Math 7827 – Problem Solving in Mathematical Analysis, Spring 2009

Jan Mandel

Department of Mathematical and Statistical Sciences
University of Colorado Denver

This web page http://math.ucdenver.edu/~jmandel/classes/7827s09 serves as the class syllabus and source of further information. Homeworks, material covered, and handouts are in the homework file. Board photographs and scans, if any, will be in the photos directory.

Midterm is on March 31. Problems to prepare: from the prelim syllabus chapter 1,2,9 except 20,30,31  

Prerequisites: MATH 4310, MATH 4320. MATH 4310 covers: “Calculus of one variable, the real number system, continuity, differentiation, integration theory, sequence and series”. MATH 4320 covers: “Convergence, uniform convergence; Taylor’s theorem; calculus of several variables including continuity, differentiation and integration; Picard’s theorem in ordinary differential equations and Fourier series.”

Textbook: Walter Rudin, Principles of Mathematical Analysis, 3rd ed. A cheaper international edition is available and OK to use in the class.  Handouts and online material.
Time and location:  Tuesday and Thursday 4-5:15
Office hours: UCD building Tuesday and Thursday 3-4 room 656 or 640, Thursday 12-1 room 640.
Contact: Phone 303-556-4475; email jan.mandel@ucdenver.edu. I am usually pretty good at answering email even at late hours.

Objective: Build problem solving and mathematical writing skills. Emphasis will be on blending creative problem solving with rigorous verification and proper communication of the result. 

 

Problem solving is an essential skill in mathematics often neglected in a traditional lecture setting. Students will be expected to present solutions at the board (including simpler proofs of the theorems) and work interactively in the class. The class level and coverage will change in response to the needs of the students. Proper mathematical writing (textbook/journal article style) is an important skill for writing theses and papers. All written work by the students will be expected to be live up to the professional standard.

 

Grading: 25% each midterm, final, homework, participation. All work will be graded on the scale 0-4: 0=nothing relevant, 1=understands definitions and the problem, or a correct formal solution 2=good progress or a correct partial solution, 3=some minor glitch, 4=OK. The final score will consist of  25% each participation, written homework, midterm, and final. Letter grades are A >= 90,  A- >= 85, B+ >= 80, B >= 75, B- >=70,  C+ >= 65, C >= 60, C- >= 55, D+ >= 50, D >= 45, D- >= 40.

 

Topics covered: The class will revisit introductory analysis topics (real numbers, limits, series, metric spaces, sequences and series of functions, Riemann integral, functions of several variables) through recalling the definitions and theorems and solving problems. Recommended problems from Rudin according to the prelim syllabus, additional problems from problem collection books.

 

Assignments and tests: There will be problems due every class period and several students will be selected randomly to present the solutions. This will be the participation part of the grade.  Separate written homework assignments will be given every week or two and always due in a week. Late written homework will not be accepted except when arranged in advance, and then at 50% if the rest of the homework was already graded.  Please do not send homework by email. There will be a midterm and final exams in class, no books, computers, or notes. The midterm will be on March 31. The final will be during the finals week as determined by the Auraria finals schedule.

 

Office hours: I enjoy discussing technical topics related to the class with my students during my office hours or any other time you walk in. Please do your homeworks ahead of time, and do not come to my office on the day the homework is due and expect me to do it for you.   Please do not try to negotiate grades (except in the case of clear error on my part), and especially not partial credit.  I usually need few minutes before the class to get organized, so please respect that and do not show up right before the class.

 

Other: In all homeworks and exams, please show clearly all your work, but do not write irrelevant things just to fill more paper - this will not help, just the opposite, because more writing means more opportunity for errors. Always copy the problem statement. The most common error in mathematics is solving the wrong problem. Do not write incorrect statements – I will not fish for ideas or correct statements in what you write. The whole solution must make sense. Points will be taken off for incorrect statements even if they are not relevant to the problem being solved. Good writing is important. It is not enough that you understand the mathematics correctly – you also need to write it so that it can be verified and understood easily. The point of most problems in analysis is the justification rather than a formal solution, so formal solutions count for little even if correct. Do not trust anything until you have verified it - this includes what I say and what is in the books.

 

Students are encouraged to study in groups, so certain similarity in the solutions (and errors) in homeworks is OK. Identical solutions, solutions clearly taken as a whole from other sources, such as another book or internet, in an obviously different setting than as done in the course, with mature elegant formulation, etc., will receive zero credit unless student can explain the solution well at the board in class when called upon. Students found plagiarizing solution during in-class exams will receive zero credit for the exam and will be reported to the department and the college for disciplinary action. Please do not eat during the class. Drinks are OK. All cell phones must be turned off before the class. Cell phone calls are very disruptive. If your cell phone rings, you will be asked to take the call outside and you cannot return to the class. If you need any accommodation because of religion or disability, please let me know; these will be handled according to University policies.

 

 

 

Spring 2009 CLAS Academic Policies

 

The following policies pertain to all students and are strictly adhered to by the College of Liberal Arts and Sciences (CLAS).

