Discrete Math 1/15

Preferred Method of Communication: Instructor prefers to discuss issues after class for easier understanding.
Encouragement to Engage: Strongly encourages students to approach for any issues or questions.
Sick Notifications: Emphasizes importance of notifying the instructor if unable to attend due to illness.

Instructor's Introduction: Introduced Chung Suling, who goes by Jay.
- Background: Jay is a junior majoring in service security.
- Availability: Encourages students to reach out via email for any questions.

Feedback from Students: Many students experiencing trouble accessing Canvas.
Support: Sun Wu, familiar to the instructor, will help on Monday and will introduce himself in class.

Current Assignments: Discussed the assignments available on Canvas and acknowledged potential mistakes made on the platform.
Acknowledgment of Issues: Instructor admits that Canvas can be unreliable at times, urging students to check assignments regularly.

Transition to New Topics: Moving from Topic 0 to Topic 1, which covers numbers and formal systems.
Student Relatability: Instructor relates to students, acknowledging that the concepts may initially seem confusing or "gobbledygook."

Purpose of Learning Formal Systems: Aim to explore the ridiculousness of what seems natural in mathematics and develop a deeper understanding.
Exploration Method: Instructor plans to show students how familiar concepts (e.g., distributivity, commutativity, associativity) can appear absurd when examined closely.
- Importance of Understanding: Highlighting that the seemingly ridiculous concepts are actually practical once comprehended.

Base 10 Discussion: Engage students in thinking why base 10 is the standard counting system.
- Reasoning Beyond Base 10: Prompting to consider other bases, such as base 60 (used by ancient cultures).
Calculating Time: Explains relation of base 60 in time measurement—60 minutes in an hour, 60 seconds in a minute—and its historical context linked to agriculture and celestial observations.

Base Comparison: Discussed advantages of other bases (e.g., base 60 and base 12) in terms of divisibility and usability.
Counting in Base 2: Instructor introduces binary counting:
- Explanation of Binary System: The concept where only 0 and 1 are used, demonstrating its relationship to base 10 and how higher numbers are constructed.
- Counting Practice in Base 2: Encourages familiarity with binary representation, showcasing how it operates compared to decimal.
- Limits of Digits: Discusses how many numbers can be represented with a limited number of binary digits (e.g., 5 binary digits can represent up to 31).

Closing Remarks: Students are encouraged to become comfortable with the material covered, as it will aid in their understanding of formal systems in mathematics.