Syllabus
Analysis I
Math 554
Fall 2025, Math 554.001


The Basics

Course Homepage: http://people.math.sc.edu/girardi/w554.html
This course homepage contains much needed course information, eg: class handouts, course resources.
Blackboard (Bb): Bb will be used mostly for homework, sending announcements, and a secure posting location.
The course homepage is posted there in case you lose it.
Prereq.: Two 500-level MATH classes requiring MATH 300 (525, 531, 532, 533, 534, 540, 541, 544, 546, 548, 551, 561, 570, 574, 575, 580) and a
C or better in MATH 241.
Required: Check your (official) USC email regularly (at least daily) for this is major form of class communication.
Have your blackboard and my.sc.edu set up so that your immediately receive emails of messages sent.
Required: Bring your class handouts to each class meeting.
Class Meeting Info.: T/TH at 1:15pm - 2:30pm in LC 422
Highly Recommended:   A 3-ring binder to help organize your notes, class handouts, homeworks, etc.
And: some colored pencils, a stapler.
Required Textbook: Introduction to Real Analysis, 4th Edition, by Robert G. Bartle and Donald R. Sherbert.

Instructor Info Office Office Hours
Prof. Girardi
girardi@math.sc.edu
LC 339 See Prof. Girardi's Weekly Schedule
for her office office hours (along with office hour information) as well as her weekly schedule.

Given the nature of mathematics, questions over mathematics should be discussed in person during an office visit.
The best way to contact Prof. G is via Blackboard's messages or email. You may send her: logical questions (needing clarity) or request an office visit outside her scheduled office hours (send her time slots you are available).

Dates

See our handy (linked, one page) Semester Calendar, which contains this semester's important dates, eg: holidays, final.
Note: an exam might be just before/after a holiday so make your plans accordingly.

Since homework due dates may depend upon where the lecture stopped, sometimes due dates are not known until the end of a lecture. (I do not like to give HW before you are ready for it.)  Thus due dates are as announced in class and/or emailed to your USC email (so check your email regularly). If in doubt of what is due when, just ask Prof. Girardi at the end of class.

Class Preparation

Before each class, read the next section(s)-to-be-covered in your textbook, even if I forget to remind you. I will assume that you have read the material and thus will hightlight/clarify the material, ask you if you have questions, and then do more examples. If in doubt of the next reading assignment, just ask at the end of class.

Collaboration

One of our goals of this course is to learn how to communicate mathematical ideas; thus, you are strongly encouraged to work together. By all means, form study groups to discuss the homework problems (give them a fair shot first before you meet with the others) and study for the course. Below are just a few benefits from collaborative work.
  • Explaining your thoughts to the others helps you deepen your understanding of the material.
  • Collectively discussing a problem's hurdles helps develop your critical thinking skills as you find how to overcome the hurdle.
  • Thus you will be able to tackle the more demanding problems.
  • Collaborative work develops essential professional skills.
Remember, you have to take the exams individually so do not become too dependent upon one another. According to the USC Student Handbook code of student academic responsibility, the first law of academic life is intellectual honesty. This is expected of all of you.

Academic Honesty in the 2020's

The work (all process work, drafts, brainstorming artifacts, final works) submitted for a grade by students must be generated by the students themselves, working individually or in groups as directed by class assignment instructions. Below are some examples of violations of our academic honesty and a violation could result in a F in the course.
  • using generative AI tools (such as ChatGPT)
  • using solutions found on the internet
  • purchasing work from a company (such as Chegg.com)
  • having or hiring another person/entity do the work for you
Furthermore (other than for group assignments), if class members utilize site/link/platform for communication (e.g., GroupMe, Discord) then Prof. Girardi must be made aware and be invited.

If you ever have any uncertainty about the ground rules then just ask for clarification from Prof. Girardi, who encourages productive collaboration.

What to do if miss class / Attendance

Attendance and class participation expectations are as stated in the following USC policy (source: https://academicbulletins.sc.edu/undergraduate/ →Undergraduate Policy and Regulations→Undergraduate Academic Regulations→Grading Policies), which states:

Enrollment in a course obligates the student not only for prompt completion of all work assigned but also for punctual and regular attendance and for participation in whatever class discussion may occur. It is the student's responsibility to keep informed concerning all assignments made. Absences, whether excused or unexcused, do not absolve the student from this responsibility.
If a student misses class, either excused or unexcused, it is the student's responsibilty to ensure they get the material missed. (Bb's "Messages" can help with this.)   For the announcements made in class, a student may email Prof. Girardi.

As long as student class attendance is regular, daily attendance will not be taken. If daily attendance becomes necessary, then there will be an announcement in class.

Excused Absences

Make-up work is provided only for an approved excused absence.

For excused absences, we will follow the University’s policy, which is at: https://academicbulletins.sc.edu/undergraduate/policies-regulations/undergraduate-academic-regulations/ → Attendance Policy. The University allows for students to petition for an excused absence due to any of the following circumstances:

  • medical conditions or illness or injury,
  • death or severe illness of an immediate/dependent family member,
  • military duty,
  • legal obligation,
  • religious holiday a Interfaith Calendar, or
  • participation in an authorized university activity.
An excused absence must be approved by the Office of Student Advocacy (also refereed to as student Ombudsman or Ombuds).
  • To petition for an excused absence, you need to fill out the proper form at Office of Student Advocacy.
    Good news: this Office will contact all your professors. Bad News: approval takes time (properly filling out petition helps speeds things up).
  • If you petition for an excused absence, you need to personally contact Prof. Girardi (ASAP, email is fine) to arrange for reasonable makeup work (to be due in a timely fashion). A reasonable amount of time for personally contacting Prof. Girardi is:
    • within 12 hours of the missed assignment (except in extreme circumstances), for excused absences that cannot be anticipated at the start of a term
    • the day after the W date, for an excused absences that can be anticipated at the start of a term.
Be aware of the regulations on arranging for an excused absence that can be anticipated at the start of a term.

