MATH 5550 - INTRODUCTION TO TOPOLOGY

Purpose: to help other instructors teaching the same course

Common Course ID:  MATH 5550
CSU Instructor Open Textbook Adoption Portrait

Abstract: This open textbook is being utilized in a mathematics course for undergraduate or graduate students by Dr. Youngsu Kim at CSU San Bernardino. The main motivation to adopt an open textbook was to provide the most suitable level of materials at a reasonable cost. Most students access the open textbook in CSUSB online library.

Introduction to Topology  MATH 5550
Brief Description of course highlights:  An introduction to topological spaces, including metric spaces. Concepts will include continuous functions, homeomorphisms, homotopies between topological spaces, notions of connectedness and compactness, Hausdorff spaces, product spaces, the quotient topology, and the fundamental group. Formerly MATH 555. Students may not earn credit for both.
Include range of majors, typical incoming knowledge and/or skills (including not meeting prerequisites). Share demographics for students who take the class e.g. common majors, previous preparation, etc

Student population: Upper-level undergraduate and graduate students, mostly in mathematics.
Learning or student outcomes:  The CSUSB Mathematics Department is committed to developing and measuring the outcomes of our teaching efforts. Please see the following website for a list of these outcomes: https://www.csusb.edu/mathematics/undergraduate/advising (Links to an external site.).

• 1.1. Students will demonstrate an understanding and apply fundamental concepts, operations, and relations.
• 2.1. Students will correctly apply mathematical theorems, properties and definitions.
• 5.2. Students will produce valid mathematical proofs.

Key challenges faced and how resolved: Topology to first-time learners can be abstract though such abstractness provides great flexibility and applicability. The primary goal was to find a book that starts with metric spaces. Metric spaces include Euclidean spaces, e.g., the real line, plane, space. Furthermore, the book needed to be affordable. Dover publishing company provides books at affordable prices. Though the content was not tailored, the instructor could see potential and find an alternative path.

Youngsu Kim 
California State University, San Bernardino
Assistant Professor of Mathematics 

Please provide a link to your university page. 
https://www.csusb.edu/mathematics/faculty-staff
https://youngsukim-csusb.github.io/

Please describe the courses you teach.  Calculus, differential equations, algebra, topology, etc.  

OER/Low Cost Adoption Process

Provide an explanation or what motivated you to use this textbook or OER/Low Cost option. The textbook used for Math 5550 starts with metric spaces. This organization of contents provides concrete examples of topological space, making the topic more approachable and accessible to first-time learners. The main motivation to adopt the textbook was to provide the most suitable level of materials at a reasonable cost.

How did you find and select the open textbook for this course? Google Search, and MathSciNet (https://mathscinet.ams.org/mathscinet)

Sharing Best Practices: Not everything is going to be included in the book. Prepare to restructure the contents and provide supplemental materials.
 

Introduction to Topology
Brief Description:   Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. Include concepts, pedagogical approach, problem sets, and overall structure including publisher platform features.
Authors:  Bert Mendelson
Student access:  CSUSB Online Libarary; https://csu-sb.primo.exlibrisgroup.com/discovery/fulldisplay?vid=01CALS_USB:01CALS_USB&tab=books_local&docid=alma991011845719702901&searchScope=01CALS_USB&context=L&lang=en

Supplemental resources:
- Quiz (instructor-written)
- Lecture summary
- LaTeX HW template (OverLeaf, https://www.overleaf.com/)

Quiz and lecture summaries were provided on Canvas which is the CSUSB LMS system

Cost Savings:  From $59.95 to $11.99 or free ebook via the CSUSB library.