Preface - Ready to Start?

Note

Song Accompanying This Section: Ready to Start - Arcade Fire

This book is a modified version of Eric Sullivan’s Numerical Methods and is also an Open Education Resource with the same license. Although the source material was not readily available, I will be modifying the original online book for the purposes of this course.

The prerequisites for this material include a firm understanding of single and multivariable variable calculus, a good understanding of the basics of linear algebra, a good understanding of the basics of differential equations.

To The Student

The Inquiry-Based Approach

The material in this book is meant to make you think, build, construct, fail, struggle, and ultimately succeed in learning numerical methods.

Setting The Stage

Let’s start the book off right away with a problem designed for groups, discussion, and critical thinking. This problem is inspired by Dana Ernst’s first day IBL activity titled: Setting the Stage.

  • Get in groups of size 3-4.
  • Group members should introduce themselves.
  • For each of the questions that follow I will ask you to:
    • Think about a possible answer on your own
    • Discuss your answers with the rest of the group
    • Share a summary of each group’s discussion

Questions:

  • What are the goals of a university education?
  • How does a person learn something new?
  • What do you reasonably expect to remember from your courses in 20 years?
  • What is the value of making mistakes in the learning process?
  • How do we create a safe environment where risk taking is encouraged and productive failure is valued?

This material is written with an Inquiry-Based Learning (IBL) flavor. In that sense, this document could be used as a stand-alone set of materials for the course but these notes are not a traditional textbook containing all of the expected theorems, proofs, code, examples, and exposition. You are encouraged to work through problems and homework, present your findings, and work together when appropriate. You will find that this document contains collections of problems with only minimal interweaving exposition.

It is expected that you do every one of the participation and homework problems and then only use other more traditional texts (or Google) as a backup when you are completely stuck. This is not the only set of material for the course. Your brain, your peers, and the books linked in the next section are your best resources when you are stuck.

You have the following jobs as a student in this class:

  • Make Mistakes! More accurately, don’t be afraid to make mistakes. You should write code, work problems, and prove theorems then be completely unafraid to scrap what you’ve done and redo it from scratch. Learning this material is most definitely a non-linear path.

  • Collaborate! You should collaborate with your peers, making sure you write your own solutions and noting who you collaborate with. The internet (or ChatGPT) is not a collaborator. Use of the internet to help solve these problems robs you of the most important part of this class; the chance for original thought.

  • Enjoy! Part of the fun of IBL is that you get to experience what it is like to think like a true mathematician / scientist. It takes hard work but ultimately this should be fun!

Online Texts and Other Resources

If you are looking for online textbooks for numerical methods or numerical analysis, I can point you to a few. Some of the following online resources may be a good place to help you when you’re stuck but they will definitely say things a bit differently. Use these resources wisely.