(Newton's method in the complex plane, computed by Michael Downs '15)
This new course fills a gap in our offerings in numerical computing, and will be useful to undergrads and grads in math and all the sciences. It is expressly designed to be full of powerful and accessible modern methods, yet to be almost orthogonal to existing courses (ENGS91 or COSC, etc). Learn how to develop good codes and libraries, spectral methods, high accuracy computing, the millionth digit of pi, a range of software tools... you pick up some diff eq and complex numbers along the way. It will also have a project rather than a final exam.
Throughout, as well as computing methods and modern software environments for solving numerical problems in math and applied sciences, we will enter the world of experimental mathematics: doing numerical experiments to learn and conjecture about mathematical objects. Despite its fancy name, this has been going on for millenia, including Gauss' conjectures on prime numbers. Computers make such exploration fun and rapid these days.
Also see last year's M56 website.
There is no single book, but I will draw from several books and articles, and give you links to these throughout the term. X-hour is Wed 3-3:50pm, and we will use mostly for coding and experimentation sessions run by our TA Dan Cianci. Do not schedule anything regular in this X-hr. Here are his materials. I encourage you to come to office hours: Mon 4pm, Tu 5pm, We 5pm.
Homework: about 7 weekly HWs due Thursdays at start of lecture. I strongly encourage you to collaborate, and to try at least some of the relevant homework problems before the next lecture (leaving it all for Wednesday night risks you getting left behind in this fast-paced course.) I encourage you to use LaTeX (see Resources); please make your working/reasoning as clear as you can. Late homework will not be accepted (unless by prior arrangement for a valid, and exceptional, reason). Your lowest HW score will be dropped.
Exams: I will try to give you ample time to complete exam questions. This course has no final exam so the 2 midterms are crucial. Practise is key (also read this).
Project: Mainly in the last 3 weeks you will work (possibly in pairs) to do numerical experiments on a topic of interest to science or mathematics. Here is a rough preliminary list of ideas; please come with ideas too. You will present it in class, along with a short (5-page) write-up. It is a sizeable fraction of your course grade. Project topics should be chosen by week 5, a 1-2 page description with references is due week 7, and in-class presentations last day of class, Tues May 27. Final write-up will be due later that week.
Honor principle. Exams: no help given or received. Homework: group discussion and collaboration on problem techniques is great and helpful. Write-ups must be done individually (ie no copying).
Grades: Will be based on HW 25%, Quizzes 5%, Midterms 2 × 20%, Project 30%. Note that HW is quite heavily weighted, and is the main chance you get to learn the concepts, practise and get feedback, so stay on top of it. Grades in Math 56 are not curved; other students' good performance will not hurt your grade. (So please work together and help each other out!)
Special needs: I encourage students with disabilities, including "invisible" disabilities like chronic diseases and learning disabilities, to discuss with us any appropriate accommodations that might be helpful. Let me know asap, certainly in first 2 weeks. Also stop by the Academic Skills Center in 301 Collis to register for support services.
Private tutoring: Tutor Clearinghouse may have private one-on-one tutors available for Math 56 - anyone with an advanced background in computing may be able to help. However, it's a new course, so, talking to me i the best way to get help. If a student receives financial aid, the College will pay for three hours of tutoring per week. If you would like to have a tutor, please go to 301 Collis and apply as early as possible.
Religious observance: Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with me before the end of the second week of the term to discuss appropriate accommodations.
Sexual assault and bias policy: Harrassment and assault whether physical, verbal, or in cyberspace, is unacceptable at Dartmouth. You can file complaints (named or anonymous) and get help from SAAP cordinators, S&S, or ugrad deans office. The same hold for racial bias incidents: report at here; also contact OPAL. Don't be silent; create the community you want to be part of.