MATH418 - Topology

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.

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.

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.

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.

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.