Mathematics 444 P13 (Elementary Real Analysis)

Instructor: Prof. Aimo Hinkkanen

Email: aimo 'at' illinois.edu

Office: 253 Computing Applications Building (CAB, southwest corner of Wright and Springfield)
Phone: 217-244-7306

Lectures: Tuesdays and Thursdays 11:00-12:20 in 441 Altgeld Hall
Office hours: Tuesdays and Thursdays 1:00-1:50 pm, or by appointment

Learning Management System: Many course materials will be made available on Moodle.

To log in to Moodle, please click here and log in using your university net-id and password, and two-factor authentication.

Then go to MY COURSES and you should see this course there (you need to be registered for the course to see it).

On Moodle, you will find pre-recorded lectures and the pdf-files corresponding to them. These materials will be added as the semester goes on.

Textbook (required, e-copies OK) : Robert G. Bartle and Donald R. Sherbert, Introduction to Real Analysis, fourth edition, Wiley, 2011.

For the course syllabus, please click here.

For information on the extension of the drop deadline for LAS and Engineering undergraduate students, please click here.

For the first-day information sheet as a pdf-file, please click here.

For the emergency information sheet for students, drawn up by the Department of Mathematics, please click here.

For emergency information provided by the University Police, please click here.

There will be three midterm exams and a final exam. Tentative dates of midterm exams (subject to change):

More precise information on the dates of the midterm exams will be provided later. All midterm exams will be held during regular class time in the regular classroom.

Final exam: Thursday, May 12, 8:00-11:00 am (according to campus schedule), in the regular classroom.

Grading: The grade for the course will be based on the total points from the best two midterm exams (the maximum score will be 100 in each midterm exam), the final exam (maximum score 100), and quizzes (points normalized so that the maximum score will be 100). Hence the maximum score will be 400 for the total points.

No books, notes or calculators will be allowed in the quizzes, the midterm exams and the final exam. Bring your university ID to the midterm exams and the final exam.

Quizzes. After the first week, there will be a quiz at the beginning of each class (apart from a few exceptions). In each quiz, there will typically be up to three questions, each graded either 5 or 0 points depending on whether your answer is completely correct or not. A certain number (at least three) of lowest quiz scores will be dropped. (The exact number of quizzes to be dropped depends on how many quizzes we end up having during the semester and will be announced later.) Dropping one midterm exam and at least three quizzes is intended to provide leeway for those times when a student is ill, or needs to go to a job interview, or has a family emergency, or just misses class or is late for the class for some other reason. If you miss a midterm exam or a quiz, you will get zero points for it. As this system allows you to miss one midterm exam and at least three quizzes without you giving any reason for it, no make-up midterm exams or quizzes will be given. Exceptions will be considered only in the case of a prolonged illness indicated by a doctor's note. Covid-related absences will be taken into account in an appropriate way, to be decided on the basis of each situation. You are encouraged to take all midterm exams and quizzes and do your best.

Academic integrity is taken seriously. Please see the student code, article 1, part 4, beginning at https://studentcode.illinois.edu/article1/part4/1-401/

Accommodations for disabilities. To obtain disability-related academic adjustments and/or auxiliary aids, students with disabilities must contact the Disability Resources and Educational Services (DRES). To contact DRES you may visit 1207 S. Oak St., Champaign, call 333-4603 (V/TTY), or email to disability 'at' illinois.edu. Please contact the instructor as soon as possible after DRES has issued a letter outlining the required accommodations.

Problems from the textbook will also be suggested. A list of all suggested problems can be found by clicking on the link to "Suggested problems" below.


Suggested problems


Midterm exam 1 will be held on Thursday February 17 at regular class time. Midterm exam 1 will cover Chapter 1, Sections 1-2; Chapter 2, Sections 1-5.


Midterm exam 2 on Thursday March 24 at regular class time will cover Chapter 3, Sections 1-5; Chapter 4, Sections 1-2. All midterm exams may include questions also from all material that was covered earlier.


Midterm exam 3 on Thursday April 21 at regular class time will cover Chapter 5, Sections 1-4; Chapter 6, Sections 1-2. All midterm exams may include questions also from all material that was covered earlier.


