Description
Book SynopsisA Transition to Advanced Mathematics: A Survey Course promotes the goals of a ``bridge'''' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-level mathematics courses (where they will have to prove theorems and grapple with mathematical abstractions). The text simultaneously promotes the goals of a ``survey'''' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics, including Logic, Abstract Algebra, Number Theory, Real Analysis, Statistics, Graph Theory, and Complex Analysis. The main objective of A Transition to Advanced Mathematics is to bring about a deep change in the mathematical character of students -- how they think and their fundamental perspectives on the world of mathematics. This text promotes three major mathematical traits in a meaningful, transformative way: to develop an ability
Trade ReviewI found the selection of material interesting and stimulating, in both the selection of general topics and the particular items chosen within each topic. It would provide useful background or supplementary reading for a student progressing from A-level to undergraduate study, where the new emphasis on proof and understanding as oppposed to computation can prove something of an obstacle to many. * Robert Low, Mathematics Today *
Table of ContentsPREFACE; ANSWERS TO QUESTIONS; ANSWERS TO ODD NUMBERED EXERCISES; INDEX OF ONLINE RESOURCES; BIBLIOGRAPHY; INDEX
