Fall Semester 2019, Introduction to Analysis
(Math 3100/5100, Section 01)


Instructor: Dietmar Bisch
HW grader: Jason Mitrovich
Lecture: TuTh, 11:00am-12:15pm, SC 1320
First lecture: Thursday, August 22, 2019
Last lecture: Thursday, December 5, 2019
Office: SC 1405, (615) 322-1999
Office hours: TuTh 12:15pm-1:00pm, Fr 3:10pm-4:00pm
Mailbox: SC 1326

Prerequisites: MATH 2501 or both MATH 2300 (or MATH 2310) with either MATH 2410 or MATH 2600.

Textbook: Introduction to Analysis, Fifth Edition, by Edward D. Gaughan (ISBN-10: 0821847872).

Course description: Introduction to Analysis is designed to bridge the gap between the intuitive calculus usually offered at the undergraduate level and the sophisticated analysis courses the student encounters at the graduate level. In this class, you will learn to read and understand mathematical proofs, and write proofs on your own. See YES for a list of topics.

Exams: Three mid-term exams will be given in class during the semester, tentatively on the following dates:

  • Thursday, September 19
  • Thursday, October 17
  • Thursday, November 21

    • All tests are closed book/notes and no calculator is allowed. There will be no final exam.

    Midterm 1, Thursday, 9/19/19, in class
  • Book, Chapters 0.1, 0.2, 0.3, 0.4, parts of 0.5 (what we covered), 1.1, 1.2 up to (excluding) Bolzano-Weierstrass theorem, and 1.3.
  • equivalence relations
  • partial order, total order
  • Basic properties of rational and real numbers (see handouts, material up to and including 9/12/19 lecture).
  • HW1, HW2, HW3, HW4

    Midterm 2, Thursday, 10/17/19, in class
  • Book, Chapters 1.2, 1.3, 1.4.
  • Book, Chapters 2.1, 2.2, 2.3.
  • Book, Chapters 3.1, 3.2, 3.3, 3.4 (up to and including theorem 3.9).
  • Material covered in lectures in class from 9/17/19 to 10/10/19.
  • HW5, HW6, HW7, HW8

    Midterm 3, Thursday, 11/21/19, in class
  • Book, Chapters 3.4 (starting with theorem 3.9).
  • Book, Chapters 4.1, 4.2, 4.3, 4.4.
  • Book, Chapters 5.1, 5.2.
  • Material covered in lectures in class from 10/15/19 to 11/14/19.
  • HW9, HW10, HW11, HW12

    Homework: Homework is an important component of this course. Assignments will be collected and graded, usually on a weekly basis. Homework must be turned in at the beginning of class on the due date. I will not accept homework put in my mailbox or slid under my office door. You are allowed, and encouraged even, to work in groups on the homework. However, you must each turn in your own written solutions. The lowest homework score will be dropped. Homework assignments will be listed on this webpage.

    Homework assignments:
    HW1, due Thursday, August 29, 2019
    Solutions HW1

    HW2, due Thursday, September 5, 2019
    Solutions HW2

    HW3, due Thursday, September 12, 2019
    Solutions HW3

    HW4, due Tuesday, September 17, 2019
    Solutions HW4

    HW5, due Thursday, September 26, 2019
    Solutions HW5

    HW6, due Thursday, October 3, 2019
    Solutions HW6

    HW7, due Thursday, October 10, 2019
    Solutions HW7

    HW8, due Tuesday, October 15, 2019
    Solutions HW8

    HW9, due Thursday, October 31, 2019
    Solutions HW9

    HW10, due Thursday, November 7, 2019
    Solutions HW10

    HW11, due Thursday, November 14, 2019
    Solutions HW11

    HW12, due Tuesday, November 19, 2019
    Solutions HW12

    HW13 (optional, for extra credit), due Thursday, December 5, 2019

    Handouts:
  • Notes on equivalence relations and (partial) order
  • Construction of the rational numbers from the integers, and construction of the integers from the natural numbers. Archimedian property of the natural numbers and the rational numbers.
  • Construction of the real numbers. Properties of the real numbers.

    Additional Reading (optional):
  • Todd Kemp's notes on the construction of the real numbers using Cauchy sequences of rational numbers

    Grades: The usual grading scale used will be: A:93-100, A-:90-92, B+:87-89, B:83-86, B- :80-82, C+:77-79, C:73-76,C-:70-72, D+:67-69, D:63-66, D-:60-62, F:0-59. The final grade will be based on the homework (34%), and the three tests (22% each). Individual exams may be curved as needed, however the final grade will not be curved.

    Grading of Math 5100 students: You will be required to hand in additional problems with each homework assignment. These will be graded and go into your course grade according to the above formula.

    Syllabus: A more detailed syllabus can be found here: Syllabus Math 3100/5100, Fall 2019