The final exam will cover Chapter 1, Sections 1-2; Chapter 2, Sections 1-5; Chapter 3, Sections 1-5; Chapter 4, Sections 1-2; Chapter 5, Sections 1-4; Chapter 6, Sections 1-2; Chapter 7, Sections 1-3; and Chapter 8, Sections 1-2.



Dates of quizzes






Information for graduate students who wish to take this course for 4 credit hours.

Extra project or work of substance: The student will read 3 sections of the text book not covered in the course, as assigned by the instructor. Then the student will solve a total of 5 problems from these sections, as assigned by the instructor, and will write each solution as an independent, complete essay using complete sentences.

Instructor method of evaluation: The deadline for turning in the work will be set for early November in a fall semester and early April in a spring semester. After the work has been reviewed by the instructor, the student will have to rewrite the work or part of it as many times as necessary until it is mathematically completely correct and at a professional level of exposition.

The extra work described above is for the purpose of earning the fourth credit hour only, and the student's grade for the course will be determined in the same way as for the other students, apart from the following extra rule: if the student does not perform the extra work, the grade for the course will be an F, regardless of any other circumstances.

Please note that once the section for 4 credit hours has been created and you have joined it, by University rules it will not be possible for you to switch back to 3 credit hours (you may still be able to drop the course, subject to appropriate deadlines). This means that you will then have 4 credit hours for this course. For this reason, there needs to be a sanction for those who thus sign up but fail to do the extra work, for otherwise such people would be able to get 4 credit hours without extra work. It is for this reason that we have the above extra rule.

Paperwork: A student who wishes to register for a fourth credit hour in this way needs to go to the Undergraduate Office of the Department of Mathematics in 313 Altgeld Hall to obtain a form to be filled in. After entering your personal information, please hand the form to the instructor for him to fill in the appropriate details and to sign. After the instructor has returned the form to you, please take it back to the Undergraduate Office of the Department of Mathematics for further processing. Typically this process needs to be completed during the first two weeks of the semester. You can contact the Undergraduate Office by email at mathadvising (at) illinois.edu


Checking your scores online: You can see your scores on Moodle.


University policies related to covid

The Campus recommended the following language to be added to syllabi:

Following University policy, all students are required to engage in appropriate behavior to protect the health and safety of the community. Students are also required to follow the campus COVID-19 protocols.

Students who feel ill must not come to class. In addition, students who test positive for COVID-19 or have had an exposure that requires testing and/or quarantine must not attend class. The University will provide information to the instructor, in a manner that complies with privacy laws, about students in these latter categories. These students are judged to have excused absences for the class period and should contact the instructor via email about making up the work.

Students who fail to abide by these rules will first be asked to comply; if they refuse, they will be required to leave the classroom immediately. If a student is asked to leave the classroom, the non-compliant student will be judged to have an unexcused absence and reported to the Office for Student Conflict Resolution for disciplinary action. Accumulation of non-compliance complaints against a student may result in dismissal from the University.

All students, faculty, staff, and visitors are required to wear face coverings in classrooms and university spaces. This is in accordance with CDC guidance and University policy and expected in this class.

Please refer to the University of Illinois Urbana-Champaign's COVID-19 website for further information on face coverings. Thank you for respecting all of our well-being so we can learn and interact together productively.

In order to implement COVID-19-related guidelines and policies affecting university operations, instructional faculty members may ask students in the classroom to show their Building Access Status in the Illinois app or the Boarding Pass. Staff members may ask students in university offices to show their Building Access Status in the Illinois app or the Boarding Pass. If the Building Access Status says "Granted", that means the individual is compliant with the university's COVID-19 policies - either with a university-approved COVID-19 vaccine or with the on-campus COVID-19 testing program for unvaccinated students.

Students are required to show only the Building Access Screen, which shows compliance without specifying whether it was through COVID-19 vaccination or regular on-campus testing. To protect personal health information, this screen does not say if a person is vaccinated or not. Students are not required to show anyone the screen that displays their vaccination status. No university official, including faculty members, may ask students why they are not vaccinated or any other questions seeking personal health information.