Advanced Calculus 

Below you will find some of my projects I am working on as a result of my extensive time spent with the Advanced Calculus material while working on my PhD at Pitt. Every graduate student at Pitt has to pass the preliminary exam in advanced calculus, and as someone who has passed the test and has been a TA for the advanced calculus courses twice I have developed a sort of passion for the material. I am now sharing this with you!

Recitation Notes for Advanced Calculus Fall 2023 to Spring 2024  (Last Updated: 20 March 2024)

Recitation Notes for Advanced Calculus Fall 2022 to Spring 2023

Advanced Calculus Problem Book (Last Updated: 11 December 2023)

There is a useful book, called the Berkeley Problems in Mathematics, which is a collection of problems from the qualifying exams at University of California Berkeley, including problems and solutions to many areas of advanced calculus. These problems are a great resource for practicing the concepts learned in advanced calculus, as they vary in difficulty and are accompanied by solutions. My goal is to work on a similar resource for my students, but using the preliminary/qualifying exams of many schools, including Pitt. This will ensure there is a wide variety of problems, as each school seems to have a particular flavor of question they like to ask. Every test I use I reference and have freely accessed through the internet, and at this point none of the questions are my own. 

My Solutions to Pitt's Analysis Preliminary Exam (Last Updated: 18 October 2023)

As the TA for the advanced calculus class at Pitt, I thought it prudent to ensure my solutions to the preliminary exam were in a form that I could understand and easily explain to other students. Thus I took it upon myself to type the solutions I had written out and, through this process, verify they were correct (or at least mostly correct). Not all of the solutions are of my own making, as my preparation for the preliminary exam involved many sources, including friends, past Pitt graduate students, and MathStackExchange. It is also very probable that some solutions contain errors, or are incomplete in some way, but any errors should be easily remedied. If not, then....ummm....oh well?