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MATH305 - Real Analysis

Course Details

Course Code: MATH305 Course ID: 4543 Credit Hours: 3 Level: Undergraduate

This course provides a theoretical foundation for single-variable calculus concepts and introduces higher level abstraction of these concepts. Topics include the structure of the real numbers, sequences, continuity, and metric spaces. This course will be run as a seminar that emphasizes mathematical constructs of real analysis and proof writing. (Prerequisites: MATH227, MATH240, and MATH320)


Course Schedule

Registration Dates Course Dates Session Weeks
05/21/21 - 10/29/21 11/01/21 - 12/26/21 Fall 2021 Session I 8 Week session
06/28/21 - 12/03/21 12/06/21 - 01/30/22 Fall 2021 Session D 8 Week session
07/27/21 - 12/31/21 01/03/22 - 02/27/22 Winter 2022 Session B 8 Week session
09/28/21 - 03/04/22 03/07/22 - 05/01/22 Winter 2022 Session D 8 Week session

Current Syllabi

After successfully completing this course, you will be able to:

CO-1 Explain the axiomatic foundation of the real number system in particular the notion of completeness and some of its consequences;
CO-2 Explain principles of sequences and apply concepts of convergence and limits in the context of sequences;
CO-3 Explain the concepts of limits, continuity, and compactness;
CO-4 Apply the results and techniques involving the concepts of limits, continuity, and compactness, to solve a variety of problems;
CO-5 Explain how completeness and continuity are generalized from the real line to metric spaces;
CO-6 Develop mathematical arguments.

Reading Assignments and Homework:
Reading assignments are provided each week. These assignments flow into the Forum discussions and homework problems. Reading assignments are not graded directly; however, required homework problems must be submitted via the Messages by Sunday at midnight. Homework problems and Forum discussion are graded jointly. Your conceptual understanding, ability to solve problems, and ability to synthesize material will be evaluated using quizzes, writing assignments, and a final exam.

Forum and Homework Assignments:
Mathematics is not a spectator sport. In order to learn the language of Mathematics, you must be engaged with the material. It is critical that you spend time thinking, considering examples, working problems, and discussing ideas with others.
+ The Homework are graded for completeness, correctness, and clarity.
+ The Forums are evaluated in three areas: quantity of posts, quality of posts, and value.

Quantity – The initial post for each Forum includes at least 250 words, and a minimum of two interaction posts are required per Forum using at least 100 words each.

Quality – High quality posts are critical to the development of everyone in the course. The overall quality of your posts is evaluated.

Value – Banal posts such as “Good work” and “Nice conclusion” provide no value to the Forum conversations. The key to the Forums is quality interaction. Superior posts promote a valuable conversation and meaningful interaction.

Evaluation criteria

Descriptive adjectives



First post (>250 words)

Two interaction posts (>100 words each)



Accuracy, logical presentation, organization, clarity, completeness, proper terminology



Contributing to the conversation, useful to your colleagues, valuable feedback


Forum Note: you cannot score points for the quality and value of a post if you fail to meet the minimum quantity.

Writing Assignments:
Written communication is a key piece of modern mathematics. The Forums as well as many of the homework problems ask you to develop an argument or proof and write it clearly. In addition to the Forums and homework, you are required to several formal proofs via four writing assignments. These assignments are evaluated according to their validity, readability, and fluency. The definitions for those concepts are given here:

Validity – Validity corresponds to the validity of your arguments. It addresses the extent to which your method is appropriate, your calculations are correct, and your deductions follow the rules of logic.

Readability – If your written work is not readable it cannot be assessed. Since the ability to communicate Mathematics is a focal point for this class, special attention will be paid to the readability of your work.

Fluency – Mathematics is a concise and precise language, and I wish to enhance your fluency. Therefore, part of every assessment will focus on your ability to incorporate correct, established notation and terminology into your written work.

Evaluation criteria

Descriptive adjectives



logical arguments, deductive reasoning, proper conclusions, complete reasoning



organization, presentation, format, clarity, effectiveness



proper notation, proper terminology, appropriate definitions, conciseness


Quizzes are the core assessment tools for the assigned readings and homework. Your work will be graded for correctness, completeness, and clarity.

Final Exam:
The final exam will be completed during the last week of the term. It will be a three-hour online exam and may include written work as well. The final exam will be open-book and open-notes but you may not receive help from anyone. The final will consist of all material covered during the term. You will not need a proctor to take the final exam.

Grading Scale:
Please see the Student Handbook to reference the University’s grading scale.

NameGrade %
Forums 23.00 %
Honor Pledge 0.96 %
Introduction Forum 0.96 %
Week 1 Forum & HW 2.88 %
Week 2 Forum & HW 2.88 %
Week 3 Forum & HW 2.88 %
Week 4 Forum & HW 2.88 %
Week 5 Forum & HW 2.88 %
Week 6 Forum & HW 2.88 %
Week 7 Forum & HW 2.88 %
Week 8 Feedback 0.96 %
Quizzes 27.00 %
Quiz 1 3.00 %
Quiz 2 8.00 %
Quiz 3 8.00 %
Quiz 4 8.00 %
Writing Assignments 30.00 %
Writing Assignment 1 7.00 %
Writing Assignment 2 7.00 %
Writing Assignment 3 8.00 %
Writing Assignment 4 8.00 %
Final Exam 20.00 %
Final Exam 20.00 %

Student Study Material:
A link to online lectures and practice problems via PowerPoint slides are included in the Resources and also within the Lesson Units provided in the classroom. Plan to thoroughly review each week’s material, including new concepts and vocabulary, as well as all proofs. The textbook, PowerPoints, and forum interaction will all be crucial parts of your learning.

Web Sites:
In addition to the required course texts, the following public domain web sites are useful. Please abide by the university’s academic honesty policy when using Internet sources.

Book Title:Elementary Real Analysis - e-book available online, link provided inside the classroom
Publication Info:Bruckner & Thomson
Author:Bruckner & Thomson

Previous Syllabi

Not current for future courses.