enumerative combinatorics

san francisco state university

universidad de los andes

federico ardila

2013

. forum . homework . lectures . people . projects . syllabus . texts .

at the request of several of you,

these are the people at the other end of the camera

and the kinds of final group projects they are interested in.

"berkeley" is math . berkeley . edu,

"davis" is math . ucdavis . edu,

"gmail" is gmail . com,

"sfsu" is mail . sfsu . edu,

"los andes" is uniandes . edu . co,

"univalle" is correounivalle . edu . co,

"yahoo" is yahoo . com,

"en" is @

. adam . alejandro . alvaro . anastasia . andrés h . andrés r . ángela . brian c . brian d . camilo . crista . daniel . david a . david k . david pa . david pe . david r . duván . emily . fabián . federico a . federico c . francisco . george . hannah . hanner . hayden . jorge . josé . juan c . juan s . julián . kyla . maría . matthew . nicolás . nina . pedro . rafael . santiago . sarah . sebastian . servando . tahir . víctor .

adam afandi . aafandi en sfsu

I was born and raised in San Francisco. I did my undergraduate degree in Math at UC Davis, and now I am a second year grad student at SFSU. My first exposure to enumerative combinatorics was fairly recent: when I was an undergrad, I wrote an expository paper on Fock Space representations, and as a result, I had to learn a bit about Young tableaux/diagrams. My research interests, at least currently, lie more in the vein of differential topology/geometry. Outside of math, I usually spend my free time: buying vinyl records on the cheap, seeing good bands when they come to SF, pub crawling with friends, doing the robot at inappropriate times, and gawking at obscenely overpriced Fender Stratocasters.

alejandro salcedo . a.salcedo49 en los andesI'm last year math student at Los Andes Univerity and graduate in computer engineer. My math interests are in cryptography, elliptic curves and computer algebra. Outside maths, I play some musical instruments and occasionally I play soccer or swim.

alvaro luis hernandez . hernandeza94019 en yahooMy name is Alvaro Luis Hernandez and I grew up in the bay area. I'm interested in mathematics in general and I would love to earn a PhD In the field eventually. I also like and continue to take physics courses. I am married and I have two dogs. I like playing guitar, fixing computers, surfing, running and hiking. I'm looking forward to this combinatorics class.

anastasia chavez . anastasia.chavez en gmailHola! I'm a third year graduate student at UC Berkeley in mathematics. My research interests are in enumerative combinatorics. I also am very interested in diversity issues in math and science, and wish to use my time as a graduate student and beyond to support the advancement of non-traditional students in STEM. Outside of school, I'm interested in (and hope to make more time for) hiking, camping, backpacking, traveling, watching stand-up comedy, and just relaxing. My other life is as a mother and wife. I have two children (Ayla is 6yrs and Asha is 4yrs), and enjoy reading, playing and talking math with them. They usually enjoy it too ;)

andrés higuera . af.higuera707 en los andesThird-year student of economics with option in mathematics. I'm working at University of the Andes as teaching assistant of Probability & Statistics and Microeconomics. I'm interested in Probability Theory, Real Analysis and Mathematical Economics. I enjoy reading and talking, not only about Economics, but also Literature, Philosophy and Poetry. Personal Website: andresfelipehiguera.wix.com/economia

andrés rodríguez . a.rodriguez336 en los andesI was born in Bucaramanga but raised in Bogota. I spent my last two years of highschool at Pembroke Pines Charter High School in Pembroke Pines, Florida. Right now I'm a third year undergraduate student of mathematics in los Andes, currently my mathematical interests are between algebra and topology (also I am starting to like Geometry but time will say). Besides Math I love literature, philosophy and history (specially Cuban and German).

ángela castañeda . am.castaneda2932 en los andesI was born in Bucaramanga. I am in fourth semester of electrical engineering and i am taking courses in mathematics just because. I have taken very few courses in math so i still dont know what could i be interested on. Besides math, i enjoy reading about psychology.

brian cruz . brian en berkeleyMy name is Brian, and I enjoy math. In fact, I enjoy it so much I am in two math programs! This semester I am completing my thesis for my M.A. from San Francisco State University, and simultaneously I am starting to work on my Ph.D. at U.C. Berkeley. My research so far has been in the field of mathematical biology. I use stochastic models and numerical methods to simulate DNA packaging in bacteriophage viruses. I not only enjoy applied math and programming, but also discrete math and combinatorics--hence this class. I also do some photography, play music, and like to travel. I hope I will get to know all of you through the course of this course!

brian davis . bevo.davis en gmailMy interests mathematically are in combinatorics and discrete geometry. For the first time since I was a little kid I don't have any serious hobbies- wow! If anyone wants to try an online music collaboration, I'm down. I have a casual interest in my kittens.

camilo hernández . mc.hernandez131 en los andesMy name is Camilo Hernández and I'm a graduate student at Universidad de los Andes. I started Uni doing a bachelor in economics but luckily ended up doing maths as well. Nowadays, my interests in economics is nearly zero. My math interests are focus on probability theory, optimisation and statistics. The thing is enjoy the most is traveling and that has taken me to really cool places like San Francisco.

