INTRODUCTION TO REAL ANALYSIS FALL 2015

MATH 4310 001 INTRODUCTION TO REAL ANALYSIS FALL 2015 Instructor Details: Troy Butler, Office AB1 4311, Phone 303-315-1734, Email (best way to reach me) Troy.Butler@ucdenver.edu Course location: AB1 4017 Course and Office hours dates/times: MW 5:00 6:15 p.m. (Class), MW 6:15 7:30 p.m. (Office hours) Text: Elementary Analysis The Theory of Calculus, 2nd Edition, Kenneth A. Ross Course description from catalog: Calculus of one variable, the real number system, continuity, differentiation, integration theory, sequences and series Prerequisites: Math 2411 (Calc. II) and Math 3000 (Intro. to abstract math.) Course Objectives and Learning Outcomes: To rigorously build the theoretical foundation required for a proper understanding of calculus so that students can read mathematical definitions and theorems proficiently. To introduce students to the commonly used proof techniques in real analysis so that they can read and write proofs proficiently. In the reading and writing of proofs, the following learning outcomes are stressed in every homework assignment, quiz, and exam: creative thinking, critical thinking, inquiry and analysis, problem solving, and written communication. Course Overview, Major Topics, and Rationale: This class is a proof-based course that rigorously covers fundamental topics involving the real number system, sequences of real numbers, and functions of real numbers (refer to the schedule below and assigned textbook for a detailed listing of material and topics covered). Much of advanced mathematics, engineering, statistics/probability and physical sciences relies on the concepts we cover in this course. Descriptions of where topics play a role in more advanced areas will be given throughout the course. Class Website: Check out the Canvas class page for notes, homework assignments, grades, etc. Assignments, quizzes, exams, grades, and policies: Homework. Homework will be assigned (approximately) weekly, will typically be due the following Monday, and will be carefully selected to be relevant to the lectures for that week. I will utilize Canvas announcements to inform you which set of problems you should be able to complete from the homework assignment using the material from the lecture and book on the topic discussed in class each day. Homework is meant to be a source of feedback for you, and while I encourage you to work in groups, the largest benefit is derived by solving difficult problems on your own and you must write up and turn in your own individual assignments. 1

2 MATH 4310 001 INTRODUCTION TO REAL ANALYSIS FALL 2015 All assignments that are 100% completed are eligible to be corrected to receive up to 50% of the missed credit and resubmitted at the beginning of the next lecture following the one where the assignment is returned to the class. Homework will count for 10% of your grade. No late assignments are accepted without prior approval. Students who complete 100% of the homework assignments in their entirety are eligible to have their the overall percentages for quizzes and exams re-weighted to arrive at a more favorable grade. The maximum of the grade (with or without re-weighting) will be used to assign a final letter grade. This option is only available for students who complete 100% of every homework assignment. There will be five cumulative quizzes throughout the semester (each about 3 weeks apart) and a final exam each counting as 15% of your grade. Grading of proofs. Each problem will be graded using a 5 point scale. A perfect proof will receive a 5. A score of 4 indicates a proof that contains only minor errors/typos but is otherwise correct. A score of 3 indicates a proof that is structured correctly but is either missing details that should have been included, contains a small logical error, or several errors/typos. A score of 2 indicates a proof that sketches out the correct steps in order but is missing significant details or has an otherwise glaring error. A score of 1 indicates that a proof contains the correct steps but are possibly out of order, contains a very significant error, or is missing significant details. A score of 0 indicates the basic outline of the proof is either incorrect, is missing a step, or has details that are completely wrong. Class attendance is recommended. Late homework is not accepted without prior written approval. Cheating or other academic misconduct will result in no credit for the assignment or exam in question, plus lowering the grade by 10% points, and will be reported to the department chair. Grades will be determined using the following scale that is based on the 5 point scale for grading proofs described above: 80-100% (A this means you can correctly sketch out, fill in the details, and make very few mistakes in most of the proofs in this course), 70-79% (B this means that you can both correctly sketch out and fill in the details for most of the proofs in this course with only minor errors), 50-69 (C this means that are able to correctly sketch out almost all of the proofs in this class and correctly fill in the details for about half of the proofs), 40-49 (D this means you can correctly sketch out most of the proofs in this course but have difficulty filling in details correctly), and 0-39 (F).

