********W2025****************W2025****************W2025****************W2025******** Math 5210 - 1 Introduction to Real Analysis Dec. 24, 2024 Tentative Syllabus for Spring 2022 Credit Hours: Four Meeting Time: M, T, W, F 10:45 - 11:35 AM, JWB 333 - - - In Person. Prerequisites: "C" or better in MATH 3220 Homepage: http://www.math.utah.edu/~treiberg/M5211.html Instructor: Prof. A. Treibergs (he/him/his) Campus Office JWB 224, 581 - 8350. Office Hours: MTF 11:50 AM - 12:55 PM E-mail: treiberg@math.utah.edu Text: Robert S. Strichartz, The Way of Analysis, revised ed., Jones & Bartlett, Pub., Sudbury MA, 2000. ISBN-13: 978-0-7637-1497-0 ISBN-10: 0-7637-1497-6 Text: N. L. Carothers, Real Analysis, Cambridge University Press, 2000 ISBN-13: 978-0-5214-9756-5 ISBN-10: 0-5214-9756-6 Free online through the Libraries website: https://www.cambridge-org.eproxy.lib.utah.edu/core/books /real-analysis/16AF2A6DBD1980FA0C18C417843AA867 Zoom: Lectures and Problem Sessions will be available via Zoom. The ZOOM meeting ID is on the syllabus in Canvas. Table of Contents * COVID INFORMATION A. COURSE DESCRIPTION B. COURSE DETAILS C. CONTENT OVERVIEW D. COURSE EXPECTED LEARNING OUTCOMES E. COURSE DESIGN F. EVALUATION METHODS AND GRADING G. CLASS SCHEDULE & IMPORTANT DATES H. COMMUNICATION I. NETIQUETTE - EXPECTATIONS FOR ONLINE LEARNING ENVIRONMENT J. ASSIGNMENTS, ASSESSMENT & GRADING K. ACADEMIC CODE OF CONDUCT L. ADDITIONAL POLICIES AND RESOURCES * COVID INFORMATION According to the CDC, wearing a mask remains an effective means of preventing infection for both unvaccinated and vaccinated people. Regardless of what someone chooses (mask or no mask), the university seeks to foster a sense of community and asks everyone on campus to be respectful of individual decisions on mask wearing. While Utah law prohibits state universities from requiring COVID-19 vaccinations, all members of the University of Utah community are encouraged to receive a COVID-19 vaccine. University leadership has urged all faculty, students, and staff to model the vaccination, testing, and masking behaviors we want to see in our campus community. These include: - Vaccination - Masking indoors - If unvaccinated, getting weekly asymptomatic coronavirus testing Vaccination Get a COVID-19 vaccination if you have not already done so. Vaccination is proving highly effective in preventing severeCOVID-19 symptoms, hospitalization and death from coronavirus. Vaccination is the single best way to stop this COVID resurgence in its tracks. Many in the campus community already have gotten vaccinated: More than 80% of U. employees Over 70% of U. students Visithttp://mychart.med.utah.edu/,http://alert.utah.edu/covid/vaccine, orhttp://vaccines.gov/to schedule your vaccination. Masking While masks are no longer required outside of Health Sciences facilities, UTA buses and campus shuttles,CDC guidelines now call for everyone to wear face masks indoors. Check the CDC website periodically for masking updates https://www.cdc.gov/coronavirus/2019-ncov/vaccines/fully-vaccinated-guidance.html Treat masks like seasonal clothing (i.e. during community surges in COVID transmission, masks are strongly encouraged indoors and in close groups outside). Testing If you are not yet vaccinated, get weekly asymptomatic coronavirus tests. This is a helpful way to protect yourself and those around you because asymptomatic individuals can unknowingly spread the coronavirus to others Asymptomatic testing centers are open and convenient: Online scheduling Saliva test (no nasal swabs) Free to all students returning to campus (required for students in University housing) Results often within 24 hours Visit alert.utah.edu/covid/testing Remember: Students must self-report if they test positive for COVID-19 via this website: https://coronavirus.utah.edu/. Students are encouraged to be vaccinated > Vaccination is proving highly effective in preventing severe COVID-19 symptoms, hospitalization, and death from coronavirus. > Vaccinations are available to everyone 12years and older. Appointments open in the U of U Health system for patients as well as additional vaccine providers throughout Utah.For up-to-date campus vaccination information go to: https://alert.utah.edu/covid/vaccine/ Testing and Exposure The university will continue to follow guidance from the CDC for testing, contact tracing and exposure management. When an exposure is reported, the contact tracing team will engage and advise next steps.Please note that vaccination status is part of the contact tracing protocol. Students are encouraged (undergraduate and graduate) to take advantage of university COVID-19 testing services:https://alert.utah.edu/covid-19-testing/. Voluntary