Basics of Ramsey Theory serves as a gentle introduction to Ramsey theory for students interested in becoming familiar with a dynamic segment of contemporary mathematics that combines ideas from number theory and combinatorics. The core of the of the book consists of discussions and proofs of the results now universally known as Ramsey’s theorem, van der Waerden’s theorem, Schur’s theorem, Rado’s theorem, the Hales–Jewett theorem, and the Happy End Problem of Erdős and Szekeres. The aim is to present these in a manner that will be challenging but enjoyable, and broadly accessible to anyone with a genuine interest in mathematics. Features Suitable for any undergraduate student who has successfully completed the standard calculus sequence of courses and a standard first (or second) year linear algebra course Filled with visual proofs of fundamental theorems Contains numerous exercises (with their solutions) accessible to undergraduate students Serves as both a textbook or as a supplementary text in an elective course in combinatorics and aimed at a diverse group of students interested in mathematics
Basics of Ramsey Theory serves as a gentle introduction to Ramsey theory for students interested in becoming familiar with a dynamic segment of contemporary mathematics that combines ideas from number theory and combinatorics. The core of the of the book consists of discussions and proofs of the results now universally known as Ramsey’s theorem, van der Waerden’s theorem, Schur’s theorem, Rado’s theorem, the Hales–Jewett theorem, and the Happy End Problem of Erdős and Szekeres. The aim is to present these in a manner that will be challenging but enjoyable, and broadly accessible to anyone with a genuine interest in mathematics. Features Suitable for any undergraduate student who has successfully completed the standard calculus sequence of courses and a standard first (or second) year linear algebra course Filled with visual proofs of fundamental theorems Contains numerous exercises (with their solutions) accessible to undergraduate students Serves as both a textbook or as a supplementary text in an elective course in combinatorics and aimed at a diverse group of students interested in mathematics
This volume contains more than 900 problems in differential calculus, covering limits, continuity, derivatives, and their applications. The applications are comprised of a variety of approximations, growth and decay, optimization, curve sketching techniques, and analytical tools to investigate properties of parametrically given planar curves. The problems are sorted by topic, each opening with with a summary of the relevant mathematical notions and their properties. Through a careful selection of appropriate problems in each chapter, the book clearly communicates some of the big ideas and applications in calculus: the notion of a function, the notion of an infinitesimal, the notion of a differentiable function, and the notion of an approximation, among others. The book provides the answers to each problem, often with a detailed sketch of the solution process.With about 260 true-false and multiple-choice questions, the book provides its users with an accessible way to assess and practice their understanding of calculus related facts and nuances. More than 180 figures are included to help readers to visualize properties of functions, illustrate word problems, depict solutions, and provide an extensive bank of polar curves.The purpose of this problem collection is to serve as a supplementary learning resource for students who are studying university-level differential calculus. The book also acts as a teaching resource for calculus instructors.
This volume contains more than 900 problems in differential calculus, covering limits, continuity, derivatives, and their applications. The applications are comprised of a variety of approximations, growth and decay, optimization, curve sketching techniques, and analytical tools to investigate properties of parametrically given planar curves. The problems are sorted by topic, each opening with with a summary of the relevant mathematical notions and their properties. Through a careful selection of appropriate problems in each chapter, the book clearly communicates some of the big ideas and applications in calculus: the notion of a function, the notion of an infinitesimal, the notion of a differentiable function, and the notion of an approximation, among others. The book provides the answers to each problem, often with a detailed sketch of the solution process.With about 260 true-false and multiple-choice questions, the book provides its users with an accessible way to assess and practice their understanding of calculus related facts and nuances. More than 180 figures are included to help readers to visualize properties of functions, illustrate word problems, depict solutions, and provide an extensive bank of polar curves.The purpose of this problem collection is to serve as a supplementary learning resource for students who are studying university-level differential calculus. The book also acts as a teaching resource for calculus instructors.
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