Discrete Mathematics
MATH 22.01W/03W
Foothill College, Fall 2023

How and when to attend our first week together

Class opens online on Monday, September 25, and both the Canvas portal and the WebAssign homework system will be available. Orient yourself to the course by visiting the Canvas, Day 1 Orientation page, and completing a brief orientation quiz. The module for Week 1 assignments will be opened after you successfully complete the orientation quiz. Week 1 will end with a quiz of material discussed in the assignments. There is a Zoom office hour on Tuesday if you want to meet me live, online.

How this course works

This course is open for 11 teaching weeks and one week for final exams. You will engage with the course by logging into the Foothill College Canvas portal and selecting Discrete Mathematics, Math 022.03W. Every week a module will open with new topics. Walk through the list of actions and lectures and participate as directed. Each week sections from one chapter of the course textbook are featured. Homework for the weekly sections is preassigned in the Cengage WebAssign online homework system, where you can see the homework due dates and follow your completion progress. A  quiz is opened in Canvas at the end of the week to reinforce your understanding of the week's material. The weekly quizzes have due dates and duration times, and rules for engagement with academic integrity, and they are not proctored. 

In the twelfth week of the quarter you will register for a one-hour, proctored, cumulative final exam that must be taken on-camera. Further details of course operation are presented on the Canvas orientation page.

My advice for success in this class

• At the beginning of every course week, scan the activities in the weekly module and create a personal schedule for reading the textbook, viewing lectures, completing homework, and taking the weekly quiz.

• Plan to take the weekly quiz as soon as possible after it opens. Quizzes open at the end of a week, but close in the middle of the next week. This flexibility in the time you take the quiz is meant to give you the room needed to deal with life circumstances. It is not a good idea to default schedule the taking of the weekly quiz to the last possible moment. Every Monday a new weekly module opens with new requirements on your time and concentration. Plan to complete your chapter studies, including the quiz, in the week allotted to the chapter.

• Communicate with fellow students via Friday Open Mic throughout the quarter (see below).

What you can expect of me

• Prompt response to your questions.

• High expectations for the quality of your work.

• Open and honest comments on the quality of your work and your engagement in the course.

• Acknowledgement and correction of mistakes that I make or misunderstandings that I foster during the course.

• Respect for and engagement with the diversity of background and knowledge that you bring to the course community.

What I expect of you

• Active, respectful participation in building the course community by interacting with me via email, and office hours, and with classmates in weekly discussions.

• Belief in your right to be in this course and your ability to succeed in this course.

• Commitment to the time, effort, and academic integrity required to succeed in this course.

• Timely pursuit of course assignments.

• Open communication with me when life intrudes in your studies

I am teaching if, and only if, I am helping you learn. I believe that students learn best by repeated activity in a community of curious others; by reading, listening, questioning, sharing, trying, testing, and repeating. And of all the steps, interacting with your classmates may be the most important. Mathematicians have always advanced knowledge by sharing their work and benefiting from its critique by other mathematicians with widely diverse backgrounds and viewpoints.

Classically, quizzes and tests are summative, are returned with brief comments on errors, and many students never deeply understand the questions they missed. My assessments are formative, and students are able to review a detailed analysis of an assessment after the fact, before they are given an opportunity to retake the assessment to correct misunderstandings. 

In an asynchronous course, interacting together to create a community needs even more attention than in an in-person course. I rely on end-of-week dialogues, called Friday Open Mic, to stimulate conversation on both the topics of the week and the human emotions of frustration, elation, boredom, and fascination, that often accompany the learning of mathematics.

I learn more every quarter about mathematics from the questions of my students. I try to share that growth in my understanding by recording micro-lectures that explain challenging homework exercises in great detail, including meta-comments on the purpose of an exercises in the course structure. The number of micro-lectures grows with every class I teach, extending the value of student questions across time.

To help to create a virtual community of all students who have ever taken my classes, all students can enter notes and videos into a Course Attic, a repository of messages from current students to future students in discrete mathematics.

