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MATH418 - Topology

Course Details

Course Code: MATH418 Course ID: 4546 Credit Hours: 3 Level: Undergraduate

Topics include definition of a topology, closed sets, relativizations, base and sub-bases of a topology, compact topological spaces, separation axioms, normal spaces, regular spaces, metric spaces, continuous mappings, product spaces, and function spaces.





Course Schedule

Registration Dates Course Dates Session Weeks
06/24/19 - 11/29/19 12/02/19 - 01/26/20 Fall 2019 Session D 8 Week session
09/30/19 - 02/28/20 03/02/20 - 04/26/20 Winter 2020 Session D 8 Week session

Current Syllabi

After successfully completing this course, you will be able to

CO-1 Determine whether a collection of subsets of a set is a topology and determine a basis for a topology.
CO-2 Use homeomorphisms and show two spaces are topologically equivalent.
CO-3 Explain and proof the basic properties of compactness and of connectedness.
CO-4 Determine if a topological space is a metric space and generate a topology from a metric.
CO-5 Use the subspace topology, the product topology, and the quotient topology.
CO-6 Explain and proof basic separation axioms and properties of Hausdorff spaces.

Reading Assignments: 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. Optional homework problems are for your benefit and are not required for submission. Your conceptual understanding, ability to solve problems, and ability to synthesize material will be evaluated using quizzes, projects, and a final exam.

Forum 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 Forums are evaluated in three areas: quantity of posts, quality of posts, and value of interactions.

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

Scoring

Quantity

First post (>250 words)

Two interaction posts (>100 words each)

33%

Quality

Accuracy, logical presentation, organization,

clarity, completeness, proper terminology

34%

Value

Contributing to the conversation, useful to

your colleagues, valuable feedback

33%

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 and write it clearly. In addition to the Forums and homework, you are required to write two formal proofs as 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

Scoring

Validity

logical arguments, deductive reasoning,

proper conclusions, complete reasoning

43%

Readability

organization, presentation, format,

clarity, effectiveness

35%

Fluency

proper notation, proper terminology,

appropriate definitions, conciseness

22%

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

Multimedia Presentation: As with the writing assignments, the multimedia presentation provides you with an opportunity to improve your Mathematical communication. For the presentation you will need to effectively communicate your ideas in a slideshow presentation that includes an audio track. Using audio files you will explain your work with clarity and precision. This assignment will be evaluated in a manner similar to the writing assignments. However, an additional criteria will be evaluated.

Multimedia – A completely integrated presentation incorporating written work with emphases and accompanying audio. The total effect of the presentation is evaluated.

Evaluation

criteria

Descriptive adjectives

Scoring

Validity

logical arguments, deductive reasoning,

proper conclusions, complete reasoning

34%

Readability

organization, presentation, format,

clarity, effectiveness

27%

Multimedia

incorporated audio, highlights, emphases,

audience engagement, integration

22%

Fluency

proper notation, proper terminology,

appropriate definitions, conciseness

17%

Final Exam: As with the quizzes, the final exam is a core assessment tools for the assigned readings and homework. The final exam is comprehensive, and your work will be graded for correctness, completeness, and clarity.

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 & Homework 2.88 %
Week 2 Forum & Homework 2.88 %
Week 3 Forum & Homework 2.88 %
Week 4 Forum & Homework 2.88 %
Week 5 Forum & Homework 2.88 %
Week 6 Forum & Homework 2.88 %
Week 7 Forum & Homework 2.88 %
Week 8 Feedback 0.96 %
Writing 26.00 %
Writing 1 8.00 %
Writing 2 8.00 %
Presentation 10.00 %
Quizzes 30.00 %
Quiz 1 10.00 %
Quiz 2 10.00 %
Quiz 3 10.00 %
Final Exam 21.00 %
Final Exam 21.00 %

Additional Resource
Topology Without Tears by Sidney A. Morris
Version of 3 March 2013
Online textbook: http://www.topologywithouttears.net/topbook.pdf

Web Sites
In addition to the required course texts, many public domain web sites are useful. Here are a few sites to consider if you want to view topology and modern mathematics from a different perspective. Please abide by the university’s academic honesty policy when using Internet sources. Note web site addresses are subject to change.

Site Name … youtube.com Web Site URL/Address
Intro to Topology by Franzosa http://www.youtube.com/watch?v=zsN_guq Ac
Topology basics http://www.youtube.com/watch?v=tWIoUZNYj1g
Topology basics http://www.youtube.com/watch?v=cBMtwB8xoTE
Intro to Topology http://www.youtube.com/watch?v=Z-4Uo1pv0mU
Neighborhoods http://www.youtube.com/watch?v=6F3iJ1utuG0
Int, Cl, Bdry part 1 http://www.youtube.com/watch?v=4N-DS2xxZAY
Int, Cl, Bdry part 2 http://www.youtube.com/watch?v=7e4zC-PLZxI
Higher Math – Infinity http://www.youtube.com/watch?v=RZL5bKk9IHs
Higher Math – Real numbers http://www.youtube.com/watch?v=YW3EDsmj9bo
Higher Math – Topology http://www.youtube.com/watch?v=FHL4udeLf9Q
Higher Math – Sequences http://www.youtube.com/watch?v=rMe8YaoyDBA
Metrics http://www.youtube.com/watch?v=QDz_D2BPVG0

Book Title:Introduction to Topology: Pure and Applied - the VitalSource e-book is provided inside the classroom
ISBN:9780131848696
Publication Info:VS-Pearson
Author:Adams, Colin
Unit Cost:$181.57
Electronic ISBN:9781269653152
Electronic Unit Cost:$37.80

Previous Syllabi

Not current for future courses.