MATH 4310 001 INTRODUCTION TO REAL ANALYSIS FALL 2015 3 Tentative Course Schedule: Wk. 1: Aug. 17 & 19 Chp. 1, Sections 1 5 Wk. 2: Aug. 24 & 26 Finish Chp. 1, Begin Chp. 2, Sections 7 12 Wk. 3: Aug. 31 & Sept. 2 Chp. 2, Sections 7 12 and Cumulative Quiz 1 Wk. 4: Sept. 9 Chp. 2, Sections 7 12 Wk. 5: Sept. 14 & 16 Chp. 2, Sections 7 12 Wk. 6: Sept. 21 & 23 Chp. 2, Sections 14 15 and Cumulative Quiz 2 Wk. 7: Sept. 28 & 30 Chp. 2, Sections 14 15 and Chp. 3, Sections 17 20 Wk. 8: Oct. 5 & 7 Chp. 3, Sections 17 20 Wk. 9: Oct. 12 & 14 Chp. 3, Sections 17 20 and Cumulative Quiz 3 Wk. 10: Oct. 19 & 21 Chp. 4, Sections 23 25 part of 26 Wk. 11: Oct. 26& 28 Chp. 4, Sections 23 25 part of 26 Wk. 12: Nov. 2 & 4 Chp. 5, Sections 28 31 and Cumulative Quiz 4 Wk. 13: Nov. 9 & 11 Chp. 5, Sections 28 31 Wk. 14: Nov. 16 & 18 Chp. 6, Sections 32 34 Nov. 23 & 25 Fall break Wk. 15: Nov. 30 & Dec. 2 Chp. 6, Sections 32 34 and Cumulative Quiz 5 Dec 7-12 Finals week

Academic Dishonesty: Students are required to know, understand, and comply with the CU Denver Academic Dishonesty Policy as detailed in the Catalog and on the CLAS website. Academic dishonesty consists of plagiarism, cheating, fabrication and falsification, multiple submission of the same work, misuse of academic materials, and complicity in academic dishonesty. If you are not familiar with the definitions of these offenses, go to http://www.ucdenver.edu/academics/colleges/clas/facultystaff/policies/pages/definitionofacademicdishonesty.aspx. This course assumes your knowledge of these policies and definitions. Failure to adhere to them can result in possible penalties ranging from lowering a grade on an assignment to dismissal from the University; so, be informed and be careful. If this is unclear to you, ask me. The College of Liberal Arts and Sciences (CLAS) Ethics Bylaws allow the instructor to decide how to respond to an ethics violation, whether by lowering the assignment grade, lowering the course grade, and/or filing charges against the student with the Academic Ethics Committee. Students who have complaints about the course or instructor should: 1) meet with the instructor face-to-face; 2) if not satisfied, meet with the Associate Chair of the math department/unit, Prof. Steve Billups or the Chair, Prof. Jan Mandel; 3) if not satisfied, appeal to the Associate Dean. No step in this process may be skipped. See "Procedures for Student Grievances about Courses or Faculty, CLAS. Missing an Exam: If circumstances arise that prevent you from attending an exam, please contact me ahead of time as I will be much more lenient. Unexplained absences will require hard evidence such as a death certificate, hospital paperwork, etc. Other resources for this course The Learning Resources Center The Learning Resource Center is where students go to get help or insight with class assignments, course-loads, and study skills. The Center also helps with arranging tutoring sessions, which take place in the days or evenings. North Classroom Building (NC) Room 2006 (303) 556-2802 Monday - Thursday 9am-7pm Friday 9am-5pm http://www.ucdenver.edu/life/services/lrc/pages/default.aspx Program Access for Persons with Disabilities The University of Colorado Denver is committed to providing reasonable accommodations and access to programs and services to persons with disabilities. Students should contact the Disabilities Resources Offices. North Classroom building 2514;

