Weekly Concepts:
· Vector Fields
o Basic idea:
o How it became a part of mathematics:
o Broader applicability:
o Connection to our course:
· Functions*
o Basic idea:
o How it became a part of mathematics:
o Broader applicability:
o Connection to our course: Contents of Chapter 5, basic object of study in nearly all future math-related courses due to representation of cause-effect relationship.
· Topology*
o Basic idea:
o How it became a part of mathematics:
o Broader applicability:
o Connection to our course: Study of properties of sets – graphs we draw are a basic example of the types of sets under consideration. Big part of optimization.
· Linear Algebra*
o Basic idea:
o How it became a part of mathematics:
o Broader applicability:
o Connection to our course: Systems of linear equations have geometric interpretations related to the structure of a space. Linear algebra provides the tools and theories for analyzing such systems and spaces.
· Probability
o Basic idea:
o How it became a part of mathematics:
o Broader applicability:
o Connection to our course:
· Exponential Growth*
o Basic idea:
o How it became a part of mathematics:
o Broader applicability:
o Connection to our course: Content of Chapter 6 provides the basis for studying the rapid type of growth known as exponential. See Chapter 7 for more.