Joseph Breen
About
Welcome! I just finished my fifth year as a Ph.D. student in the department of mathematics at UCLA working under the advisement of Ko Honda. I graduated with a B.A. in mathematics from Northwestern University in 2016. My research interests are in contact and symplectic geometry.
Here is a copy of my CV: (pdf)
You can find and contact me at:
- Office: previously MS 3915C, currently my bedroom
- E-mail: josephbreen@ucla.edu
Preprints and Publications
- Morse-Smale Characteristic Foliations and Convexity in Contact Manifolds. Preprint, 2019. (arXiv link)
- On the sign characteristic of Hermitian linearizations in DL(P). Joint work with M. Bueno, S. Ford, and S. Furtado. Linear Algebra and its Applications, 519 (2017), 73-101. (link)
Teaching
I am currently not teaching anything in Summer 2021.Helpful links for courses I am not teaching right now:
- In Spring 2021, I was an instructor for Math 115A. I wrote a set of notes on what we covered in the course, linked here: (pdf).
- All of my lectures were recorded, and they are available in a private playlist. If you want access to the recordings, just let me know.
- In Fall 2020, I was the instructor for Math 32AH. I wrote a fairly extensive set of notes on what we covered in the course, linked here: Advanced Differential Multivariable Calculus. Currently a work in progress, but it does contain everything we covered in the course.
- All of my lectures were recorded, and they are available in a private playlist. If you want access to the recordings, just let me know.
- Extra practice problems:
- Infinite series practice problems.
- Extra challenging integral problems.
- Extra challenging sequence and series problems.
- Extra challenging power series and Taylor series problems.
- Additional practice problems in solving differential equations with power series.
- Miscellaneous links and notes:
- Topics in Integration and Infinite Series (work in progress) This is manuscript detailing a number of supplemental topics and techniques in the world of integrals and infinite series. There is (or will eventually be) a lot of fun and fascinating stuff in here, if you're curious.
- My version of an infinite series convergence flowchart.
- A collection of well-written "model" solutions for most types of 31B problems.
- Casual notes on computing Taylor polynomials and series with some standard examples worked out.
- Casual notes on the intuition behind whether a series converges or diverges.
- A guide to the limit comparison test. This discusses just about anything you could want to know about when and how to use limit comparison. This includes a number of solved examples that you can treat as extra practice problems.
- Unhelpful but interesting links:
- Here is a link to a lecture I gave in the UCLA Math graduate student seminar where I did a really insane integral.
- Two very challenging calculus problems. One of them is the integral from the above lecture, and the other is a really hard infinite series.
- Extra practice problems:
- A practice midterm for midterm 2. This is just an example of an exam that I would write and may or may not be indicative of the actual exam! Here is a link to solutions.
- Conceptual true/false questions. Some true/false statements to test how well you know the intricacies of the course topics. Will be updated throughout the quarter.
- A practice midterm for midterm 1. This is just an example of an exam that I would write and may or may not be indicative of the actual exam! Here is a link to solutions.
- Plane practice problems. Practice problems for finding equations of planes, solutions included. This collection includes just about every standard type of question, as well as some fun and challenging extra problems.
- A large collection of practice problems corresponding to different categories in 32A. This set of problems is most relevant for the second midterm. Here is a link to extensive solutions to all problems.
- Practice problems for minimization, maximazation, and Lagrange multipliers.
- Miscellaneous notes:
- In Fall 2020 I was an instructor for 32AH, an honors version of 32A. I wrote a comprehensive set of notes: Advanced Differential Multivariable Calculus. The material in here is typically at a much higher level than that of 32A, but if you're interested in seeing the material in a more sophisticated setting, or if you want more insight on some of the topics, you can check it out.
- A short note on the gradient vector. In particular, this describes how you can use the gradient vector to find tangent planes and tangent lines and makes explicit the notion of using different perspectives to tackle the same kind of problem.
- A review study guide for most of the main topics in class. These notes are very brief and should not be a replacement for reading the textbook, attending lectures, etc. Also, I wrote this study guide a long time ago for a comparable class at a different institution. The exact material covered may be slightly different!
- Some casual notes explaining the dot product and cross product. Again, these notes were written a long time ago --- sorry if the quality is subpar!
- Four different ways to find the distance from a point to a plane.
- Recent links:
- How to succeed in calculus. The advice that I usually give to students who want to get better at math.
- Old links: (these are notes and problems I wrote a long, long time ago, but could be relevant)
- Casual notes explaining the meaning of line and surface integrals.
- A brief summary of how to directly evaluate a surface integral.
- Casual notes explaining Green's Theorem.
- Casual notes explaining all of the major fundamental theorems in multivariable calculus.
- A fun graphic which summarizes all of the integrals and fundamental theorems in multivariable calculus.
- A collection of extra practice problems for 32B. The document says "Math 234" because that is the 32B equivalent course at a different institution. Extensive solutions can be found here.
Music
Perhaps my main contribution to the world of math is mathematical music. Here is a link to a YouTube playlist of all of the songs I've made so far, which includes songs about LaTeX, mathematical love, the Fourier transfom, TQFTs, knot theory, contact geometry, calculus, and more.Writing
- Liouville and Weinstein Domains (pdf)
- A set of notes based on a lecture I gave in Math 234: Contact Geometry.
- Lectures in Harmonic Analysis (pdf)
- An incomplete work on harmonic analysis, adapted from my own lectures notes taken during Monica Visan's Winter 2017 247A and Spring 2017 247B courses.
- Fredholm Operators and the Family Index (pdf)
- My undergraduate senior thesis, written under the advisement of Ezra Getzler.
- An Introduction to Index Theory (pdf)
- An expository version of some of the above senior thesis.
- Path Connectedness and Invertible Matrices (pdf)
- Notes prepared for a lecture I gave for the Northwestern Undergraduate Math Society in the spring of 2016.