About this Course

The goal of this class is to teach you about six principles:

Decomposition
Transformation
Rigidity
Symmetry
Finite Approximation
Local Linear Approximation

Think of principles as organizational tools that you can use to solve complicated problems.

Breakdown of the Course

This course is broken up into chapters which are broken up into sections.

Chapter 1 is all about the principle of Decomposition, which states that to understand something, determine the properties of its simpler separate components.

Chapter 2 is all about the principle of Transformation, which states to study concepts by studying how the simplest examples of the concepts transform into more complicated examples.

Chapter 3 is all about the principle of Rigidity, which states to study the objects in a collection by examining the properties that uniquely specify the objects.

Chapter 4 is all about the principle of Symmetry, which states to identify the transformations that do not change a thing in order to understand that thing.

Chapter 5 is all about the principle of Finite Approximation, which states to understand infinite things and things with infinitely many parts, study their approximation by things that are finite and have finitely many parts.

Chapter 6 is all about the principle of Local Linear Approximation, which states to study nonlinear functions by studying their local linear approximations.

Structure of Each Chapter and Section

Each chapter and section contains

notes,
linguistic mapping exercises,
knowledge checks,
practice

I am going to break down what each of these things means for you.

Notes

The notes are what you will use to initially learn the material. I recommend you try to be as active as possible when you are engaging with the material. Specifically, you should be ready to take notes as you are reading the material. To help you engage, you should have a notebook or tablet with you to write down notes, definitions, formulas, and so on. Anything you think is important, write it down. Any questions you have, write it down.

To be able to do all this effectively, you will likely have to stop reading the notes at various points. This is okay and natural.

Linguistic Mappings Exercises

In our in-class meetings, we will go over exercises to help with language acquisition and give guided instruction on use of the principles. These are avaliable for printing. I reccommend looking over these ahead of time and try them out on your own.

Knowledge Checks

You will check your understanding by engaging in some low-stakes practice, which are called knowledge checks.

In each chapter and section, you will see questions that are called knowledge checks. Some of these questions are very similar to the type of questions covered in the notes.

When you have finished doing the knowledge checks, you will go to the Canvas and complete the knowledge checks survey for each chapter and section. You will be asked some multiple choice questions about how well you did on the knowledge checks, how much time it took you, and so on. There will also be a place for you to upload your work that you did on the knowledge checks.

Don’t worry; you will receive full credit for attempting these as long as you submit the knowledge check survey.

Online Assignment

Once you have gone through the notes and knowledge checks, you will work on graded online assignments that are available on Canvas. This means that you will receive a grade on these assignments based on how many of the questions you answer correctly.

However, you get 100 attempts per problem. This means, you should aim for getting full credit on these assignments. If you get stuck, feel free to attend my office hours.

Course Schedule

If you want to learn more about the breakdown of each week, go to the course schedule.