Office: 310 Altgeld Hall
Phone: 333-2768 (office); 365-0024 (home)
Email: henson AT math DOT uiuc DOT edu  (Email gets checked frequently. Responses to queries of general interest will be sent to the entire class.)
WWW: http://www.math.uiuc.edu/~henson/Math424/Fall2009/ (Bookmark this address; further course information will be posted there.)

Office Hours: Mon. 4, Tues. 3, Fri. 3, and by appointment. In addition, Prof. Henson will be glad to meet with students at more or less any time he is in his office. Inquiries can also be made by email and will usually get a quick response. To be absolutely sure of meeting with him, it is advisable to make an appointment.

Required Text: M. Rosenlicht, Introduction to Analysis (Dover). Chapters 3--5 and 7, as well as an alternate treatment of Riemann integration, will be the main content of the course.   The treatment of integration will be similar to what is presented in Chapter 17 of the textbook for Math 347 (Mathematical Thinking by D'Angelo and West).

Math 424 provides a rigorous treatment of basic real analysis via metric spaces. Metric space topics include continuity, compactness, completeness, connectedness and uniform convergence. Analysis topics include the theory of differentiation, Riemann-Darboux integration, sequences and series of functions, interchange of limit operations.

Honors Sequence: Like all courses in the Mathematics Honors Sequence, Math 424 is a rigorous mathematics course which puts emphasis on proofs and on mathematical abstraction. There will be emphasis on harder problems and on a good understanding of the reasons why things work the way they do.

To be eligible for this course, a student must have been admitted to the Mathematics Honors Sequence by the Director of Undergraduate Programs in Mathematics. This requires doing well in an honors section of Math 347 (Fundamental Mathematics) or the equivalent. More information about the Honors Sequence is available online at http://www.math.uiuc.edu/UndergraduateProgram/curricula/honors_sequence.html

Homework: Daily homework will be assigned, discussed in class, and partially graded, to give feedback. Come to class prepared to discuss the homework problems assigned in the previous class. For certain homework problems (approximately one per class, clearly designated) a solution must be handed in and those points will be taken into account in the course grade (100 pts out of 700). These solutions will be handed in once per week, in the Monday classes.

Preparation for Each Class: Of course you should have done the homework that was assigned at the previous class. Also, it is expected that you will always have read each section of the text before the class in which it is to be discussed. At the end of each class, be sure you know what section is going to be discussed next. Effective participation in class will be impossible if you have not done the reading.

No Late Work: As a general rule, late work is not accepted and makeup exams are not possible. Excuses based on documented, solid reasons (illness, family difficulties, university trips, etc) will be honored; in such cases, grades will be based on the remaining work.

Exams: There will be five in-class exams during the semester and a three-hour final exam. The in-class exams will take place during the regular class periods on Sept 9 (50 pts), Sept. 25 (100 pts), Oct. 23 (100 pts), Nov. 13 (50 pts), and Dec 4 (100 pts); the final exam (200 pts) is scheduled at 7--10pm on December 15 and it covers the entire course. Exams take place in the regular classroom.

During the class immediately preceding each of the three 100-point exams there will be a practice exam (ungraded) on the same material.  The day before each exam (all five hour exams and the final exam) there will be a problem session in which students can ask any questions about the material to be covered on the exam.

Grading: In-class exams and the final exam are the most important factors in determining the grade for the course. The main function of the homework is to provide practice and feedback. The following weights will be used in determining the final average for Math 424: homework = 100 pts; hour exams = 400 pts total (see the list above for a breakdown); final exam = 200 pts. If scores are borderline or inconsistent, the course grade may take into account such factors as class participation and trends in scores.

Students should feel completely free to ask the instructor for information about their standing and performance at any time.