Syllabus
Course: Math 230A (Section 1)
Title: Real Analysis
Credit Hours: 3
Modality: Fully in-person (Location: Brighton Hall 115)
Prerequisites: Math 130B, or equivalent.
Instructor: Ali Behzadan (You may click on your instructor's name to send an email to your instructor.)
Tentative List of Topics:
The real number system, basic topology of metric spaces, sequences and series, continuity.
The main objective will be to have a clear understanding of certain fundamental concepts and procedures in mathematical analysis. Emphasis is placed on careful reasoning and proofs. Students should grasp the concept of
metric spaces and topological notions such as compactness and connectedness.
Additionally, students will develop proficiency in analyzing the convergence of sequences and series, and in understanding the rigorous foundations of continuity for functions between metric spaces. Students will be able to apply mathematical analysis techniques to solve a variety of mathematical
problems and demonstrate proficiency in constructing rigorous mathematical proofs.
Textbook: The recommended textbook is
- Rudin, Walter. Principles of Mathematical Analysis. 3rd ed. New York: McGraw-Hill, 1976.
Homework: Homework is a very important part of the course and in order to fully master the topics it is essential that you work carefully on every assignment and try your best to complete every problem. The homework assignments will be announced on the course homework page. You should make every effort to complete the homework assignments and seek help with problems you have not been able to solve. Assignments should be submitted through Gradescope.
- Late homework will not be accepted.
- You will be able to access Gradescope through the course Canvas page.
Attendance: Your assumption should be that you are a responsible teacher who is teaching the course. So it does not make sense to miss any class or arrive late or leave early. Missing more than five lectures will result in an automatic "C" in the course (if you miss more than five lectures, then your course letter grade will be C). This policy may appear to be harsh, but please know that the aim of our attendance policy is by no means to add to your stress. The goal is to ensure that everyone is keeping up with the course. Many of us have the habit of procrastination. It has been repeatedly proven to me that it is less likely for my students to fall behind if they attend the lectures. Your education is of paramount importance and I care about you and your education.
- Note: There is no need to email me if you miss a lecture. Each missed lecture (for any reason) will be counted as one of the five lectures you are allowed to miss. If you miss more than five lectures, then your course letter grade will be C.
Announcements: It is absolutely essential that you check your Sac State email and course announcements on Canvas at least once a day. I may give you important information with 24 hours' notice. Also please check our course homework page regularly for possible updates.
Problem Sessions: If the entire class agrees, I will hold problem sessions almost every Friday from 3:00 pm to 5:00 pm. If another time on Fridays works better for everyone, we can adjust the schedule accordingly.
Exams: There will be two midterm exams and a final exam.
- Midterm Exam 1: Monday 10/07/2024 (subject to change if we all agree on a different date)
- Midterm Exam 2: Wednesday 11/13/2024 (subject to change if we all agree on a different date)
- Final Exam: Wednesday 12/11/2024 (3-5 pm)
Grading: Your Math 230A weighted average will be calculated as follows:
- 5% Homework, 45% Midterm Exams, 50% Final Exam
| A | A- | B+ | B | B- | C |
| ≥95 | [91,95) | [87,91) | [83,87) | [80,83) | [0,80) |
In addition,
There will be no curve. Your score will be solely based on your own performance and not how others perform in class. Also your final percentage grade will NOT be rounded up. So 94.9999% is an A-. Please do not be more concerned with your grade than with what you learn. Remember "Grades don't measure your intelligence, age doesn't define your maturity and disabilities don't define your worth."
Note: Please notice that outside factors, including the need for a certain grade for admission/retention in any academic program, scholarship or transfer credit, graduation requirements or personal desire for a specific grade DO NOT appear in the above calculations. Your letter grade will be determined solely based on your performance as described above. Financial aid status, delay in graduation, etc. cannot be used as reasons for a grade change. Such requests are absolutely unacceptable and will be processed as a form of academic dishonesty.
Grade Recording Errors: This course will have a Gradescope page; your homework and midterm grades will be recorded on the Gradescope page (or the Canvas page) for our class. Please always make sure that your grades have been inputted and inputted correctly. In particular, if there is any mistake in the recording of your exam or homework scores, you must notify me within two days after the score was posted to Gradescope page (or the Canvas page) for our class (otherwise your request will not be considered).
Make-up Exams: Make-up exams will not be given. You cannot take any exam early or late. In particular, it is your responsibility to ensure that you do not have a schedule conflict involving the final examination; you should not enroll in this class if you cannot take the final exam at the scheduled time.
Be on Time: Please arrive on time; in fact, it will help if you make sure to be in class at least 5 minutes early. Also please do not leave class early.
Office Hours: I have scheduled a large number of office hours. Study the lecture notes regularly and make sure to bring your questions to my office hours. There is nothing that I like more than talking with you about math. In the unlikely case that all my office hours will conflict with your classes, you must let me know by the end of Week 1 so that we investigate the issue and possibly schedule even more office hours.
How to Succeed in My Course: The main objective of my class is to ensure that you will learn the basics of mathematical analysis, and to achieve that goal it is absolutely essential that you do the following:
- 1- Please attend EVERY SINGLE class and be engaged by active listening. You must not arrive late or leave early.
- 2- Please carefully study the lecture notes of the previous lecture at least twice before the next lecture and bring your questions to my office hours. Please study every lecture line by line and try to understand every detail. Please make sure that you fully understand the meaning of each statement and the purpose of each single statement in the lecture notes and bring your questions to my office hours.
- 3- You must spend adequate time on each homework assignment and bring your questions to my office hours.
- 4- It is essential that you keep your cellphone and laptop away while studying individually or in groups for this class.
Spend Sufficient Time on the Course: Since Math 230 is worth 3 credits, you should be willing to spend at least 9 hours per week on the course during a regular semester.
Electronic Devices: Please do NOT use devices such as laptops, tablets, cell phones for non-class-related purposes while in class.
Academic Dishonesty: Academic dishonesty is considered a serious offense at CSUS. All problems in exams should be solved using terminology, ideas, and methods that were introduced in lecture. If in any of your solutions you use ideas, notations, or techniques that have not been discussed in lecture, that will be considered as cheating. Students caught cheating will face an administrative sanction which may include suspension or expulsion from the university. It is in your best interest to maintain your academic integrity. (Click here for more information.)
Lastly, I believe that we are so incredibly fortunate to live in this wonderful place and have the opportunity to work or study at CSUS. If you share this sentiment, if you believe in the power of honesty and integrity, if you believe in the power of hard work and determination, and if you believe in lifting people up and not tearing them down, please do take my class. I will stop at nothing to help you succeed in this class.