Constructing Numbers
An Inquiry-Based Capstone Mathematics Course
Published on 30. May 2015
Book
Paperback/Softback
84 pages
978-1-63189-459-6 (ISBN)
Description
The discovery-based Constructing Numbers: An Inquiry-Based Capstone Mathematics Course helps students synthesize material from elementary analysis, linear algebra, algebraic structures, and geometry while providing perspective on how mathematical thought has developed.
The book opens with the history of numbers. It moves on to cover axiomatic systems, real, complex, and constructible numbers, and an algebraic formulation of field construction. The final chapters are devoted to finite fields, probability, and permutation groups.
By actively participating in the exercises and proofs, students learn how the material progresses in a logical way. They master the content by doing the work and presenting their results.
Working through Constructing Numbers gives students a deeper understanding of the discipline of mathematics. They understand the importance of moving beyond a strictly mechanical approach to "doing" mathematics and to instead ask "why" mathematical processes are as they are.
Intended for one-semester upper-division classes, Constructing Numbers can be used in capstone courses in the major, or classes for pre-service secondary mathematics teachers.
The book opens with the history of numbers. It moves on to cover axiomatic systems, real, complex, and constructible numbers, and an algebraic formulation of field construction. The final chapters are devoted to finite fields, probability, and permutation groups.
By actively participating in the exercises and proofs, students learn how the material progresses in a logical way. They master the content by doing the work and presenting their results.
Working through Constructing Numbers gives students a deeper understanding of the discipline of mathematics. They understand the importance of moving beyond a strictly mechanical approach to "doing" mathematics and to instead ask "why" mathematical processes are as they are.
Intended for one-semester upper-division classes, Constructing Numbers can be used in capstone courses in the major, or classes for pre-service secondary mathematics teachers.
More details
Language
English
Place of publication
San Diego
United States
Target group
Professional and scholarly
Product notice
Paperback (trade)
Unsewn / adhesive bound
Dimensions
Height: 277 mm
Width: 215 mm
Thickness: 10 mm
Weight
222 gr
ISBN-13
978-1-63189-459-6 (9781631894596)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Mark L. Daniels is a clinical professor of mathematics in the UTeach Natural Sciences Program at the University of Texas, Austin. Professor Daniels' mathematical interests include discrete deterministic chaos, inquiry-based instruction in undergraduate mathematics, and the development of secondary mathematics teachers.
Efraim P. Armendariz (1938 - 2013) was an algebraist and professor of mathematics at the University of Texas, Austin. Professor Armendariz devoted much of his career to enhancing the content knowledge of undergraduate and graduate mathematics students as well as both pre-service and in-service mathematics teachers.
Efraim P. Armendariz (1938 - 2013) was an algebraist and professor of mathematics at the University of Texas, Austin. Professor Armendariz devoted much of his career to enhancing the content knowledge of undergraduate and graduate mathematics students as well as both pre-service and in-service mathematics teachers.