Math 405: Introduction to Real Analysis
Fall 2018


Course Assistant:




We will basically cover the material detailed in the official 110.405 Analysis I Course Syllabus. I strongly recommend that you read the relevant sections of the textbook before each lecture and take notes in class.

Exams: There will be a midterm exam and a final exam:

Exams are closed book, closed notes. There will be no make-up exams. For excused absences, the grade for a missed exam will be calculated based on your performance on all remaining exams. If you miss an exam, you will have to provide documentation and a valid excuse. Unexcused absences count as 0.

Grade Policy:

The course grade will be determined as follows:


Weekly homework assignments will be posted to blackboard or here. Every Monday the homework sets are collected at the beginning of class and the graded homeworks will be returned in section on Friday the same week. No late homeworks will be accepted. The lowest homework score will be dropped from the final grade calculation.

You are encouraged to do your homework in groups. However, you must write up your solutions on your own. Copying is not acceptable.

Tentative Course Schedule

Here is a tentative schedule for the course. I strongly recommend to you to read the relevant sections of the textbook before each lecture.


Aug 30

Infinite Sets and the Rational Numbers

Read §1.1, 1.2, 1.3, 1.4

Sep 5

Construction of the Real Number System

Read §2.1

2,3 on pg. 13 and 4,5 on pg. 37

Sep 10, 12

Construction of the Real Number System

Read § 2.2, 2.3

4,5,11,12 on pg. 48 and 3,8 on pg 54

Sep 17, 19

Topology of the Real Line

Read §3.1, 3.2

1 on pg. 54 and 2, 3, 5, 7 on pg. 84

Sep 24, 26

Topology of the Real Line

Read §3.3

1, 4, 6, 8 on pg 98

Oct 1, 3

Continuous Functions

Read §4.1

1, 6, 8 on pg 106 and 4 on pg. 126

Oct 8, 10

Continuous Functions

Midterm exam on Wednesday in class

Read §4.2

1, 8 on pg. 125 and 3, 7 on pg. 138

Oct 15, 17

Differential Calculus

Read §5.1, 5.2

10 on pg. 126, 4,6 on pg 138 and 1,5,6 on pg. 152

Oct 22, 24

Differential Calculus

Read §5.3, 5.4

8, 11, 13 on pg 165 and 1,4 on pg 176

Oct 29, 31

Integral Calculus

Read §6.1

10, 13 on pg. 177 and 2,3, 14 on pg. 192

Nov 5, 7

Integral Calculus

Read §6.2

1, 4, 9, 13 on pg. 217

Nov 12, 14

Sequences and Series of Functions

Read §7.1, 7.2

3, 4, 5, 7, 8, 10 on pg. 262

Nov 19, 21


Nov 26, 28

Sequences and Series of Functions

Read §7.3, 7.4

2, 5, 12 on pg. 274

Dec 3, 5

Sequences and Series of Functions

Read §7.5, 7.6

December 13

Final exam

Special Aid:

Students with disabilities who may need special arrangements within this course must first register with the Office of Academic Advising. I will need to have received confirmation from the Office of Academic Advising. To arrange for testing accomodations please remind me at least 7 days before the midterm or final exam by email, during office hour or after class.

JHU Ethics Statement:

The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. 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, as in many math courses, working in groups to study particular problems and discuss theory is strongly encouraged. Your ability to talk mathematics is of particular importance to your general understanding of mathematics. You should collaborate with other students in this course on the general construction of homework assignment problems. However, you must write up the solutions to these homework problems individually and separately. If there is any question as to what this statement means, please ask the instructor.