Grading Policies
(tentative)

There will be 2 hourly (really 75 minutes) exams along with a cummulative final exam. All exams are closed books/notes. Calculators are not allowed (nor needed). No exam grade is dropped. There will be no make-up exams (except with an approved excused absence).

Each progress check (e.g.: one problem on a homework exercise set, a group work, an announced-or-unannounded quiz) is worth 5 points. The goal of the progress checks is to master the material by learning from mistakes as so to do well on the exams. Since progress checks are your place to learn, the lowest (approx./at least) 10% of your collected progress checks assignment scores will be dropped. If you miss a progress checks assignment then the zero you receive on that work will be part of your dropped lowest 10%. A late progress check is not accepted and no progress check make-ups (without an approved excused absence). If your progress checks scores are posted on Bb, then the Overall Grade is your current points on the progress checks without the lowest 10% dropped. Exercise (problem) Homeworks are graded on accuracy.

Your goal is to gain a working knowledge of the course material; you have some personal freedom in this pursuit. By the end of the semester, demonstrate that you have mastered the material and your grade will be agreeable. With this in mind, your course grade (tentatively) will be based on your (personal) higher percentage in the below 2 schemes.

 scheme 1scheme 2
Progress Checks
20 % 20 %
Hourly Exams 60% = 2 * 30% 40% = 2* 20 %
Cummulative Final Exam 20% 40 %
total 100 % 100 %

The baseline score is indicated below. These thresholds may be lowered (at the end of the semester) if appropriate.

F D C B A
x< 60% 60% ≤ x < 70% 70% ≤ x < 80% 80% ≤ x < 90% 90% ≤ x

If taking daily attendance becomes necessary, the USC 5% rule will apply. Having more than 5% unexcused absences will result in lowering your course grade by one full letter grade. For a class that meets twice a week, this translates to 1 unexcused absence allowed for the entire semester. Of course, only absences after daily attendance begun will be (can be) be counted.

Students taking this course as Math 703i are required to complete additional work and are evaluated on a more rigorous basis than the students taking the course as Math 554. Math 703i students must speak with Prof. Girardi for further details the first week of classes.

Prof. Girardi is glad to answer questions over graded work but you must ask within 6 days from the date the graded work is returned. Bring a photo ID to each exam.

Learning Outcomes

By the end of the semester, students will demonstrate that they have mastered the fundementals analysis, via topics such as: least upper bound axiom, the real numbers, compactness, sequences, continuity, uniform continuity, differentiation, Riemann integral and fundamental theorem of calculus.

Common Sense / Courtesy / Integrity

Academic Honesty. According to the UofSC Student Handbook code of student academic responsibility, the first law of academic life is intellectual honesty. We expect this of all of you. If you ever have the least bit of uncertainty about the ground rules, just ask Prof. Girardi for clarification. Cheating and plagiarism will not be tolerated (such are grounds for a F in this course). Other than on our class Blackboard page, no electronic posting of the course class notes nor other course material without prior written permission from Prof. Girardi. No improper emailing of students. Violations of this policy will be dealt with according to University guidelines. Cheating on any assignment (or exam) is grounds for a F in this course. A Statement of Academic Integrity can be found at http://www.sc.edu/academicintegrity.

Attendance/Timeliness/CellPhones. UofSC policy states:

Enrollment in a course obligates the student not only for prompt completion of all work assigned but also for punctual and regular attendance and for participation in whatever class discussion may occur. It is the student's responsibility to keep informed concerning all assignments made. Absences, whether excused or unexcused, do not absolve the student from this responsibility.
To create a classroom environment conducive to learning and to help you personally succeed, we have the below policies.
  1. Students are expected to attend the entire class meeting: late arrivals and early depatures disrupt the class. Repeated late arrivals and/or early departures will not be tolerated. If you must leave class early, inform the instructor before the class begins, sit near the door, and gracefully exit. If you must arrive late, discretely find an open seat (and inform the instructor before hand if you know this will happen).
  2. During class, cell phones (as well as other electronic devices such as smart watches) are to be turned off and stored in a closed (e.g., zipped or buttoned) bag (e.g., backpack or purse); they may not be stored in the person's clothing (e.g., jacket pocket). If you do not have proper storage with you, you may give the device to the instructor to babysit it during class. Improper use or storage of cell phones could result in the device being confiscated (and not returned).

Electronic Tablets. If you use an electronic tablet to take class notes during class, then your tablet must remain flat on your desk (as one does when writing). Otherwise you will lose the privilege of using a tablet in class.

Tutor. USC Student Success Center (SSC) offers (peer) tutoring for several math classes. Even if this class is not on their official Supported Courses list, if you fill out a Request a Tutor Form, then the SSC will try to find you a tutor. You may visit the SSC page or phone them at (803) 777-1000. In Fall 2021, Prof. Girardi made a short video showing how to fill out a Request a Tutor Form.

ADA. If you have special needs as addressed by the Americans with Dissabilities Act and you have registered with the UofSC Office of Student Disability Resource Center (SDRC), you need to speak with Prof. Girardi before using an approved accommodation. We will discuss how to best handle your SDRC accommodations as so to meet your needs. We will not discuss of your specific disability.

Recording of Class. Recording (of any type, including but not limited to: audio, visual) of any part of the class is prohibited without the prior written permission the Prof. Girardi.

This syllabus is subject to change.


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