Math 5201: Introduction to Real Analysis I
Autumn Semester, 2019
Instructor/Recitation Instructor: Professor Adrian Lam
Office: Math Tower 612
E-mail:lam.184@math.ohio-state.edu
Telephone: 614-688-3919
Instr. Office Hrs: MTWThF 9:15-10:15pm or by appointment
Lecture: MWF 10:20 - 11:15am Caldwell lab 220
Recitations: TR 10:20 - 11:15 Enarson Classroom Building 014
Set 1: (Rudin Ch. 1) #2, 4, 7. Due Aug 27, 2019. Suggested Solution
Set 2: (Rudin Ch. 2) #6, 7, 19; (Bergman) #2.2:6. Due Sep 6, 2019.
Set 3: (Rudin Ch. 2) #15, 16, 17. (Bergman) #2.3:1, 2.3:3. Due Sep 16, 2019. Suggested Solution
Aug 14, 2019: Example of a bounded above subset of Q that does not have the least upper bound property
Aug 14, 2019: Supplemental Exercises by G.M. Bergman
Aug 14, 2019: On Construction of R by Dedekind Cuts
Aug 14, 2019: Proof of Theorem 2.20 of Rudin.
Aug 14, 2019: Supplementary note: Construction of a transcendental number.
Aug 14, 2019: Proof of Theorem 2.27(a) in Rudin, with idea of proof.
Aug 14, 2019: Definition of connectedness.
Aug 14, 2019: Compactness is equivalent to sequential compactness. (Rudin Ch.2, #22-25, 26 plus the converse)
Aug 14, 2019: Solution to Rudin Ch.2 #6(ii). Feedback to HW 2.
Aug 14, 2019: A proof that "e" is transcendental.
Text: W. Rudin, Principles of Mathematical Analysis, 3rd Ed., McGraw-Hill
Reserve List: In SEL (list attached)
Prerequisite: Students should be familiar with the material of Math 4547-4548 (or Honors Calculus).?
Specifically, experience in constructing proofs and exposure to epsilon-delta arguments
for studying limits will be assumed.
Goal of Course: This is the first semester of a two-semester sequence intended to teach students the basics
of graduate-level analysis.? This semester will cover the real and complex number systems,
basic topology, sequences and series (of numbers and of functions), continuity, differentiation
and Riemann integration of functions of a single variable, the Riemann-Stieltjes integral, uniform
convergence, the Arzela-Ascoli Theorem and the Stone-Weierstrass Theorem.
Syllabus: The course will cover the first seven chapters of Rudin.
Homework: Homework will be assigned and graded weekly.
Midterm: There will be an in-class midterm. The date is set tentatively on Friday, October 18.
Final Exam: The final exam is Tuesday, Dec 10, 10:00 -11:45 am.
Grading: Homework (35%), midterm (30%) and final exam (35%).
DISABILITY STATEMENT: ?Students with disabilities that have been certified by the office for Disability Services will
be appropriately accommodated, and should inform the instructor as soon as possible of their needs. The Office for Disability
Services is located in 150 Pomerene Hall, 1760 Neil Avenue; telephone (614) 292-3307 and VRS (614) 429-1334;
webpage?http://www.ods.ohio-state.edu.
ACADEMIC MISCONDUCT STATEMENT: ?It is the responsibility of the Committee on Academic Misconduct to investigate
or establish procedures for the investigation of all reported cases of student academic misconduct. The term academic misconduct
includes all forms of student academic misconduct wherever committed; illustrated by, but not limited to, cases of plagiarism and
dishonest practices in connection with examinations. Instructors shall report all instances of alleged academic misconduct to the
committee. For additional information, see the Code of Student Conduct: http://studentaffairs.osu.edu/csc/ (15 pages)