Phone # 303-556-3450, TTY 303-556-4766. Monday Friday 8am 5pm http://www.ucdenver.edu/academics/colleges/clas/faculty-staff/facultyresources/teaching/supporting-students/pages/students-disabilities.aspx Academic Success and Advising Center This office serves as the first point of contact for students who are pre-business, pre-engineering, or who have not declared a major in CLAS or CAM. In addition, the center provides general information and resource referral to all students. North Classroom Building (NC) Room 2024 Phone # 303-352-3520 Career Center The Career Center offers a full array of services that prepare students for career success, such as resume help, internship and career counseling and they have a large career library. Tivoli Student Union Room 267 Phone # 303-556-2250 Definition of Academic Dishonesty Students are expected to know, understand, and comply with the ethical standards of the University. In addition, students have an obligation to inform the appropriate official of any acts of academic dishonesty by other students of the University. Academic dishonesty is defined as a student's use of unauthorized assistance with intent to deceive an instructor or other such person who may be assigned to evaluate the student s work in meeting course and degree requirements. Examples of academic dishonesty include, but are not limited to, the following: Plagiarism: Plagiarism is the use of another person s distinctive ideas or words without acknowledgment. The incorporation of another person s work into one s own requires appropriate identification and acknowledgment, regardless of the means of appropriation. The following are considered to be forms of plagiarism when the source is not noted: 1. Word-for-word copying of another person's ideas or words. 2. The mosaic (the interspersing of one s own words here and there while, in essence, copying another's work). 3. The paraphrase (the rewriting of another s work, yet still using their fundamental idea or theory). 4. Fabrication of references (inventing or counterfeiting sources). 5. Submission of another s work as one's own. 6. Neglecting quotation marks on material that is otherwise acknowledged. Acknowledgment is not necessary when the material used is common knowledge.

Cheating: Cheating involves the possession, communication, or use of information, materials, notes, study aids or other devices not authorized by the instructor in an academic exercise, or communication with another person during such an exercise. Examples of cheating are: 1. Copying from another's paper or receiving unauthorized assistance from another during an academic exercise or in the submission of academic material. 2. Using a calculator when its use has been disallowed. 3. Collaborating with another student or students during an academic exercise without the consent of the instructor. Fabrication and Falsification: Fabrication involves inventing or counterfeiting information, i.e., creating results not obtained in a study or laboratory experiment. Falsification, on the other hand, involves deliberately alternating or changing results to suit one s needs in an experiment or other academic exercise. Multiple Submissions: This is the submission of academic work for which academic credit has already been earned, when such submission is made without instructor authorization. Misuse of Academic Materials: The misuse of academic materials includes, but is not limited to, the following: 1. Stealing or destroying library or reference materials or computer programs. 2. Stealing or destroying another student s notes or materials, or having such materials in one s possession without the owner s permission. 3. Receiving assistance in locating or using sources of information in an assignment when such assistance has been forbidden by the instructor. 4. Illegitimate possession, disposition, or use of examinations or answer keys to examinations. 5. Unauthorized alteration, forgery, or falsification. 6. Unauthorized sale or purchase of examinations, papers, or assignments. Complicity in Academic Dishonesty: Complicity involves knowingly contributing to another s acts of academic dishonesty.

