Spring 2016 110.421 Dynamical Systems Syllabus

Math 110.421, Dynamical Systems

Spring 2018 Course Syllabus

http://www.mathematics.jhu.edu/brown/courses/s18/421.htm

Prof. Richard Brown		TTh 3:00pm - 4:15pm
brown “at” math.jhu.edu		Room: Krieger 309
403 Krieger Hall
410-516-8179
Office Hours:	M	2:00-3:00 pm	by appt. other times
	Th	1:00-2:00 pm

Below is some basic information relevant to this course. A more detailed schedule of course material, homework assignments, and testing dates will follow shortly.

		The Text: R. Brown, A Modern Introduction to Dynamical Systems, 0^th edition, Oxford University Press (July 2018). PDF-version

	Course Material:	The material for this course is scattered throughout this text. We cannot possibly cover everything, but we will tour through most all of the topics.

	Grading Policy:	There will be homework sets, possibly a final exam, and maybe a project. The schedule of homework and the exams will be given below in time.

	Homework:	Homework based on the current week’s lectures will be posted here on the course web site sometime on Thursday after lecture. These assignments will be due the following Thursday in lecture. Mathematics is best learned in an environment where active discussion is a fundamental part of the learning process. You are strongly encouraged to work together in the understanding phase of the homework preparation process. You are required, however, to work alone when writing up homework solutions for submission. Homework is the essential educational part of this course. You will be graded not only on your ability to work through problems completely and concisely, but also on the presentation of your solutions and the arguments you make. It is the process with which you develop your argument that must be clearly and comprehensively represented in your proofs and calculations. If the audience (the reader of your submissions) must read between the lines to understand your arguments, then your work is not complete. This is a proof-based course. This means that many, if not most, of your homework problems will be to establish facts through argument rather than calculation. This means that you will be working with ideas more than numbers in many cases. I do understand that you may not be proficient at or have any experience in proof-writing. However, in time, you will adapt and learn.

	Course Policy:	You are responsible for lecture notes, any course material handed out, and attendance in class. There are no actual attendance requirements. However, I will easily get to know you and your rate of presence over time. And even though I will be using the book, the lectures will be serious embellishment of the material. *Good advice is the following: Treat the lectures as if you have already read the material and attempted some homework problems.* In this manner, you can focus mainly on parts of the lectures not found in the text or that covering areas of your reading you found difficult to understand. My teaching style is that of interactive discussion and I will rely on your input in developing the material. Active participation in the classroom is a great way to generate the discussion necessary to fully grasp the material.

	Help Room:	213 Kreiger Hall. The hours are 9am – 9pm on Monday through Thursday, and 9am – 5pm on Friday. This free service is a very valuable way to get one-on-one help on the current material of a class from other students outside the course. It is staffed by graduate students and advanced undergraduates. Outside of me and the Grader for the course, definitely take your questions to the Help Room. This course is simply an analysis course directed toward particular maps and differential equations. Most graduate students should be able to "see" through the many problems stated in this course. And your attempts to help guide them will be of huge benefit to you also.

	Ethics Statement:	The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Cheating is wrong. Cheating hurts our community by undermining academic integrity, creating mistrust, and fostering unfair competition. The university will punish cheaters with failure on an assignment, failure in a course, permanent transcript notation, suspension, and/or expulsion. Offenses may be reported to medical, law, or other professional or graduate schools when a cheater applies. Violations can include cheating on exams, plagiarism, reuse of assignments without permission, improper use of the Internet and electronic devices unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Ignorance of these rules is not an excuse. In this course, as in many math courses, working in groups to study particular problems and discuss theory is strongly encouraged. Your ability to talk mathematics is of particular importance to your general understanding of mathematics. You should collaborate with other students in this course on the general construction of homework assignment problems. However, you must write up the solutions to these homework problems individually and separately. If there is any question as to what this statement means, please see the professor or the grader. For more information, see the guide on "Academic Ethics for Undergraduates" and the Ethics Board web site (http://ethics.jhu.edu).

Math 110.421, Dynamical Systems

Spring 2018 Tentative Schedule

The details of this material may be updated and reformed as the semester progresses.

Week	Sections in H&K Text	Homework (in Notes)	Due	Selected Solutions
January 30 – February 1	Course Orientation Chapter 1; What is a Dynamical System		February 8
February 6 – 8	2.1 Preliminaries 2.2 The Contraction Principle		February 15
February 13 – 15	2.3 Interval Maps		February 22
February 20 – 22			March 1
February 27 – March 1
March 6 – 8
March 13 – 15
March 20 – 22	Spring Break
March 27 – 29
April 3 – 5
April 10 – 12
April 17 – 19
April 24 – 26
May 1 – 3

	Final Exam Slot	Thursday, May 17, 9am - noon.