  • Every student MUST check and verify their schedule prior to the published drop/add deadlines.  Failure to verify a schedule is not sufficient reason to justify a late add or drop later in the semester.  It is the student’s responsibility to make sure that their schedule is correct prior to the appropriate deadlines.
  • CLAS students must use their email.cudenver.edu email address.  Email is the official method of communication for all University of Colorado Denver business.  All email correspondence will take place using your UCDHSC email address.  Go to http://www.cudenver.edu/registrar to update and/or change your email address.
  • Students are NOT automatically added to a course off a wait list after wait lists are dropped.  If a student is told by a faculty member that they will be added off the wait list, it is the responsibility of the student to complete the proper paperwork to add a course.
  • Students are not automatically notified if they are added to a class from a wait-list.  Again, it is the responsibility of the student to verify their schedule prior to any official dates to drop or add courses.
  • Students must complete and submit a drop/add form to make any schedule changes.  Students are not automatically dropped from a class if they never attended, stopped attending or do not make tuition payments.  
  • Late adds will be approved only when circumstances surrounding the late add are beyond the student’s control and can be documented independently.  This will require a petition and documentation from the student.  Late adds will only be approved if the student has not taken any exams, quizzes, or has not completed any other graded assignments.  Independent verification of this from the professor of record will be required.  Please note that the signature of a faculty member on an add form does not guarantee that a late add petition will be approved.  Petitions are available in NC 4011.
  • Late drops will be approved only when circumstances surrounding the late drop have arisen after the published drop deadlines, are beyond the student’s control, and can be documented independently.  This will require a petition and documentation from the student.  Pre-existing circumstances (circumstances that existed prior to the published drop deadlines) regarding illness, work, family, or other confounding issues will not be considered adequate reason to drop or withdraw from courses after the published University and/or College drop deadlines.  Please note that the signature of a faculty member does not guarantee that a late drop petition will be approved.  Petitions are available in NC 4011.
  • Undergraduate students wishing to graduate in spring of 2009 must meet with their academic advisor by the end of the drop/add period to obtain a graduation application.  This application must be completed and submitted by 5 PM on February 4, 2009.  You can obtain an application ONLY after meeting with your academic advisor. There are no exceptions to this policy or date.
  • Graduate students wishing to graduate in spring semester 2009 must complete their Intent to Graduate form and have a Request for Admissions to Candidacy on file with the CLAS Dean’s office no later than 5 PM, February 4, 2009.
  • Students are responsible for completing financial arrangements with financial aid, family, scholarships, etc. to pay their tuition.  Students will be responsible for all tuition and fees for courses they do not officially drop using proper drop/add procedures and forms. 

Students who drop after the published drop/add period will not be eligible for a refund of the COF hours or tuition.

Important Dates

 

  • January 20, 2009: First day of Class
  • January 25, 2009: Last day to be added to a wait list using the SMART system.
  • January 25, 2009: Last day to add a course using the SMART system.
  • January 27-February 4, 2009: Students are responsible for verifying an accurate spring 2009 course schedule via the SMART registration system.  Students are NOT notified of their wait-list status by the university.  All students must check their scheduled prior to February 4, 2009 for accuracy.
  • January 26, 2009: LAST DAY TO DROP WITHOUT DROP CHARGE – THIS INCLUDES SECTION CHANGES.
  • January 26, 2009: Wait Lists are dropped.  Any student who was not added to a course automatically from the wait list by this date and time MUST complete a drop/add form to be added to the class.  Students are NOT automatically added to the class from the wait list after this date and time.  If your name is not on the official student roster, you are not registered for the course.
  • January 27, 2009: First day instructor may approve request to add a student to a full course with a Schedule Adjustment Form.
  • February 4, 2009 at 5 PM: Last day to add structured courses without a written petition for a late add.  This is an absolute deadline and is treated as such. This deadline does not apply to independent study, internships, project hours, thesis hours, dissertation hours, and late-starting modular courses.
  • February 4, 2009 at 5 PM: Last day to drop a spring 2009 course with a tuition adjustment minus the drop charge and no transcript notation – this includes section changes.  Drops after this date will appear on your transcript.  This is an absolute deadline and is treated as such.
  • February 4, 2009 at 5 PM: Last day to completely withdraw from all spring 2009 courses with a tuition adjustment and no transcript notation. Drop charge applies. Drops after this date will appear on your transcript.  This is an absolute deadline and is treated as such.
  • February 4, 2009 at 5 PM: Last day to request pass/fail option for a course.
  • February 4, 2009 at 5 PM: Last day to request a no credit option for a course.
  • February 4, 2009 at 5 PM: Last day to register for a Candidate for Degree.
  • February 4, 2009 at 5 PM: Last day to petition for a reduction in thesis or dissertation hours.
  • February 4, 2009 at 5 PM: Last day to apply for spring 2009 graduation.  You must make an appointment and see your academic advisor before this date to apply for graduation.
  • February 16-25: Faculty can use the early alert system.
  • April 6, 2009 at 5 PM: Last day for non CLAS students to drop or withdraw from all classes without a petition and special approval from the student’s academic Dean.  This is treated as an absolute deadline.
  • March 23-29, 2009: Spring Break.
  • April 20, 2009 at 5 PM: Last day for CLAS students to drop or withdraw from all classes without a petition and special approval from the student’s academic Dean. Students still need signatures from the faculty and Dean.  This is treated as an absolute deadline.
  • After April 20, 2009 all schedule changes require a petition.  Petitions are available in NC 4011.
  • No schedule changes will be granted once finals week has started.  There are NO exceptions to this policy.