William Meyerson's Teaching Assistant FELLOW Webpage

If you want to see my LaTeX files, you can see my raw tex file at this location and my pdf file here.

Further, if you are planning on taking the Analysis Qual, you should find this guide helpful (the current version, 2.1, incorporates all the suggestions made by Anush Tserunyan, AND IS UPDATED FOR THE RECENT S09 QUAL.)

If all you want to is to see how hard Analysis Qual problems can get, this is the solution to the hardest real analysis problem asked on a qual here and this is the solution to the hardest complex analysis problem asked on a qual here.

My name is William Meyerson and I am in the summer between my fourth and fifth years of graduate school at UCLA; in particular, I am a member of the math department (and one of many students in the Analysis Group).  'Summer' begins a week and a half earlier for me than for everyone else because I am going to Italy for a summer school during finals week.  Currently, I am working with the professor John Garnett; if all goes according to plan I could be his last PhD student ever!  (It should be noted that Garnett's own definition of 'his last PhD student' is different from my own; under his definition, I am merely his antepenultimate student.)  Last year (August 6, 2008), I took my oral exam to advance to candidacy, passed, and have received the exalted status of "GD2" as a result.

I am not TAing for the rest of 2009; in fact, I don't even expect to be in the country for the fall quarter.

This quarter, I am not TAing (Professor Garnett bought me out so that I could go to  Italy for a conference during finals week).

Last quarter, I was the TA for Section 1a of Math 120A, which was taught by professor Gang Liu.  Homework solutions can be found at the following links:  HW1 HW2 HW3 HW4 HW5 HW6 HW7 HW8 HW9

In the fall, I was the TA for Section 1a of Math 131A, which was taught by professor John Garnett.  Homework solutions can be found at the following links:  HW1 HW2 (just in time for the midterm!) HW3 HW4 HW5 HW 6 HW7 (in time for the second midterm) HW8 HW9

As for my office:  I have been relegated even deeper into the dungeons, into MS 2961 (in the second floor of the mathematical sciences building, three floors below ground level).  As I am not TAing this quarter, I do not have official office hours (but if you insist on meeting me, email me and something can be arranged...)

For those of you who are considering having me as a TA in the near future, the Field Guide to Your TA should be helpful (though it may be slightly less applicable for graduate courses, where the emphasis may be a little more on qual questions than homework questions...)

My previous TA assignments were as follows:

Year 4 (08-09)

In the Fall of 2008, I TAed Section 1a of Math 131A, which was taught by professor John Garnett.  Homework solutions can still be found at the following links:  HW1 HW2 HW3 HW4 HW5 HW 6 HW7 HW8 HW9

In the Winter of 2009, I TAed Section 1a of Math 120A, which was taught by professor Gang Liu.  Homework solutions can still be found at the following links:  HW1 HW2 HW3 HW4 HW5 HW6 HW7 HW8 HW9

In the Spring of 2009, I did not TA because Professor Garnett was nice enough to buy me out so that I could go to Italy for a summer school during finals week.

Year 3 (07-08)

In the Fall of 2007, I TAed Sections 1c and 1d of Math 32B, which was taught by professor Bailin Song.
In the Winter of 2008, I TAed Section 1a of Math 135, which was taught by professor Arthur Szlam.

The first homework assignment's solutions can be found here.  Homework 2 solutions are now here.  Homework 3, the last assignment before the midterm, has its solutions here.
Homework 4's solutions are here.  Homework 5 solutions are now here.  Homework 6 solutions are now here.  Homework 7 solutions are now here.  Finally, Homework 8 solutions are here.

In the Spring of 2008, I TAed Section 1a of the graduate complex analysis course Math 246A, which was taught by professor John Garnett.  The first homework solutions are here.  The second homework solutions are here.   The third homework solutions are here.  Finally, homework four has its solutions here; these solutions are not nearly as pretty as Garnett's, though they do go into a bit more detail.
Also, my notes for Week 7 are here.  Notes pertaining to qual problems for Week 8 and 9 are here.

