Fall 2007

110.415 - Honors Analysis I
MTW 1:00  // Hodson 301
Michael Goldberg

Section: Fri. 9:00am, also in Hodson 301.   The TA is Christine Breiner.

Office Hours:  Held in Krieger 313.
Fri. 10:00am - 12:00m, or by appointment.
Office Phone: (410) 516-7406
Email: mikeg@math.jhu.edu

Textbook: Real Analysis by Neal Carothers, Cambridge University.
ISBN 978-0521497565 (paperback);   ISBN 978-0521497497 (hardcover)

Our goal is to covere the first half of this book (Chapters 1-11), with some exceptions and amendments. Major topics to be addressed are likely to include:

  • Construction of real numbers. Countable vs. uncountable sets.
  • Topology of metric spaces, normed vector spaces. Open and closed sets, sequences and limits.
  • Bounded linear transformations. The derivative as a linear transformation.
  • Properties of compact metric spaces. The Heine-Borel Theorem. The Bolzano-Weierstrass Theorem.
  • Continuous functions, connectedness and completeness. Contraction Mapping Principle and applications. Inverse and Implicit function theorems.
  • Baire category theorem.
  • Sequences and series of functions. Uniform convergence. The Arzela-Ascoli theorem. The Weierstrass approximation theorem.

Homework: The course syllabus and a list of homework assignments will be posted here.

Homework assignments are due in lecture on Monday. Late homeworks will not be accepted without a valid explanation in advance.

You are permitted, perhaps encouraged, to discuss homework problems with other students. This collaboration should not extend to the process of writing up solutions. The work that you turn in should be written by you, in your own words, without supervision or other well-meaning influence from anyone else.

Grading:   30% Homework,   30% Midterm Exams,   40% Final Exam.

Exam Dates:   Midterms in class on Wednesday, Oct. 10 and Wednesday, Nov. 7.

Take-home Final:   Due in my office by 5:00pm on Monday, Dec. 17.

Please Note: The final exam will be given in a take-home format. Unlike the homework assignments, active collaboration (e.g. discussing problems, reviewing the textbook and/or class notes together) is not permitted. Further instructions will be given at the end of the course, and on the exam paper itself.

You are expected to attend class and take exams as they are scheduled. Unexcused absence from the midterm exam carries a penalty of one full letter grade reduction from your final course grade. Students who miss the final exam, without a valid and well-documented explanation will automatically fail the course.

Medical Contingencies: Missed midterm exams will not be made up; the remaining homework and final exam will be given correspondingly more weight to take up the slack. In order to do this, I must receive written confirmation of the severity of your illness, and preferably a letter from the Dean's office requesting special consideration.

The Student Health Center recently adopted new guidelines for the issuance of written Medical Excuses. Please read this memorandum for more information. A one-sentence summary is that the Health Center will now only document serious and/or prolonged illnesses for which they have actively provided treatment.

Students with disabilities requiring accommodation should notify me as soon as possible so that we can make the appropriate arrangements.

Ethics Statement: 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 you may collaborate with other students while attempting to solve homework problems, but only under the guidelines described above. Your work on any exam, whether in class or take-home, must be entirely your own. If you are having difficulty with a particular exam question, it is permissible to ask the instructor (but no-one else) for clarification.

For more information, see the guidebook "Academic Ethics for Undergraduates" and the Undergraduate Ethics Board web site.

Feedback: You may submit comments about the course at any time using this form which is provided by the Mathematics department. Your comments are then e-mailed to the undergraduate program coordinators and to the department chair (but not to me).