26s M554

Analysis I - Math 554.001 - Spring 2026

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.

Handouts^⊕ Semester
Calendar
e.g. exam/holiday info Prof. G's
Weekly Schedule
with Office Hours Syllabus Homework is on
Blackboard^⊕

Writing Guidelines:

Writing Guidelines (WG)
List and Details IF ≠ IS mistake Math Induction
(PMI)

Course Resources

Math 554/555 books on web.

[BS]. Bartle and Sherbert. Introduction to Real Analysis. (4^th edition)

[IA]. Interactive Real Analysis (interactive textbook)

[Lebl]. Lebl. Introduction to Real Analysis, Volume I.

[LLN]. Lafferriere, Lafferriere, and Nguyen. Introduction to Mathematical Analysis I. (LibreTexts)
This PDF is available on Open Texbook Library.
[Za]. Zakon. Mathematical Analysis. (LibreTexts)
[Ag]. Aguilar. An Introduction to Real Analysis. (Real Analysis I and II at Cesar O. Aguilar)

[Trench]. Trench. Introduction to Real Analysis. (Free Hyperlinked Edition 2.04 December 2013. Limit of function is before limit of sequence.)

[TBB]. Thomson, Bruckner, Bruckner. Elementary Real Analysis (2nd Ed., 2008)

Math 300 books on web (commonly used at USC).

Mathematical Reasoning: Writing and Proof by Ted Sundstrom. (Version 3)
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
Math 554/555 books on web. [BS]. Bartle and Sherbert. Introduction to Real Analysis. (4^th edition) [IA]. Interactive Real Analysis (interactive textbook) [Lebl]. Lebl. Introduction to Real Analysis, Volume I. [LLN]. Lafferriere, Lafferriere, and Nguyen. Introduction to Mathematical Analysis I. (LibreTexts) This PDF is available on Open Texbook Library. [Za]. Zakon. Mathematical Analysis. (LibreTexts) [Ag]. Aguilar. An Introduction to Real Analysis. (Real Analysis I and II at Cesar O. Aguilar) [Trench]. Trench. Introduction to Real Analysis. (Free Hyperlinked Edition 2.04 December 2013. Limit of function is before limit of sequence.) [TBB]. Thomson, Bruckner, Bruckner. Elementary Real Analysis (2nd Ed., 2008) Math 300 books on web (commonly used at USC). Mathematical Reasoning: Writing and Proof by Ted Sundstrom. (Version 3) 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.

LaTex. Click here to learn how to typeset (using LaTeX) STEM homework/reports/etc .

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

Useful Links: A ^⊕ indicates link should opens in new tab.
Handouts^⊕	Semester Calendar e.g. exam/holiday info	Prof. G's Weekly Schedule with Office Hours	Syllabus	Homework is on Blackboard^⊕

Writing Guidelines:
Writing Guidelines (WG) List and Details	IF ≠ IS mistake	Math Induction (PMI)

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