Finally, in Summer Session A of 2008 I was the TA for Sections 1a and 1b of the Summer Sessions course Math 2, which was taught by professor Cathy Lee. 

Year 2 (06-07)
In the Fall of 2006, I was a TA for Section 1a of the algebra course Math 110A, which was taught by professor Veeravalli Varadarajan.

In the Winter of 2007, I TA'd Section 1a of the graduate analysis course Math 245B,  which was taught by professor John Garnett.

Homework 1 solutions can be found at this link; Homework 2 solutions can be found at this link.  Further, Homework 3 solutions are here.  Also, homework 4 solutions are here. Finally, homework 5 solutions are here.

Further, my primer on L^p spaces is over here; the list of all L^p problems (with one-line hints) which have appeared on quals since F01 are here.

In the Spring of 2007, I had a fellowship and did not TA.

Year 1 (05-06)
I ran Sections 1a and 1b of Math 32A (Fall 05), which was taught by Professor Rodolfo De Sapio and Section 2a of the complex analysis course Math 132, (Winter 06) which was taught by Professor Meera Thillainatesan.  Then, in Spring 2006, I was a Teaching Assistant for
Section 1a (the only section) of the differential equations course Math 135, which was taught by professor Paul Roberts.
If you want to see my solutions for the homework assignments for that class (to check out my TAing style, for example), you can check here for Homework 1, here for Homework 2, here for Homework 3, and here for Homework 4.
Homework 5 and Homework 6, which are significantly longer, are here and here, respectively.
Homework 7, which isn't quite as long, is here.
Finally, homework 8 has made its way here.

If you want, you also email me at meyerson@math.ucla.edu.

Courses I am taking this quarter (Summer 2009, Session A):  I am not taking any courses this session; in fact, I will only be in LA for the last week or two of this session.

Courses I have taken here in previous quarters (UPDATED 6/3/09):

Fall 05 - I was taking:  Math 220a, which was a logic course focusing on basic set theory and model theory, Math 245a, which was an analysis course focusing on measure theory, Math 210a, which was an algebra course focusing on group theory and basic ring theory, and Math 495, which taught me how to make webpages such as this one (but was officially focused on teaching me how to become a teaching assistant).

Winter 06 - I continued with my work from the fall quarter with Math 220b, which was a logic course focusing on advanced model theory and incompleteness, Math 245b, which was an analysis course focusing on topology and basic functional analysis, and Math 210b, which was an algebra course focusing on module, field, and Galois theory. 

Spring 06 - I finished the real analysis sequence by taking Math 245c, which was an analysis class focused on the Fourier transform.  I also took  Math 246a, the first course in the complex analysis sequence, and Math 205a, the first course in the number theory sequence.  Further, although it (like the analysis sequence) was much harder this quarter, I also finished the algebra sequence by taking Math 210c, which dealt with commutative and noncommutative algebra along with representation theory.  To bring my total up to five (and my total for the year to eleven) I also took the topology course Math 225c, which was supposed to be some type of topics course in topology. 

After taking these courses, the UCLA Department of Mathematics decided to award me an MA degree... just another step along the way to the elusive Ph.D.!

Fall 06 - I continued along with the complex analysis sequence by taking Math 246b and started the functional analysis sequence with Math 255a.  I also started the Fourier analysis sequence with the notorious Math 247a (taught by Terry Tao) and because it was time for me to start looking at seminars, I signed up for the analysis seminar Math 290g (the section run by Professors Garnett, Tao, and Thiele) where I gave presentations on Koebe's one-quarter theorem concerning univalent functions.

Also during this quarter, I managed to pass my German language exam (aber ich habe fast alles meines Deutsches vergessen) and begin working with Professor John Garnett; it appears that I'm now within a year of being able to do actual research!

