discussion of mathematical programming within the context of algebraic modelling languages. Further, it includes material on matrix games, decision analysis, multicriteria optimization and non-directed networks.
Designed as an introductory resource for upper-level undergraduate and graduate students, the book assumes only a modest mathematical background. Readers who have completed a second course in linear algebra, multivariable calculus, and an introductory course in probability and statistics will find the more advanced portions of the text especially accessible. Researchers and professionals in mathematics, engineering, technology, economics, business, and other quantitatively oriented fields will also find this book a valuable reference.
A distinguishing feature of this text is its strong emphasis on case studies. Numerous examples are developed in detail, either worked out within the text or explored through exercises and abstract model formulations. This pedagogical approach fosters both intuition and a structured understanding of the representative models that form the foundation of the field. A rich collection of end-of-chapter exercises enables readers to apply concepts and deepen their mastery of the material. A chapter dependency chart further supports independent learners by suggesting an effective study sequence and assists instructors in organizing coherent course structures.
List of contents
1 Introduction.- 2 Linear programming models—a collection of case study examples.- 3 Towards a theory for mathematical programming problems.- 4 Introduction to Tucker Tableau and duality theory for linear programming.- 5 Simplex Algorithm via Tucker Tableau.- 6 Using computer software to solve linear programming problems.- 7 Transportation and assignment problems.- 8 Network Flow problems.- 9. Selected introduction to nonlinear programming.- 10 More general convex functions, Lagrangians and KKT conditions.- 11 Using computer software to solve selected nonlinear programming.- 12 Introduction to game theory, decision analysis and multicriteria optimization.- 13 Introduction to non-directed networks.- Appendix A Solving systems of linear equations.- Appendix B Convexity and optimization of smooth functions in dimensions one and two.- Appendix C Solution sketches to selected problems.- References.- Index.
About the author
Nathan Grieve holds a dual position at both Acadia University in Nova Scotia and Carleton University in Ottawa. He has broad mathematical interests within the areas of Geometry, Algebra and Number Theory. In addition to his expertise within Pure Mathematics, he has strong secondary interests in Computer, Managerial, Information and Data Science. The author has a unique breadth and depth of undergraduate and graduate level teaching. Over the years, he has held a number of academic research and teaching appointments at academic institutions within North America and abroad. Further, he has significant research and teaching experience within government.
Summary
This text provides a practical, hands-on introduction to the fundamental concepts of mathematical programming and network science. Particular emphasis is placed on linear programming, mathematical modelling and case studies, the implementation of the Simplex Method in Python, and classical techniques from nonlinear convex programming. The text also features a discussion of mathematical programming within the context of algebraic modelling languages. Further, it includes material on matrix games, decision analysis, multicriteria optimization and non-directed networks.
Designed as an introductory resource for upper-level undergraduate and graduate students, the book assumes only a modest mathematical background. Readers who have completed a second course in linear algebra, multivariable calculus, and an introductory course in probability and statistics will find the more advanced portions of the text especially accessible. Researchers and professionals in mathematics, engineering, technology, economics, business, and other quantitatively oriented fields will also find this book a valuable reference.
A distinguishing feature of this text is its strong emphasis on case studies. Numerous examples are developed in detail, either worked out within the text or explored through exercises and abstract model formulations. This pedagogical approach fosters both intuition and a structured understanding of the representative models that form the foundation of the field. A rich collection of end-of-chapter exercises enables readers to apply concepts and deepen their mastery of the material. A chapter dependency chart further supports independent learners by suggesting an effective study sequence and assists instructors in organizing coherent course structures.