asymptomatic testing will continue to be available weekly for all members of the campus community. To schedule a COVID-19 test, https:// alert.utah.edu/covid-19-testing/ > Reminder: students must self-report if they test positive for COVID-19 via this website: https://coronavirus.utah.edu/. > If you have been exposed, or are experiencing symptoms, self-report and follow university guidelines for exposure. https://coronavirus.utah.edu/wp-content/uploads/sites/2/2020/11/COVID-19- Guidance-for-Suspect-or-Confirmed-Cases-and-Close-Contacts-April-27-2021.pdf > Follow the Exposure Management Guidelines https://coronavirus.utah.edu/wp-content/uploads/sites/2/2020/11/Faculty- Response-for-Student-Report-of-COVID-19-V5.pdf for responding to and managing student reports of COVID-19 infection including contact tracing and reporting exposure to college and department leaders A. COURSE DESCRIPTION Four credits. Prerequisites: "C" or better in MATH 3220 B. COURSE DETAILS > Course Type: In person. > Location & Meeting Times: JWB 333. M, T, W, F 10:45 - 11:35 AM - - - In person. > Optional office hours and problem sessions may be conducted via ZOOM. > Attendance & Punctuality: It is strongly recommended that students attend class at the scheduled class time. Exams will take place during these times. Since we will strive to encourage class discussion, is a matter of courtesy to be on time. > Canvas Page and Zoom Broadcast: There will be a CANVAS page associated to this class. It will be used to post exam scores and grades and to make video material available. You will be able to access the zoom broadcast of this class via Canvas. In addition, some office hours and problem sessions may be held using ZOOM from the canvas page. > COVID-19 Considerations: Students must self-report if they test positive for COVID-19 via coronavirus.utah.edu. > Instructional Support Team: Instructor will grade the exams and weekly homework. > Course Materials: Text: N. L. Carothers, Real Analysis, Cambridge University Press ISBN-13: 978-0-5214-9756-5 ISBN-10: 0-5214-9756-6 Free online through the Libraries websie: https://www.cambridge.org/core/books/real-analysis/16AF2A6DBD1980FA0C18C417843AA867 Available to rent or buy as Kindle, hardcover or paperback. Students may purchase another edition, but the student is responsible for solving the correct homework problems, which will be assigned from the 7th edition. Course materials other than the textbook will be available on line at the course webpage or in canvas. Course materials other than the textbook will be available on line at the course webpage or in canvas. > Technical requirements: Students are expected to be computer literate and Canvas and zoom navigation skills are expected. Knowledge and navigation of canvas and zoom is critical to access all features and resources of this course. It is expected expectation that students log into Zoom for class with audio and video enabled. A strong internet connection and adequate bandwidth is needed. Exams will be taken in class at the scheduled times. Additional software/computing requirements: students will be asked to solve differential equations numerically. It does not matter which software is used, but students should start to familiarize themselves with software. e.g., Maple or Macintosh's Grapher. For technical assistance, review the Canvas Getting Started Guide for Students and/or contact TLT, Knowledge Commons. > Syllabus subject to change: This syllabus is meant to serve as an outline and guide for our course. Please note that I may modify it with reasonable notice to you. I may also modify the Course Schedule to accommodate the needs of our class. Any changes will be announced in class and posted on the course webpage. C. CONTENT OVERVIEW Course Description: This is a semester course devoted to real analysis. We'll build on topics from Math 3210-20 such as properties of real numbers, topology, sequences, continuous functions, derivatives, Riemann integral. We'll construct the real numbers. Many models from mathematical physics and mathematical biology reduce to differential equations, whose analysis depends on the study of function spaces that abstract the real number spaces. Finally, we'll develop the powerful Lebesgue integral. Topics: We will follow the text and try to cover as many topics as time allows. - Review and Construction of the Real Numbers - Metric Spaces - Various Applications, such as - Differential Equations - Fourier Series - Implicit Functions - Lebesgue Integral - Multiple Integrals D. COURSE EXPECTED LEARNING OUTCOMES Upon successful completion of Math 5210 - Introduction to Real Analysis, students will be