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MATH 4093 – Advanced Analysis
Catalog Description:
A study of the theory of the calculus of functions of a single variable.
Topics may include the topology of the real line, functions, sequences and their limits,
continuity, differentiation, and integration.
Prerequisite: MATH 2094.
Expanded Course Description:
An introductory course in real analysis is universally
foundational for undergraduate study in mathematics. As such, this course is a core requirement
for the Bachelor of Science degree in Mathematics and is primarily intended for advanced
undergraduate mathematics majors. The course topics include an introductory development of
the real number system, sequences and their limits, and the continuity and differentiation of real
functions.
Objectives:
Students will be introduced to fundamental techniques for developing the theory of
integrals, derivatives, and limits in one dimension, which will serve as a foundation for further
mathematical study.
Students will also study the development of the real number system and
real valued functions.
Finally, students will learn to use the styles and formats common to
professional publications in mathematics to write definitions and proofs in real analysis.
Upon
completing MATH 4093, a student should be able to do the following:
1.
Comprehend definitions,
2.
State and rigorously prove related mathematical theorems using styles and formats
appropriate to the disciplen,
3.
Perform the computations related to the material,
4.
Demonstrate the use of the theoretical results and computational aspects on required
applications, and
5.
Connect the material to other courses.
Strategy:
Students will study the material outlined in the goals through class assignments and
technological assignments.
Students will be given the opportunity on homework, quizzes,
projects and/or major exams to develop and maintain sophistication in using the basic techniques
of Analysis.
In addition, students will be required to present the concepts of this course in a
written format consistent with the styles and format represented in the professional literature.
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This note was uploaded on 01/17/2012 for the course MATH 409 taught by Professor Dr.peterwhite during the Fall '11 term at Tarleton.
 Fall '11
 Dr.PeterWhite
 Topology, Continuity, Limits

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