Clicking on a course title will allow you to download a compressed course pack. After downloading, decompress the folder, open it and open the local .html file giving you easy access to instructional videos, their transcripts, problem sheets and class notes.
This material is to be used for pedagogical purposes only. If you make use of this material, I would appreciate you letting me know. You can leave a comment on my YouTube channel slcmath@pc or send me an email at pcamire@gmail.com. Thank you!
UPDATES
2024-08-26: An updated version of the course pack for Advanced Calculus (201-BNK-05) has just been uploaded; it now contains two new chapters on vector fields in which flux/divergence and flow/curl are covered intuitively and rigorously. We of course cover the Divergence Theorem, Green's Theorem and Stokes' Theorem and provide multiple practice problems that also include complete solutions. Anyone who seeks a deep and intuitively satisfying treatment of these topics should be excited! (There is one technical result about constructing the divergence of a three-dimensional vector field in full generality that is currently missing, but I plan to add it eventually. )
2023-07-16: An updated version of the course pack for Advanced Calculus (201-BNK-05) has just been uploaded; the section on Fourier series now contains a 12-page fourth part on convolution and Fourier series as the last part of the now 162-page complete document and it provides a visual comparison between the truncated Fourier series and the convolution of an explicit function, which is fun to see!
2023-07-16: An updated version of the course pack for Advanced Calculus (201-BNK-05) has just been uploaded; it now contains a fully rigorous proof of l'Hospital's rule for both the zero over zero case, which is the easier case to prove, and the infinity over infinity case, which is the fun one to prove! ;-)
2023-07-11: A MASSIVE update has just been posted for the course Probability and Statistics (201-BNM-05). I have added so much good stuff from detailed class notes to problem sheets that it would not be reasonable to list everything here, but let me just say that I am particularly happy about the chapter on Markov chains where I provide an elementary, but fully rigorous proof of the Fundamental Theorem of Markov Chains.
2023-07-11: An updated version of the course pack for Linear Algebra (201-105-RE) has just been posted and it now contains new documents about Markov chains and complete hand written solutions to some of the problems for certain chapters.
2023-06-27: An updated version of the course pack for Advanced Calculus (201-BNK-05) has just been uploaded and what follows are the details. First, the section on Taylor's theorem is now more extensive and interesting. Second, a completely rigorous and self-contained proof of Stirling's formula is now available, one that does not simply quote the dominated convergence theorem without proof, but instead goes through all of the gritty details! Third, and definitely best, is a 150-page document on Fourier series providing my own personal take on how to best understand the topic from both an intuitive and fully rigorous perspective! As a student, I was fairly dissatisfied about how this topic was presented, and this is me attempting to right that wrong for anyone interested who may have had a similar experience or if you are simply curious to perhaps see a different presentation. I do plan to add more to the current version of the document, but I have enough now that I wanted to share it. I hope you enjoy!
2023-06-01: An updated version of the course pack for Math NYB has just been uploaded and what follows are the details. Three minor typos/errors have been corrected from the answer keys. Two new documents under chapter 24 of the class notes have been added: the first is a beautiful example of solving a nasty definite integral using Maclaurin series, and the second is a proof of Euler's formula and identity using Maclaurin series as well. Two new documents under chapter 25 of the class notes have been added: the first is a beautiful application of integration by parts where we provide a rigorous proof of Taylor's theorem with integral remainder and then proceed to work out some related examples in full details, and the second is a document where we visualize the convergence of Taylor series to the original function in order to gain a deeper and more intuitive understanding of the subject. Finally, a section called "A Little Physics" contains three documents that will allow students to discover Einstein's famous equation E=mc^2 for themselves!
2022-03-26: The chapter on Leibniz rule from the Math BNK course pack has undergone a massive update; it is now a much more interesting document.
2022-01-19: The course packs for Math NYB and Math NYC have been updated; the problem sheets now contain complete solutions to certain problems.
2021-10-24: The course Advanced Calculus (201-BNK-05) now contains a nearly complete set of class notes and problem sheets; the only chapter missing is on differential equations. As you will see, the class notes are not your average class notes on the topic. They are a fusion of the foundational ideas in real analysis , topology and advanced calculus and should be of great interest to anyone looking for a rigorous treatment of the subject. Although the treatment of the subject is rigorous, I have tried my best to present the ideas in their cleanest and most intuitive form. I also make use of as much linear algebra as possible, which makes for the most elegant, modern and general presentation of the subject. This is the version of the course that I wish I had experienced as a student and I hope that others will appreciate it and benefit from it.