able to: construct the real numbers; manipulate basic topological notions such as open closed, compact, connected sets in the context of metric spaces and function spaces; show familiarity with limiting processes such as convergence, derivative, series; and be able to construct and handle the Lebesgue integral. Students will able to use analytical methods for such applications as to differential equations, Fourier Series and implicit surfaces. Students show an appropriately more sophisticated proficiency in writing proofs and making a mathematical argument. E. COURSE DESIGN Material will be presented in lectures and read from the text and other sources. Students will solidify their learning by solving problems assigned weekly. Students will ask questions and present solutions in regular classroom discussions and zoom office hours. Students may benefit from one-on-one instruction by consulting the instructor during office hours. The student is expected to take the responsibility to ask for help when needed. All exams for this course will be held in person during class times. Students will solidify their learning by solving problems assigned weekly. Students will prepare written solutions to weekly homework. F. EVALUATION METHODS AND GRADING Homework: To be assigned weekly. Homework will be due Fridays and will be collected in class. Papers turned into my mailbox in the math mail room (JWB 228) by 4:00 PM Fridays will be regarded as being turned in on time. Homework that is late but not more than one week late will receive half credit. Homework that is more than one week late will receive no credit at all. Exams: Exams will be taken in person during class time. Exams will be closed book except that you may bring a "cheat sheet," an 8.5" x 11" piece of paper with notes on both sides. Your text, other books, notes, homework papers, calculators laptops, tablets, phones and text messaging devices will not be allowed. Midterms: There will be three in-class one-hour midterm exams on Wednesdays Jan. 29, Feb. 26 and Apr. 2. Final Exam: Tue., Apr. 29, 10:30 AM - 12:30 PM. Half of the final will be devoted to material covered after the third midterm exam. The other half will be comprehensive. Students must take the final to pass the course. Course grade: Best two of three midterms 32% + HW 44% + final 24%. Grades will be assigned by the following cutoffs, based on previous classes. If the total point values are 80 for midterms, 220 for homework and 120 for the final, then if the sum of points is at least S then your grade will be S Grade --- ----- 390 A 360 A- 340 B+ 290 B 230 B- 210 C+ 180 C 160 C- 150 D+ 145 D G. CLASS SCHEDULE & IMPORTANT DATES Class meets at M, T, W, F from 10:45 - 11:35 am in person starting January 6 and ending April 22. There may be an optional ZOOM problem session at class time on Thursdays. Last day to register is Jan. 10. Last day to drop class is Jan. 17. Until Feb. 28 you can withdraw from class with no approval at all. After that date you must petition your dean's office to be allowed to withdraw. Please check the academic calendar for more information pertaining to dropping and withdrawing from a course. Withdrawing from a course and other matters of registration are the student's responsibility. Exam Dates: There will be three in-class 50 minute midterm exams on Wed. Jan.29, Feb.26 and Apr.2. The final exam is Tue., Apr. 29, 10:30 AM - 12:30 PM. The final is at the University scheduled time. Students must take the final to pass the course. Holidays: There will be no classes Monday, Jan. 20 (Martin Luther King Day), Monday Feb. 17 (President's Day) and Mar. 10 - 14 (Spring Break), H. COMMUNICATION Clarification which forms of communication and responsibilities of students. - The course syllabus, homework, and supplementary material such as old solved exams will be posted on the class website http://www.math.utah.edu/~treiberg/M5211.html The syllabus and course materials will also be posted on canvas. Other sensitive materials such as grades and recordings of our meetings will also be available on the course canvas page for Math 3210-002. https://utah.instructure.com/courses/ Class announcements will be done via email. You will be responsible for any information contained in them as well as the information announced in class. - It is your responsibility to also regularly check your Umail (make sure you set up forwarding if you do not check it regularly), your Umail is the only way for me to communicate privately with you, there will be occasions during the semester that we may need to reach out to you individually (e.g. regarding a grade or assignment) and it is in your best interest to respond