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Basic Analysis: Introduction to Real Analysis

(Complete Item Description)

Abstract:: This free online textbook is a one semester course in basic analysis. These were my lecture notes for teaching Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in fall 2009. The course is a first course in mathematical analysis aimed at students who do not necessarily wish to continue a graduate study in mathematics. A Sample Darboux sums prerequisite for the course is a basic proof course. The course does not cover topics such as metric spaces, which a more advanced course would. It should be possible to use these notes for a beginning of a more advanced course, but further material should be added.

Subject:: Mathematics and Statistics
Grade Level:: Post-secondary
Collection:: University of Illinois at Urbana-Champaign

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Introduction to Topology, Fall 2004

(Complete Item Description)

Abstract:: Introduces topology, covering topics fundamental to modern analysis and geometry. Topological spaces and continuous functions, connectedness, compactness, separation axioms, and selected further topics such as function spaces, metrization theorems, embedding theorems, the Tychonoff theorem.

Subject:: Mathematics and Statistics
Grade Level:: Post-secondary
Collection:: MIT OpenCourseWare

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Top Keywords

Compactness Connectedness Continuous Functions derivative Embedding Theorems Function Spaces mathematics Metrization Theorems Real Numbers Riemann Integral Separation Axioms Sequences Sequences of Functions Series The Fundamental Group Topological Spaces topology

Conditions of Use

No Strings Attached
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Read the Fine Print

No restrictions on your remixing, redistributing, or making derivative works. Give credit to the author, as required.

Your remixing, redistributing, or making derivatives works comes with some restrictions, including how it is shared.

Your redistributing comes with some restrictions. Do not remix or make derivative works.

Copyrighted materials, available under Fair Use and the TEACH Act for US-based educators, or other custom arrangements. Go to the resource provider to see their individual restrictions.

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