Fall 2015 CLAS Academic Policies The following policies, procedures and deadlines pertain to all students taking classes in the College of Liberal Arts and Sciences (CLAS). They are aligned with the Official University Academic Calendar: http://www.ucdenver.edu/student-services/resources/registrar/documents/academiccalendars/downtown/fall/academiccalendarfall2015.pdf Schedule verification: It is each student s responsibility to verify that their official registration and schedule of classes is correct in their CU Denver PassportID portal before classes begin and by the university census date. Failure to verify schedule accuracy is not sufficient reason to justify late adds or drops. Access to a course through Canvas is not evidence of official enrollment. E-mail: Students must activate and regularly check their official CU Denver e-mail account for university related messages. Administrative Drops: Students may be administratively dropped from a class if they never attended or stopped attending, if the course syllabus indicates that the instructor will do this. Students may be administratively dropped if they do not meet the requisites for the course as detailed in course descriptions. Late adds and late withdrawals require a written petition, verifiable documentation and dean s approval. CLAS undergraduate students should visit the CLAS advising office (NC1030) and graduate students should visit the Graduate School (12 th floor LSC) to learn more about the petition process and what they need to do to qualify for dean s approval. Waitlists: The Office of the Registrar notifies students at their CU e-mail account if they are added to a class from a waitlist. Students are not automatically dropped from a class if they never attended, stopped attending, or do not make tuition payments. After waitlists are purged, students must follow late add procedures to be enrolled in a course. Students will have access to Canvas when they are on a waitlist, but this does not mean that a student is enrolled or guaranteed a seat in the course. Students must obtain instructor permission to override a waitlist and this is only possible when there is physical space available in a classroom, according to fire code. August 17, 2015: First day of classes. Important Dates and Deadlines All dates and deadlines are in Mountain Standard Time (MST). August 23, 2015: Last day to add or waitlist a class using the CU Denver PassportID portal. August 24, 2015: Last day to drop a class without a $100 drop charge--this includes section changes. August 24, 2015: All waitlists will be eliminated today. Please check your schedule in your CU Denver PassportID portal to confirm in which classes you are officially enrolled. August 25-September 2, 2015, 5 PM: Students must obtain instructor permission to add a course using the Instructor Permission to Enroll Form and bring it to the CLAS Dean s Office (NC 5014) or have their instructor e-mail it to CLAS.Courses@ucdenver.edu. September 2, 2015: Census date. o 9/2/15, 5 PM: Last day to add full term classes with instructor approval. Adding a class after this date (late add) requires a written petition, verifiable documentation and dean s approval. After this date, you will be charged the full tuition amount for additional classes added College Opportunity Fund hours will not be deducted from eligible student s lifetime hours. o 9/2/15, 5 PM: Last day to drop full term classes with a financial adjustment. After this date withdrawing from classes require instructor signature approval and will appear on your transcript with a grade of W. After this date, a complete withdrawal (dropping all classes) from the term will require the signature of the dean and no tuition adjustment will be made. Signature of Financial Aid Office is required if you have accepted financial aid (loans, grants or scholarships). o 9/2/15, 5 PM: Last day to apply for Fall 2015 graduation. Undergraduates must make an appointment and see their academic advisor before this date to apply. Graduate students must complete the Intent to Graduate and Candidate for Degree forms. o 9/2/15, 5 PM: Last day to request No Credit or Pass/Fail grade for a class using a schedule adjustment form. o 9/2/15, 5 PM: Last day to petition for a reduction in Ph.D. dissertation hours. September 3-October 26, 2015, 5 PM: Students must obtain instructor permission to withdraw from a course using the Schedule Adjustment Form and must bring the signed form to the Office of the Registrar. To add a course, students must petition through undergraduate advising or the Graduate School as appropriate. September 7, 2015: Labor Day observed--no classes, campus closed. October 27, 2015: The Office of the Registrar now requires both the instructor s signature and a dean s signature on a Schedule Adjustment Form to withdraw from a class. Students should consult their home college advising office for details. November 9, 2015, 5 PM: Deadline for undergraduate CLAS students to withdraw from a course without filing a petition. Contact CLAS Advising. November 23-29, 2015: Fall Break no classes, campus open. November 26, 2015: Thanksgiving Holiday observed no classes, campus closed. December 12, 2015: End of semester. December 21, 2015: Final grades available on CU Denver PassportID portal and on transcripts (tentative)

Please contact an academic advisor if you have questions or concerns.