promptly. - Feel free to contact me by email for questions at treiberg@math.utah.edu This is the only email address that I will respond to. I will do my best to answer emails sent to this address promptly. If you use the canvas Inbox it may take a week for me to respond. I would like to encourage you to email me only if it is something personal that requires individual attention. If instead you have questions about logistics of the class, course material and assignments, and anything else your classmates may wonder as well, please ask me in class. - I will always do my best to ensure the communication relevant to the course is clear and transparent, it is your responsibility as well to keep yourself updated by regularly checking your university listed email. - Course Canvas Page: Students are expected to log in and check canvas regularly for posted announcements, grades and handouts. Zoom meetings will be held through the canvas page. - Course Home Page: Students are expected to log in and check the course home page for homework assignments and solved sample exams. http://www.math.utah.edu/~treiberg/M5212.html I. NETIQUETTE - EXPECTATIONS FOR ONLINE LEARNING ENVIRONMENT Here are some norms of communications for online settings. - Classroom equivalency: Respectful participation in all aspects of the course will make our time together productive and engaging. Zoom lectures, discussion threads, emails and canvas are all considered equivalent to classrooms and student behavior within those environments shall conform to the student code. Specifically: - Posting photos or comments that would be off-topic in a classroom are still off-topic in an online posting. - Disrespectful language and photos are never appropriate. - Using angry or abusive language is not acceptable, and will be dealt with according to the Student Code. The instructor may remove online - Do not use ALL CAPS, except for titles, or overuse certain punctuation marks such as exclamation points and question marks. - Course e-mails, e-journals, and other online course communications are part of the classroom and as such, are University property and subject to the Student Code. Privacy regarding these communications between correspondents must not be assumed and should be mutually agreed upon in advance, in writing. - Other expectations for online communication (on Discussion Board, Emails, Zoom chat etc.: - Emails: When emailing your Instructor and Teaching Team keep a professional tone (e.g. Use a descriptive subject line, avoid "Hey" and always use your professors proper title: Dr. or Prof., Sign your message with your name and return e-mail address. Please consult this page for tips on how to write appropriate professional emails: https://academicpositions.com/career-advice/how-to-email-a-professor - Treat your instructor, teaching team and classmates with respect in email or any other communication. - Remember that all college level communication should have correct spelling and grammar (this includes discussion boards). - Avoid slang terms such as "wassup?" and texting abbreviations such as "U" instead of "you" - Be cautious when using humor or sarcasm as tone is sometimes lost in an email or discussion post and your message might be taken seriously or be offensive to others. - Be careful with personal information (both yours and others). - Electronic or equipment failure: It is your responsibility to maintain your computer and related equipment in order to participate in the online portion of the course. Equipment failures will not be an acceptable excuse for late or absent assignments. - Online submissions: My preference is that you submit homework on paper in person. Occasionally you will be allowed to submit papers on line. Please submit files with the required naming convention and correct file extension. Homework will normally be submitted as a single pdf file. The file name should be your name and assignment number, e.g., "Einstein_HW6.pdf" and not "math homework.pdf". - Canvas and CIS allows students to change the name that is displayed AND allows them to add their pronouns to their Canvas name. Additionally, students can indicate their pronouns in Zoom. J. ASSIGNMENTS, ASSESSMENT & GRADING Here are some details about course grading. - The total score is the weighted sum of best two of three midterms, homework and the final. The two midterms will be weighted 32% the homework 44% and the final 24%. total score = best two midterms 32% + HW 44% + final 24% Grades will be assigned by the schedule above, which is based on my experience of previous classes. If the total score is at least S then grade will be as in the table. For example a student receives 45/80, 