Winter 07 - This quarter, I finished up the complex analysis sequence by taking Math 246c and the functional analysis sequence with Math 255b (even though this meant waking up three hours early!)  I am also did a reading course (listed as Math 596g) with Professor Garnett this quarter; further, I presented again at the analysis seminar Math 290g (the section run by Professors Garnett, Tao, and Thiele).

Spring 07 - This quarter, pretty much all the advanced analysis sequences have finished.  Consequently, I jumped into the PDEs sequence with Math 251C (if all goes well, I'll run through the entire sequence backwards).   Further, I enrolled for another quarter of Math 596g with Professor Garnett (finishing my Heinonen book and moving to trying to solve a problem involving the first Heisenberg group) and continued to attend Math 290g (though I didn't give a presentation this quarter).  Finally, to diversify my portfolio of skills I tried and aced Econ 1, which is an introductory course in economics.  Unfortunately, this still left me one course shy of the PhD coursework requirements; well... there's always F07 for that!

Fall 07 - This quarter, I easily completed the PhD coursework requirements with the following three courses:  Math 254a, which is an advanced analysis course focusing on geometric measure theory (from Mattila's perspective), Math 229a, which is an introductory course on the theory of Lie groups (to help me understand the Heisenberg group), and Math 251a, which is an introductory PDE course which appears to focus on distribution theory.  I also continued economics with Econ 2, which focuses on introductory macroeconomics.

Winter 08 - This quarter, I just finished Math 229b, which appears to be a course on Lie algebras to go with the Lie groups, and another course called Math 254a, which is actually a course in ergodic theory.  I presented at 290g for the first time in about a year (though I had been continuously attending since Fall 2006); this time the topic was quasiconformal maps of the plane.

Spring 08 - I completed Econ 11, a theoretical (though still elementary) course introducing microeconomic theory.  (I also wanted to take Math 238a, a course in dynamical systems, but it was cancelecd before the second day of classes).  I also presented at 290g about my recent generalization of a theorem of Peter Jones to Carnot groups.

Summer 08 - I completed Econ 101,  a theoretical course on microeconomic theory which is the natural continuation of Econ 11.

I also presented at the summer version of 290g; the topics were extensions of quasiconformal maps on Euclidean spaces and biLipschitz maps on the Heisenberg group.

Fall 08 - I completed Math 275A, which is an introductory graduate level course on probability theory and Math 226A, which is a graduate level differential geometry course (the focus seems to be on Riemannian manifolds).

Winter 09 - I completed Math 275B, which is a graduate level course on probability theory (focusing on random walks, martingales, and ergodic theory) and Math 226B, which is an advanced graduate level differential geometry course (dealing with the Bochner technique, Ricci curvature, and notions of convergence for Riemannian manifolds); these are continuations of courses I took last quarter.  I also took the econometrics course Econ 103.

Spring 09 - I completed the introductory graduate sequence on probability theory with Math 275C (this course focused on Brownian motion from a rigorous perspective) and learned some advanced complex analysis with Math 285G, which served as a FOURTH course in complex analysis (a capstone to Garnett's 246ABC sequence, which I actually had served as the TA for) focusing on harmonic measure.

The Past

For most of my childhood, I lived in the great state of Maryland, which, contrary to popular belief, is actually SOUTH of the Mason-Dixon Line.  This state is known for being next to our nation's capital, its unusual shape, and sumptuous blue crabs.  While in Maryland, I was a student at Wilde Lake High School, where I was the first runner-up for Homecoming Court two years in a row, won the Howard County Math League three years in a row, and ultimately graduated in 2001.

After Wilde Lake, I studied at Harvard University, where I concentrated (DO NOT call it "majoring"!) in mathematics and lived in Pforzheimer House.  Life was made slightly more difficult by the fact that my primary interest in mathematics, real analysis, is not well-represented in Harvard's math department; nevertheless, I was able to graduate cum laude in the year 2004 and had fun times there as well.

