Analysis I   -   Math 554.001    -    Fall 2025

Textbook (required):  Introduction to Real Analysis, 4th Edition, by Robert G. Bartle and Donald R. Sherbert. The following formats of the 4th edition are fine: international edition, electronic copy, soft cover, hard cover. A free legal PDF is available for download from the Internet Archive.

Useful Links:   A ⊕ indicates link should opens in new tab.   Blackboard will be used minimally (mostly for a secure location for posting items).
	Handouts⊕	Semester Calendar e.g. exam/holiday info	Prof. G's Weekly Schedule with Office Hours	Syllabus

LaTex: LaTeX is the de facto standard for the communication and publication of scientific documents.   ⊕ indicates opens in new tab/window
do first Getting Started with LaTex prepared by Prof. G.	our course homework LaTex template See Getting Started with LaTex		Overleaf log in⊕
Latex Lessons prepared by Prof. G. under expansion	Commonly Used LaTex Symbols licensed by Ted Sundstrom	Overleaf's Help⊕ excellent! menu in left column	Detexify

Announcements.

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Course Resources

A Math 554/555 Interactive Real Analysis self-tutor website.    (Student feedback welcome on the helpfulness of this, and similiar, websites.) Other Math 554/555 books on web. Introduction to Real Analysis by William F. Trench (Free Hyperlinked Edition 2.04 December 2013). Elementary Real Analysis (2nd Ed., 2008) by: Thomson, Bruckner, Bruckner. Math 300 books on web (commonly used at USC). Mathematical Reasoning: Writing and Proof (Version 3) by Ted Sundstrom along with corresponding book homepage and Prof. Girardi's course homepage (with handouts). Book of Proof by Richard Hammack. Hilbert's Hotel (countability): Hilbert's Infinite Hotel and The Infinite Hotel Paradox. If you came across another website that you think students will find helpful, please just email Prof. Girardi the link. Thanks.

URL: http://people.math.sc.edu/girardi/w554.html