47/80 on 53/80 on midterms, 188/220 on homework and 77/120 on the final, her weighted total will be 47 + 53 + 188 + 77 = 365 which earns her the grade A-. Note that the percentages of grades computed by Canvas is at best an approximation of your grade. The homework makes up a whopping 44% of your total. You have complete control of this part of your score. Take advantage of any ZOOM problem sessions come to my office hours or ask in class for help. The midterms and final will consist of in-class exams. There will be three midterm exams on Wednesdays Jan. 29, Feb. 26 and Apr. 2. These exams are to be completed during the class period. The sum of the midterm scores makes up 32% of your grade. Students will be able to submit an optional analysis of their midterm exams on the class day after exams are returned. The analysis will be a discussion of two exam problems. This gives students a chance to make corrections of the their exam problems. For each analysis I will increase the test score by up to 10% of the exam. Students must analyze the entire problem, not just the parts that were correct. The final exam will be half on the material since the last midterm and half comprehensive. Students will not be able to submit an analysis of the final. Students must take the final to pass the class. Homework will be assigned weekly. The homework problems will be listed on the class webpage. Students may discuss homework with each other, but are expected to write up assignments on their own. Copying from another student or from the internet is cheating and will be treated as academic misconduct. If you use any reference other than the textbook, you are expected to quote the reference in full and provide a complete citation. Refer to the American Mathematical Society style guide https://www.ams.org/publications/authors/AMS-StyleGuide-online.pdf or the APA, MLA or Chicago styles recommended by University of Utah Writing Program https://writingcenter.utah.edu/writing-resources/index.php - The Mathematics Department strongly recommends an in class final for all undergraduate classes. Students must take the final to pass this class. The final exam will be held in the normal classroom. It will be given during the final exam period according to the University final exam schedule. - Students should check their grades and notify me if they notice any mistake. For instance, it is the student's responsibility to ensure the accuracy of all recorded homework, midterm and exam grades. Also you should keep as record all your graded assignments. If you see any error in your grades on Canvas, reach out to the instructor as soon as possible, or at the latest within two weeks from when the assignment was returned. Late Assignments/Missed Assignments/Regrading Policies: - Homework will be due every Friday at 4:00pm. Homework that is late but not more than one week late will receive half credit. Homework that is more than one week late will receive no credit at all. If there are any queries on homework, please write your question and submit them to me with a copy of the homework and its grading. Incompletes: According to university policy, to be considered for an incomplete, a student must have 20% or less of the course work remaining and be passing the course with a C or better. You must request an incomplete grade and I will consider giving that grade only under exceptional circumstances. - Students seeking academic accommodations should contact me and make necessary arrangements before the first exam. Students will have to arrange an alternative with me beforehand if they are unable to take the exam at the scheduled time. Otherwise, except in extraordinary circumstances, no makeup exams will be given. Disability accommodations are arranged by the Center for Disability & Access and are not by the instructor. K. ACADEMIC CODE OF CONDUCT AND ADDITIONAL POLICIES AND RESOURCES Current mandatory University syllabus policies regarding ADA Act, Safety at the U, Addressing Sexual Misconduct, and Academic Misconduct are listed here. They can also be viewed at: https://cte.math.utah.edu/instructor- education/syllabus/institutional-policies.php Americans With Disabilities Act (ADA) The University of Utah seeks to provide equal access to its programs, services, and activities for people with disabilities. All written information in this course can be made available in an alternative format with prior notification to the Center for Disability & Access (CDA). CDA will work with you and the instructor to make arrangements for accommodations. Prior notice is appreciated. To read the full accommodations policy for the University of Utah, please see Section Q of the