Lina Fajardo Gómez

When teaching precalculus in person for the first time since going online for COVID shutdown, students struggled a lot with the material. These boot camps were created as “exercise regimes” aimed to prepare for exams. The exercises are split into manageable workloads designed for a day each, and each day’s exercises graduallly build up in difficulty from warm up to challenge, separating out the components of competence assessed: memory recall, algorithmic computation, translation of real world scenarios into mathematical expressions, or critical thinking. The series cover sequences and various topics of trigonometry.
Boot camp on sequences
Boot camps on trigonometry: parts 1, 2, 3 and 4.

These worksheets were designed to support a flipped classroom version of the course. The plan to flip was scrapped before the semester started, but the worksheets weren’t. Also available in dark mode for students who use tablets and prefer lower contrast.

In the Engineering Calculus series, I prepared a series of projects students could opt to take to replace one test score. Every project gave a choice between writing (and solving) practice tests or diving into an application. The projects merge calculus concepts with applications, often with additional soft skills or learning objectives in mind.

• Coding with Python to understand limits
• Using technology to visualize and understand differentiation
• Algorithm complexity and optimization
• Science communication in a business application

Here projects combined more technical skills (like using Solidworks, or comparing the running time of algorithms) with calculus topics.

• Designing an object and checking its volume
• The calculus of rocket science and uses of approximations
• Introduction to Laplace transforms and cryptography
• Rate of convergence of series for faster accuracy

At a more advanced level, these projects probe students’ deeper understanding of how tools work and how to make sense of advanced mathematics.

• Education theory in ML and the limitations of AI
• Curves in games and design
• Gradient descent method in statistics and product development
• Visualizing math expressions and equations

When there is finally enough math background to fall down interesting rabbit holes, there aren’t enough hours on the schedule to teach them. The topics that were too interesting to completely leave out made it into director’s cut notes. Here are some on curves and on polar coordinates.

The projects for this course build on the idea developed for the calculus sequence and move from textbook applications to areas of active research.

• Modeling in pharmacokinetics
• The physics in differential equations
• Laplace transforms in signal processing
• The original neural networks

In addition to projects, there was also a typeset version of the lecture notes, to put all references to various textbooks as used in a convenient place.