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  • Book

  • 104 number theory problems : from the training of the USA IMO team

    • Authors: Titu Andreescu (2007)

  • This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.
  • Book

  • 102 Combinatorial Problems

    • Authors: Titu Andreescu (2002)

  • 102 Combinatorial Problems consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. The text provides in-depth enrichment in the important areas of combinatorics by systematically reorganizing and enhancing problem-solving tactics and strategies. The book gradually builds combinatorial skills and techniques and not only broadens the student's view of mathematics, but is also excellent for training teachers.
  • Book

  • The IMO compendium

    • Authors: Dušan Djukić (2010)

  • The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems and is an invaluable resource not only for high-school students preparing for mathematics competitions, but for anyone who loves and appreciates mathematics.
  • Book

  • Linear programming and network flows

    • Authors: Mokhtar S. Bazaraa (2010)

  • The only book to treat both linear programming techniques and network flows under one cover, Linear Programming and Network Flows, Fourth Edition has been completely updated with the latest developments on the topic. This new edition continues to successfully emphasize modeling concepts, the design and analysis of algorithms, and implementation strategies for problems in a variety of fields, including industrial engineering, management science, operations research, computer science, and mathematics. Linear Programming and Network Flows, Fourth Edition is an excellent book for linear programming and network flow courses at the upper-undergraduate and graduate levels. It is also a valuable resource for applied scientists who would like to refresh their understanding of linear program...
  • Book

  • Mathematics of Economics and Business

    • Authors: Frank Werner (2006)

  • Today, a firm understanding of mathematics is essential for any serious student of economics. Students of economics need nowadays several important mathematical tools. These include calculus for functions of one or several variables as well as a basic understanding of optimization with and without constraints, e.g. linear programming plays an important role in optimizing production programs. Linear algebra is used in economic theory and econometrics. Students in other areas of economics can benefit for instance from some knowledge about differential and difference equations or mathematical problems arising in finance. The more complex economics becomes, the more deep mathematics is required and used. Today economists consider mathematics as the most important tool of economics and b...
  • Book

  • Ordinary differential equations

    • Authors: Gabriek Nagy (2017)

  • This is an introduction to ordinary differential equations. We describe the main ideas to solve certain differential equations, like first order scalar equations, second order linear equations, and systems of linear equations. We use power series methods to solve variable coefficients second order linear equations. We introduce Laplace transform methods to find solutions to constant coefficients equations with generalized source functions. We provide a brief introduction to boundary value problems, eigenvalueeigenfunction problems, and Fourier series expansions. We end these notes solving our first partial differential equation, the heat equation. We use the method of separation of variables, where solutions to the partial differential