Instruction & Evaluation regulations. https://regulations.utah.edu/academics/6-100.php In compliance with ADA requirements, some students may need to record course content. Any recordings of course content are for personal use only, should not be shared, and should never be made publicly available. In addition, recordings must be destroyed at the conclusion of the course. If you will need accommodations in this class, or for more information about what support they provide, contact: Center for Disability & Access 801-581-5020 disability.utah.edu 162 Union Building 200 S. Central Campus Dr. Salt Lake City, UT 84112 Safety at the U The University of Utah values the safety of all campus community members. You will receive important emergency alerts and safety messages regarding campus safety via text message. For more safety information and to view available training resources, including helpful videos, visit safeu.utah.edu. To report suspicious activity or to request a courtesy escort, contact: Campus Police & Department of Public Safety 801-585-COPS (801-585-2677) dps.utah.edu 1735 E. S. Campus Dr. Salt Lake City, UT 84112 Addressing Sexual Misconduct Title IX makes it clear that violence and harassment based on sex and gender (which includes sexual orientation and gender identity/expression) is a civil rights offense subject to the same kinds of accountability and the same kinds of support applied to offenses against other protected categories such as race, national origin, color, religion, age, status as a person with a disability, veteran’s status, or genetic information. If you or someone you know has been harassed or assaulted, you are encouraged to report it to university officials: Title IX Coordinator & Office of Equal Opportunity and Affirmative Action 801-581-8365 oeo.utah.edu 135 Park Building 201 Presidents' Cir. Salt Lake City, UT 84112 Office of the Dean of Students 801-581-7066 deanofstudents.utah.edu 270 Union Building 200 S. Central Campus Dr. Salt Lake City, UT 84112 To file a police report, contact: Campus Police & Department of Public Safety 801-585-COPS (801-585-2677) dps.utah.edu 1735 E. S. Campus Dr. Salt Lake City, UT 84112 If you do not feel comfortable reporting to authorities, the U's Victim- Survivor Advocates provide free, confidential, and trauma-informed support services to students, faculty, and staff who have experienced interpersonal violence. To privately explore options and resources available to you with an advocate, contact: Center for Student Wellness 801-581-7776 wellness.utah.edu 328 Student Services Building 201 S. 1460 E. Salt Lake City, UT 84112 Academic Misconduct It is expected that students comply with University of Utah policies regarding academic honesty, including but not limited to refraining from cheating, plagiarizing, misrepresenting one’s work, and/or inappropriately collaborating. This includes the use of generative artificial intelligence (AI) tools without citation, documentation, or authorization. Students are expected to adhere to the prescribed professional and ethical standards of the profession/discipline for which they are preparing. Any student who engages in academic dishonesty or who violates the professional and ethical standards for their profession/discipline may be subject to academic sanctions as per the University of Utah’s Student Code: Policy 6-410: Student Academic Performance, Academic Conduct, and Professional and Ethical Conduct. https://regulations.utah.edu/academics/6-410.php Plagiarism and cheating are serious offenses and may be punished by failure on an individual assignment, and/or failure in the course. Academic misconduct, according to the University of Utah Student Code: “...Includes, but is not limited to, cheating, misrepresenting one’s work, inappropriately collaborating, plagiarism, and fabrication or falsification of information... It also includes facilitating academic misconduct by intentionally helping or attempting to help another to commit an act of academic misconduct.” For details on plagiarism and other important course conduct issues, see the U's Code of Student Rights and Responsibilities. https://regulations.utah.edu/academics/6-400.php Dignity/Belonging Statement I stand in support of compassion, dignity, value-of-life, fair treatment, belonging, and justice for all individuals regardless of color, race/ ethnicity, sexual orientation, religion, language, socioeconomic status, ability, gender, gender identity or expression, immigration status, or any type of marginalization. I stand in support of making our society more fair and compassionate for all individuals. I stand against discrimination in all its various forms.