A Transition to Advanced Mathematics

by William Johnston, Alex McAllister

2009 · Oxford University Press

A 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 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 to communicate with precise language, to use mathematically sound reasoning, and to ask probing questions about mathematics. In short, we hope that working through A Transition to Advanced Mathematics encourages students to become mathematicians in the fullest sense of the word. A Transition to Advanced Mathematics has a number of distinctive features that enable this transformational experience. Embedded Questions and Reading Questions illustrate and explain fundamental concepts, allowing students to test their understanding of ideas independent of the exercise sets. The text has extensive, diverse Exercises Sets; with an average of 70 exercises at the end of section, as well as almost 3,000 distinct exercises. In addition, every chapter includes a section that explores an application of the theoretical ideas being studied. We have also interwoven embedded reflections on the history, culture, and philosophy of mathematics throughout the text.

Calculus

by William G. McCallum, Deborah Hughes-Hallett, Andrew M. Gleason

2017 · Wiley Global Education

With Wiley’s Enhanced E-Text, you get all the benefits of a downloadable, reflowable eBook with added resources to make your study time more effective, including: • Embedded Example Videos • Built-In Assessments • Interactive Exploration applets • Searchable Appendices & chapter summary reviews Calculus: Multivariable, 7e continues the effort to promote courses in which understanding and computation reinforce each other. The 7th Edition reflects the many voices of users at research universities, four-year colleges, community colleges, and secdondary schools. This new edition has been streamlined to create a flexible approach to both theory and modeling. The program includes a variety of problems and examples from the physical, health, and biological sciences, engineering and economics; emphasizing the connection between calculus and other fields. Calculus: Multivariable, 7e will include Wiley's seamlessly integrated adaptive WileyPLUS ORION program, covering content from refresher Algebra and Trigonometry through Multi-Variable Calculus. Calculus: Multivariable, 7e is the first adaptive calculus program in the market.

Calculus

by Deborah Hughes-Hallett, Andrew M. Gleason, William G. McCallum

2021 · Wiley Global Education

The ideal resource for promoting active learning in flipped classroom environments, Calculus: Multivariable, 8th Edition brings calculus to real life with relevant examples and a variety of problems with applications from the physical sciences, economics, health, biology, engineering, and economics. Emphasizing the Rule of Four—viewing problems graphically, numerically, symbolically, and verbally—this popular textbook provides students with numerous opportunities to master key mathematical concepts and apply critical thinking skills to reveal solutions to mathematical problems. Developed by Calculus Consortium based at Harvard University, Calculus: Multivariable uses a student-friendly approach that highlights the practical value of mathematics while reinforcing both the conceptual understanding and computational skills required to reduce complicated problems to simple procedures. The new eighth edition further reinforces the Rule of Four, offers additional problem sets and updated examples, and supports complex, multi-part questions through new visualizations and graphing questions powered by GeoGebra.