MATH 4300: Real Analysis

Purpose: to help other instructors teaching the same course

Common Course ID: MATH 4300
CSU Instructor Open Textbook Adoption Portrait

Abstract: A “Research Guide” that is created by the instructor and some open textbooks are being utilized in a math course for undergraduate students by Min-Lin Lo at CSU San Bernardino. The materials provide needed coverage and practice questions that are suitable for this course. The main motivation to adopt open textbooks was to save students money on textbook expenses. Most students access the “research guide” and open textbooks with links provided on Canvas course site.

Course Title and Number: MATH 4300: Real Analysis

Brief Description of course highlights:  In this course, we will DISCOVER: Properties of the set of real numbers and foundations of calculus: Equivalence relations, functions, cardinality, convergence of sequences and series of real numbers, topology of the real line, continuity, and differentiation. Emphasis on rigorous proof and mathematical communication. Professional mathematical typesetting and visualization technology. We might not be able to cover as many sections as in a regular lecture class do, but the important thing for me is to teach the students the ability to learn by themselves, not just rushing to cover lots of sections.

Student population: MATH 4300 Real Analysis is a required course for math majors with the prerequisite: MATH 2320 Multivariable Calculus and MATH 3100 Mathematical Thinking: Communication and Proof.

Learning or student outcomes:  This course is designed to support the Mathematics Department undergraduate program learning goals, namely, that by completing the program students will build the following proficiencies: (1) Demonstrate a conceptual understanding of mathematics; (2) Attain procedural fluency in mathematics; (3) Demonstrate adaptive reasoning and problem-solving skills in mathematics; (4) Demonstrate mathematical communication skills; and (5) Understand and produce correct mathematical proofs.  In particular, MATH 4300 will emphasize and assess the following learning outcomes:

1.1 – Demonstrate an understanding of fundamental concepts, algorithms, operations, and relations
2.1 – Correctly apply mathematical theorems, properties, and definitions
3.3 – Critique mathematical reasoning, both correct and flawed
4.1 – Demonstrate mathematical communication skills using appropriate mathematical vocabulary and references
5.1 – Understand valid mathematical proofs
5.2 – Produce valid mathematical proofs

Syllabus and/or Sample assignment from the course or the adoption: Syllabus will be provided. “Learning/Training Guide” posted on our Canvas course site is updated after each class, so students know what pages/questions and tasks they need to work on to be prepared for each coming class. They are encouraged to read the open textbooks for understanding and preparation.
4300-02 Syllabus F23.pdf4300 Sec3.1 Notes-IBL.pdf

Instructor Name:  Min-Lin Lo
Department of Mathematics, California State University, San Bernardino (CSUSB) 

Please provide a link to your university page.
https://sites.google.com/csusb.edu/mlo/home

Please describe the courses you teach.
I teach a wide range of courses such as: Mathematical Thinking: Communication and Proof, Applied Linear Algebra, Applied Statistics, Combinatorics, and Analysis.

Describe your teaching philosophy and any research interests related to your discipline or teaching.  

I believe students learn better when they "do" the math, not just listen and copy from professors, therefore most of my lecture time is spent guiding students by asking questions and give them time to do problems in class before we discuss the solutions.

OER/Low Cost Adoption Process

Provide an explanation or what motivated you to use this textbook or OER/Low Cost option. Save students money and customize materials for inquiry-based learning.

How did you find and select the open textbook for this course? Consulted other faculty and browsed OER sites.

Sharing Best Practices: Besides completely switching to a new OER textbook from a traditional textbook used before that already have prepared teaching materials, can also considering still using the same teaching materials, but find OER books that cover similar topics so instructor can assign homework from the OER and students can read detail explanation from the corresponding sections in the OER book

Describe any key challenges you experienced, how they were resolved  and lessons learned. Sometimes, I need to find multiple OER reference books to cover all topics I need to teach. Although time consuming, it also provides students with different perspectives on the same topic from multiple books.

OER/Low cost Material

Brief Description: No textbook is required. In this course, students will write most of the text. Classes are conducted from packets of course notes, aka “Research Guide”, I created (sample attached) that they can download from our Canvas course site containing problems to solve. The notes follow closely to the sections in the book: Introductory Real Analysis (ISBN: 0-395-95933-0), by Dangello and Seyfried. Students are not required to buy the book.

Reference Text:  The main purpose of the reference books is for students to understand definitions that are involved in a statement that they are trying to prove or a problem that they are trying to solve. However, students are not allowed to look into the proofs of theorems or solutions to problems in our research guide, and I encourage students to use paper to cover the proofs in the book to limit the temptation to “cheat”. Students are also encouraged to search online or other real analysis books for terms/definitions (only) they are confused on.

Online e-Books:

• How We Got from There to Here: A Story of Real Analysis by Eugene Boman and Robert Rogers.
  License: Attribution-NonCommercial-ShareAlike CC BY-NC-SA.
• Students can find several analysis e-books at this website.
   License: CC BY-NC 4.0 DEED.

Student access:  "Research Guide” file and reference e-textbook links are posted on our Canvas course site. 

Supplemental resources: Annotated “Research Guide” are posted on Canvas course site after each class so students can focus on thinking and asking questions in class instead of busy copying what I and their peers wrote on the board and on my iPad in class.

Provide the cost savings from that of a traditional textbook.  Introductory Real Analysis (ISBN: 0-395-95933-0), by Dangello and Seyfried costs $149.10 new.

License: openly licensed. See details above under each link