In the next year, I studied mathematics at the University of Cambridge where I was a member of the MCR (Middle Combination Room) of Churchill College.  In particular, I was a student in Part III of the Mathematical Tripos where I took various courses in functional analysis, Banach algebras, Noetherian algebras, group theory, Lie algebras, and groups of Lie type.  Somehow, I wound up with a Distinction and ended up losing 40 pounds that year (weight, not money; I spent A LOT more than 40 pounds) in addition to doing other fun things such as learning how to ski.

In the summer of 2003 I was a student in the Trinity REU, where I specialized in the field of monoid theory.  In order to produce research in monoid theory, we went to the Karl-Franzens-Universitat Graz (KFU Graz; this does not stand for the "Kentucky Fried University"!) for ten days to be lectured in monoid theory by the great Austrian mathematics professors Franz Halter-Koch and Alfred Geroldinger.  Back in Texas, my advisor was Scott T. Chapman; I discovered a general formula for the elasticity of arithmetic congruence monoids, which is (n + k - 1)/k.

Over the next three summers (2004 - 2006), I was also a counselor at MathPath which is an elite summer camp for the nation's top 12-to-14-year-olds in mathematics (and a few from other countries as well, such as Canada, England, Romania, Australia, and the People's Republic of China!).

The following summer (2007), I spent eight weeks working for Los Alamos.  After that, I went to an amazing conference in Helsinki followed by the annual analysis summer school, where I presented counterexamples concerning weights on the plane.

The past summer (2008) was far less exciting for me as I spent most of it here, doing exactly what I would do if it were the regular school year (plus earning a little extra money by serving as an expert in probability and statistics for my dad)!  Of course, I made up for it by traveling to Argentina during my last week of vacation; the delicious food, favorable exchange rate, and amazing relatives made it all worth it!

The current summer (2009) begins with two mathematical conferences in my area of specialization:  one in Italy and one in Barcelona.  After that, I plan on returning to UCLA to work on research, preparing for what I expect to be a fall term abroad in Switzerland where I learn more about Carnot groups from experts in the field such as Jeremy Tyson and Zoltán Balogh.

Although my mathematical interests have always leaned towards real analysis (or "the theory of ordered fields with the least upper bound property" if you're an algebraist), the Trinity REU had been pushing me in the direction of algebra; in fact, I officially specialized in algebra at the University of Cambridge with the group theorist Jan Saxl as my advisor.  During my first year in UCLA, although my (first-year) advisor was the analyst Christoph Thiele, I spent a few weeks thinking that I might want to specialize in logic, algebra, or even number theory.  However, as my logic class became more and more abstruse and convoluted, and I realized that the emphasis of the algebra group here is more on categorical and homological matters and less on the aspects of algebra I had been interested in (groups and rings, with emphasis more on elements than on maps), I have come to realize that if I'm going to study here, it would have to be in analysis.

I also spent a while wondering whether I wanted to join the Analysis Group or the functional analysis group (where my Cambridge training seemed to guide me); however, as my first year courses pushed me towards more classical analysis, I decided that this was the direction in which I wanted to head.  My choice was confirmed in Fall 2006 when I took my first functional analysis course here and realized that UCLA's take on the material was far from that which interested me... which is why on December 1, 2006 I started working with the professor John Garnett.  My specific interests in analysis focus on 'analysis on metric spaces' (named after the book of the same title by the late Juha Heinonen), which asks whether you can use the tools of calculus and analysis when equipped with nothing more than a distance function.  In particular, most of my work over the past few years has focused on Carnot groups (which are Euclidean spaces with weird multiplication and distance laws) and the quasiconformal Jacobian problem (asking which real-valued functions on a space S are approximately the same size as derivatives of 'nice' homeomorphisms from S to itself).

If you want to find out more about me, you can always read my journal, which gives a pretty good chronicle of my life since 2002.