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Topics in Math-Introduction to Graph Theory

Common Course ID: MATH 510-01

 CSU Instructor Open Textbook Adoption Portrait

Course ID: MATH 510-01, Introduction to Graph Theory

Abstract: This open textbook has been adopted in an Intro to Graph Theory course for Undergraduate Seniors and Graduate students by Min-Lin Lo at California State University, San Bernadino. No textbook is required. In this course, students will write most of the text. Classes are conducted from packets of course notes/research guide I created (sample attached) that they can download from our course web site containing problems to solve. The notes follow closely to the sections in the book: Chromatic Graph Theory, by Chartrand and Zhang, CRC Press. No textbook is required and students are encouraged to check out any introduction to Graph Theory books. By not requiring a textbook and providing students with “research guide/lecture notes” I designed, I intend to make this class an Inquiry-based Learning class so that the conduct of this course will be student-oriented. 


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About the Textbook

Textbook Title: No textbook required for course. Students use packets of course notes and a research guide I created that they can download from our course website containing problems to solve.

Authors: Min-Lin Lo, Professor, Department of Mathematics

Formats: Students download from Blackboard course in digital format.

Reference resources [not required]

  • Chromatic Graph Theory, by Chartrand and Zhang, CRC Press.
  • A First Course in Graph Theory by Chartrand and Zhang
  • Part II of Combinatorics: Enumeration, Graph Theory, and Design Theory [pdf]

Cost savings: Course notes and research guide are provided free of charge to students. This saves students $116.00 from previous hardback book in use or $37.67 for e-book version. 

About the Course

Course Number: MATH 510-01

Description:  

Major course

In this course, students will learn about: Ideas and techniques of proof with an emphasis on Graph Theory. Topics chosen from: properties of graphs, trees, directed graphs, graph isomorphisms, Eulerian and Hamiltonian graphs, planarity, and graph coloring problems.

Prerequisites: Prerequisite: MATH 345 Number Theory and Proof or MATH 355 Analysis and Proof.

Learning outcomes:  

Upon successful completion of the course the student will be able to: 

1.1 Students will demonstrate an understanding of and apply fundamental concepts, operations, and relations 

1.2 Students will make connections between mathematical ideas verbally, numerically, analytically, visually, and graphically 

2.1 Students will correctly apply mathematical theorems, properties and definitions 

3.1 Students will demonstrate adaptive reasoning and problem solving skills in mathematics 

3.2 Students will use and produce valid arguments 

3.3 Students will explain and justify solutions using a variety of representations 

3.4 Students will be able to reflect on and learn from previous problems 

3.5 Students will be able to evaluate reasonableness of proposed results using estimation and context 

3.6 Students will be able to critique mathematical reasoning, both correct and flawed 

4.1 Students will demonstrate mathematical communication skills using appropriate mathematical vocabulary and references 

5.1 Students will understand correct mathematical proofs 

5.2 Students will produce correct mathematical proofs

Curricular changes: Explain any curricular changes made to the course as a result of the open textbook adoption.


Teaching and learning impacts: 

I Collaborate more with other faculty No
I use a wider range of teaching materials: Yes
I believe my students' learning has improved Yes
I believe student retention has improved : Unsure
There have been unexpected results: Unsure

Share other lessons learned from using OER.

I have provided students for reference materials.

Based on students’ interaction during the in class Q&A sessions, I believe student learning has improved.

Sample syllabus 

Sample assignment:  Sample research guide/lecture notes

Textbook Adoption

OER Adoption Process

I adopted OER in this class to save students money and foster an inquiry-based learning environment that was more student-centered. 

Student access: Links to some reference sites, e-book, and the research guide/lecture notes PDF files are provided on our BlackBoard course site.

Student feedback about using OER:  No formal survey is conducted, but students appreciate that they do not need to spend money on a textbook.

Min-Lin Lo 

I am a mathematics professor at the California State University, San Bernardino. 

I teach a wide range of courses such as: discrete math, applied statistics, Calculus, and analysis.

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.

My research interested is in graph theory which is a subject that provide good problems that I can mentor undergraduate student to do research on.