Monitor yourself. Are you following your plan for reading chapter sections, viewing lectures, completing homework? If not, adjust your plan and recommit to it. Share your experience with your classmates in Friday Open Mic.

Ask questions of yourself, others, and me. If something still doesn't make sense after reading, viewing lectures, talking with tutors and other students, send me an email and point me to the problem--in the textbook, in the lecture, in the homework--and I will respond.

Be kind to yourself. New vocabulary and methods take time, and repetition, to durably understand. Make sure to rest, relax, and return, when the details are not sticking with you.

Mistakes are just measures of what still needs more attention. Use mistakes to help you adjust your study habits, and try again.

Sometimes you need to push on. New concepts, or embellishments of old concepts that reappear in new material, are sometimes just what is needed to break through a mental road block.

Remind yourself that you are not alone. Many students, just like you, have had to struggle with the pace and content of discrete mathematics, and by persistence, and with help from each other, have succeeded.

Student Learning Outcomes

 With a good-faith effort, growth mindset, and successful completion of the activities in this course, you will reach the following goals: 

1. Use formal logic in constructing valid arguments.

2. Write proofs formally, including writing proofs using symbolic logic and Boolean algebra.

3. Use number theory to solve problems.

4. Understand the basics of set theory, including solving problems in combinatorics and probability theory.

5. Prove combination and permutation principles and use them to solve problems.

6. Understand the definition of functions.

7. Use recursive thinking and method to solve recurrence relations, including using recursion to analyze algorithms and programs.

8. Analyze and write algorithms.

9. Identify relations and their properties.

10. Draw and analyze graphs and trees, including applying matrices to analyze graphs and trees.

11. Solve application problems from computer science.

12. Discuss mathematical problems and write solutions in accurate mathematical language and notation.

13. Interpret mathematical solutions.

Student Support Services

• Student Support Portal: The first place to look for student services.

• Canvas Help: When having problems with the course management system.

• Counseling: Whether you are looking for academic, career, or personal counseling, we can support you!

• Tutoring: If you need help in a class, you are not alone! We offer tutoring programs to help you succeed with your academic goals.

• Financial Aid: If you need help paying for your college education or vocational training, we can help you.

• Disability Resource Center (DRC): If your learning is being impacted by cognitive or physical differences, mental or physical health, or if you require an accommodation, please contact the DRC to arrange a confidential discussion regarding equitable access and reasonable accommodations. Call the DRC at 650.949.7017.

• EOPS: We have support services and programs for financially and educationally disadvantaged students.

• DREAMERS: We are committed to supporting and empowering all students. We stand fiercely in support of our undocumented community and care proud to offer resources and services for all.

• Veteran's Services: We have dedicated counselors and staff who understand your needs and will help you. 

Health & Wellness

• Health Services provides free or low-cost confidential health services.

• Psychological Services helps students cope with difficult emotions and life stressors. Psychological Service is staffed by experienced, professional psychologists and counselors, who are attuned to the needs of college students. The services are free and completely confidential. Sessions can be provided for problems big or small.

• Food Pantry offers access to a selection of nutritional groceries at no charge. 

• Housing Insecurity and Homeless Students Program will help if you are in need of housing.

Communities & Activities

• Umoja Community: Umoja, a Kiswahili word meaning unity, is a year-long learning community and critical resource at Foothill College dedicated to enhancing the cultural and educational experiences of African American and other students.

• Puente Project: Puente, the Spanish word for Bridge, is a national award-winning student leadership program that provides a structured pathway for transfer to the UCs and CSUs while engaging participants in community service.

• Student Affairs & Activities: We provide a caring, inclusive environment for students to get involved and get assistance and support in understanding your student rights.

Some important syllabus information for this course can be found only in the Foothill College, Canvas course portal. The information is available only to students officially registered for Math 22.01W/03W at Foothill College. For example, invitations to online office hours, the course key for WebAssign, and details of grading and assessment.