Math 405: Introduction to Real Analysis
This is an introduction to real analysis. Topics covered in the course will include, The Logic of Mathematical Proofs, Construction and Topology of the Real Line, Continuous Functions, Differential Calculus, Integral Calculus, Sequences and Series of Functions. There will be 10 problem sets (20% of final grade), two in class midterm exams (20% each) and one final exam (40%).
Lectures are Monday and Wednesday 1:30-2:45 in Hodson 315. Section meets Friday 1:30-2:20 in Hodson 315.
Problem sets will be due in class on Wednesdays (see below for dates). No late homework will be accepted. The lowest grade will be dropped.
Lecturer: Jacob Bernstein. Lecturer Office hours: Monday, 3-4pm and Tuesday 10-11am or by appointment in Krieger 408.
TA: Letian Chen. TA Office hours: Tuesday, 3-5pm in Krieger 211.
ReferencesThe course text is
ExamsThere will be three exams. Two in class midterms and a final.
Week 0 and 1 (8/29 & 9/4) : Logic of Mathematical Proofs
Week 2 (9/9 & 9/11): Construction of the Real Numbers
Week 3 (9/16 & 9/18): Construction of the Real Numbers (cont.); Topology of the Real Number Line
Week 4 (9/23 & 9/25): Topology of the Real Number Line (cont.)
Week 5 (9/30 & 10/2): Topology of the Real Line (cont.)
Week 6 (10/7 & 10/9): First Midterm; Continuous Functions
Week 7 (10/14 & 10/16): Continuous Functions (cont.)
Week 8 (10/21 & 10/23): Differential Calculus
Week 9 (10/28 & 10/30): Integral Calculus
Week 10 (11/4 & 11/6): Integral Calculus (cont.)
Week 11 (11/11 & 11/13): Second Midterm; Sequences and Series of Functions
Week 12 (11/18 & 11/20): Sequences and Series of Functions (cont.)
Week 13: Thanksgiving Break
Week 14: (12/2 & 12/4): Picard iteration and the existence theory for ODEs.
Students with disabilities
Students with documented disabilities or other special needs who require accommodation must register with Student Disability Services. After that, remind the instructor of the specific needs at least two weeks prior to each exam; the instructor must be provided with the official letter stating all the needs from Student Disability Services.
JHU ethics statement
The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition.
Report any violations you witness to the instructor. You may consult the associate dean of students and/or the chairman of the Ethics Board beforehand. Read the "Statement on Ethics" at the Ethics Board website for more information.
If a student is found responsible through the Office of Student Conduct for academic dishonesty on a graded item in this course, the student will receive a score of zero for that assignment, and the final grade for the course will be further reduced by one letter grade.