MATH/APPM 4650 Syllabus

• Goals of this course:
  • Learn how to analyze an algorithm to determine whether it converges and how fast, so you'll know how long your programs will take to run.
  • Understand the role of roundoff error, how it can accumulate, and how to compensate for it. Understand why sometimes decreasing step size or increasing the number of computations will actually make your errors worse because of roundoff error.
  • Learn algorithms for the most common numerical computations in mathematics: solving nonlinear equations, approximating functions, numerical integration, linear algebra, and basic ordinary differential equations. Understand when some algorithms are better than others and how to know which one to use in any particular application.
  • Develop an intuition for what makes an algorithm run well, and how to translate a mathematical formula or principle into a useable algorithm.
  • Learn good programming technique, such as: always know exactly what your program is doing, always avoid infinite loops, comment your programs thoroughly, test your programs with a hand computation or known result, use modular programming to reduce repetition, make your programs as efficient as possible, save multiple versions (always have one that works!), and save early, save often!
• The course textbook is Numerical Analysis, Eighth Edition, by Richard L. Burden and J. Douglas Faires.
• You will need to use mathematical software for programming in this class: the choices are Maple, Mathematica, and MATLAB. You must obtain access to one of these programs by Wednesday, January 23. If you would prefer to use some other software or programming language, you will need approval from me first.
  • Maple is used for examples in the textbook, and I will use it in class. It's the one I'm most familiar with, so it's easiest for me to help you with it. It is available in some computer labs on campus, and the student edition can be purchased for $125.
  • Mathematica is freely available to all students and has basically the same functionality as Maple. You can download it for free here.
  • MATLAB is more of a computational tool than the other two (which are good for symbolic computations). For Applied Mathematics students, this is the preferred software, and you probably have some experience with it already. It is available in computer labs on campus, and the student edition can be purchased for $100.
• Homework will be assigned weekly and due each Monday (except for the first homework, which will be due Wednesday because of Martin Luther King Day). Some problems will be on paper, analyzing an algorithm or writing pseudocode. Other problems will involve programming, and you will email me your program as an attachment. Programs will be graded both on how well they are written and commented, as well as on whether they produce the correct answer. You are strongly encouraged to work together on homework and programming.
• Exams will be a midterm and a final exam. The midterm will be in class on Friday, March 7. The final exam will be on Saturday, May 3, 1:30 p.m. - 4:00 p.m. The final will not be cumulative.
• Projects will be assigned midway through the semester.
• Grades will be computed based on the following scheme: homework 45%, projects 15%, midterm 20%, final exam 20%.
• Standard university policy statements follow.
• If you qualify for accommodations because of a disability, please submit to me a letter from Disability Services in a timely manner so that your needs may be addressed. Disability Services determines accommodations based on documented disabilities. Contact: 303-492-8671, Willard 322, and http://www.colorado.edu/disabilityservices.
• Campus policy regarding religious observances requires that faculty make every effort to reasonably and fairly deal with all students who, because of religious obligations, have conflicts with scheduled exams, assignments or required attendance. In this class, homework assignments will be due the next day of regular attendance, while missed quizzes and exams will be dropped without penalty. See full details at http://www.colorado.edu/policies/fac_relig.html.
• Students and faculty each have responsibility for maintaining an appropriate learning environment. Students who fail to adhere to such behavioral standards may be subject to discipline. Faculty have the professional responsibility to treat all students with understanding, dignity and respect, to guide classroom discussion and to set reasonable limits on the manner in which they and their students express opinions. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with differences of race, culture, religion, politics, sexual orientation, gender variance, and nationalities. Class rosters are provided to the instructor with the student's legal name. I will gladly honor your request to address you by an alternate name or gender pronoun. Please advise me of this preference early in the semester so that I may make appropriate changes to my records. See polices at http://www.colorado.edu/policies/classbehavior.html and at http://www.colorado.edu/studentaffairs/judicialaffairs/code.html#student_code.
• All students of the University of Colorado at Boulder are responsible for knowing and adhering to the academic integrity policy of this institution. Violations of this policy may include: cheating, plagiarism, aid of academic dishonesty, fabrication, lying, bribery, and threatening behavior. All incidents of academic misconduct shall be reported to the Honor Code Council (honor@colorado.edu; 303-725-2273). Students who are found to be in violation of the academic integrity policy will be subject to both academic sanctions from the faculty member and non-academic sanctions (including but not limited to university probation, suspension, or expulsion). Other information on the Honor Code can be found at http://www.colorado.edu/policies/honor.html and at http://www.colorado.edu/academics/honorcode/.
• The University of Colorado at Boulder policy on Discrimination and Harassment http://www.colorado.edu/policies/discrimination.html, the University of Colorado policy on Sexual Harassment and the University of Colorado policy on Amorous Relationships applies to all students, staff and faculty. Any student, staff or faculty member who believes s/he has been the subject of discrimination or harassment based upon race, color, national origin, sex, age, disability, religion, sexual orientation, or veteran status should contact the Office of Discrimination and Harassment (ODH) at 303-492-2127 or the Office of Judicial Affairs at 303-492-5550. Information about the ODH and the campus resources available to assist individuals regarding discrimination or harassment can be obtained at http://www.colorado.edu/odh.