Teaching and Educational Materials

This page describes (and provides links for) teaching materials that might be helpful for students and instructors. Please feel free to use these notes as you like, and email me aboocher@sandiego.edu if you have any questions, comments or corrections. Many thanks to Project NExT ('19 cohort) and especially Annalisa Crannell, for sharing Calculus materials.

Notes, Interactive Worksheets, Homework and Quizzes:

For many years now, I have been teaching in a way that uses interactive classroom worksheets for each lesson. Sometimes these are outlines of lecture notes with examples, and they often also include problems for discussion.

• Calculus I - Worksheets / Quizzes / Exams
• Calculus III - Worksheets , Quizzes , Exams
• Discrete Math - Worksheets / Quizzes / Final / Projects
• Linear Algebra - Worksheets / Homework / Quizzes and Exams
• Real Analysis - Daily Activities , Quizzes and Review , Homeworks (27 of them!)
• Problem Solving Seminar - Problem List (Updated August 2023)
• Introduction to Number Theory - Lecture Notes for a course I taught at the University of Edinburgh in 2014. These were originally written by Chris Smyth and later updated by me and Andrew Ranicki. (Updated August 2023)
• Workshop for High School Teachers - In Summer 2017, with Troy Jones and Ray Barton, I organized a workshop for high school teachers in Sandy, Utah. The theme was symmetry, and here is a link to some of the math activities we did each morning.
• Commutative Algebra Writings
  • My Undergraduate Thesis The Module of Differentials, Evolutions, and the Eisenbud-Mazur Conjecture>
  • Homological algebra and the Hilbert Syzygy Theorem - Lecture notes and problems from the Undergraduate Program at Notre Dame in May 2019.
  • Degenerative Techniques in Commutative Algebra - Lecture notes and problems from a Graduate Workshop at the University of Utah in 2018.

Projects

Larger Scale (Calculus I) Projects

• Concerning our Hero Percy Precal: a 3-part project where all three parts are independent. In the three parts, "Math on the Beach", "The Locked Chest", and "Elvis?", you will help the whimisical hero find hidden treasure.
• The Mysterious Orb Incident in the Land of Calculia: a 3-part fairly non-linear project. There is a story about math, friendship, and treachery at the grand festival in a land far away, including over 100 potential suspects. Students will have to narrow down the list of suspects one step at a time by first figuring out when is the day of the festival, who dropped the orb, and then finally, who was running along the beach!
• Hallowe'en Party: a 3-part fairly non-linear project. Terrifying ghostly appearances have been plaguing the San Diego area and mathematics students are called in to help identify the ghoul. Students will narrow down the list of suspects by navigating a corn maze, unrvaeling the mystery of the tower, and optimizing a swim-run scenario.

Mini-Projects

• A collection of mini-projects for a Discrete Math Class - in the context of my course, students had to choose a total of 4 different projects to complete. Projects include questions about graph theory, quantifiers, 1-1 and onto functions, induction, proof by contradiction and number theory.
• A bare-bones introduction to least-squares and inner products for a linear algebra class. At the end there is a brief discussion about Fourier Series and how inner products can be defined between functions. It culminates with one of my favorite facts, namely that $$\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$$

Experimental

As a side project, I'm trying to learn some Javascript to create a place to practice your Real Analysis skills. This page is very much under construction.

Please contact me via email aboocher@sandiego.edu or visit my office in 161 Saints Hall.