25f M554

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!
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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.)

A website with elaborations on the some material in the Bartle-Sherbert book. (by Cesar O. Aguilar)
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.

Course Resources
A Math 554/555 Interactive Real Analysis self-tutor website. (Student feedback welcome on the helpfulness of this, and similiar, websites.) A website with elaborations on the some material in the Bartle-Sherbert book. (by Cesar O. Aguilar) 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

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