crista moreno . morenocrista en gmailMy math interests include algebra, linear algebra, discrete mathematics, topology, and in particular mathematics with applications to the biology and medicine. My thesis project is in DNA topology. I study the structural structural changes of circular DNA that result from specific enzymes that act on the DNA. I was born in the hot dry desert of Phoenix, Arizona but I have lived in many parts of the US. My family is from the beautiful country of Colombia. I like to consider myself a world citizen since my family is spread all over the planet. My sister is currently working in South Korea, my cousin lives in Italy, and my other family members are located in other places including Colombia, Spain, Australia, Puerto Rico and Germany. Outside of math interests and family, I love to dance, be Eco friendly, solve real world problems, and just have fun.

daniel ávila . df.avila353 en los andesHi!! Im an undergraduate math student at los Andes, my math interests are Algebraic Geometry, Combinatorics and in general stuff related with algebra. In my free time I like to play guitar, and hang out with some friends. If i had to describe my life, it would be like FRIENDS just theres no joey, no rachel, no ross, no monica, no phoebe, just chandler, laughing at his own jokes.

david arcila . davidarcila93 en gmailI was born in Cali, Colombia. I am in fourth year of maths at Universidad Nacional de Colombia in Bogota. I've participated in math contest since i was in school, that's why i decided to study maths, and more recently I started to take part in programming contests. Besides maths I love playing guitar and dancing salsa. In the moment my main interests in maths are combinatorics and algebra, but I'm still searching.

david klein . dklein en sfsuI've been pretty much hooked on combinatorics ever since taking discrete math my final semester as an undergraduate. I'm now starting my second year in the M.A. program at SF State, working with Federico on enumeration questions pertaining to matroids. A proper subset of my less mathematical interests includes language (particularly the English language, since, unfortunately, it's the only one in which I'm fluent); epistemology; funk/soul/rap/dance music (past and contemporary, domestic and international); the writings of Lydia Davis and David Foster Wallace; the films of Hirokazu Kore-eda; India Pale Ales; and kittens.

david pardo . davidpb90 en gmail
I'm David Pardo, I'm in my third semester of the Masters program of Mathematics at Universidad de los Andes. I'm mainly interested in applied mathematics, more specifically in probability and statistics. This course also interested me because my brother studies magic and i've seen that a lot of card tricks imply counting and permutations.

Among my hobbies are football (soccer), literature, photography, diving and traveling. I'm looking forward to begin a Ph.D. in Europe next year.

My name is David Alejandro Perdomo Meza. I just finished my undergrad in pure mathematics in Universidad de Los Andes in Bogota, and am now doing my masters here as well. I was born in Bogota but lived in Florida from 1997 to 2003. My principal mathematical interest I would say remains undefined. I saw a handful of course in real and functional analysis but ended up doing my thesis in Morse Theory after seeing a bit of geometry/differential topology courses as well. My plan for my masters is to see a mix between applied mathematics and pure areas. For example this semester im seeing a course in Stochastic Processes, a course and Algebraic Topology and this one of course. My thesis director is urging me to read some papers by Gunnar Carlson on applied algebraic topology to see if we can take some ideas for my new thesis.

Aside from math, my main interests in life are football (soccer) and travelling. Im a complete football nut, spend most of my free time reading blogs on football, go every weekend to see Millonarios play here in Bogota and fly out to London as often as possible to see Arsenal play (that shirt I have on in the picture is an underground symbol saying "Arsenal"). I havent ruled out pursuing a career in football management after my masters.

My name is David Rodriguez I was born and raised in southern California. I did my undergraduate studies at a small private college called the University of Redlands. At that time, I majored in math and have loved it ever since. I am currently studying at SFSU to get my Master's of Arts in Math.

If I were to pick a field that interests me I would probably say something like 'Algebra'. I understand some people might have very specific interests and so this sounds a little fuzzy. But it feels right to me for now.

I look forward to meeting everyone on the discussion boards and collaborating with you :)

My name is Duvan Cardona, I study in Universidad del Valle in Colombia. This year I will finish my undergraduate studies. I have many interest in Mathematics. I work on Pseudo-differential Operators, also, I like Functional Analysis and Number theory.

emily mccullough . emily.m.mccullough en gmailMy name is Emily McCullough. I am from the San Francisco Bay Area. I am a Master's student at SFSU. I am interested in algebra, number theory and combinatorics. In my free time I like to read and to spend time outdoors. In particular, I like camping, hiking, mountain biking and snowboarding. Here is a picture of me in Bishop, California after my first outdoor rock-climbing experience.

fabián latorre . fr.latorre2009 en los andesI«m a graduate student at los Andes. I enjoy different research areas like probability, statistics, combinatorics, analysis and optimisation. I have a passion for music, party and stuff, that's why I hand in my homework late.

federico ardila . federico en sfsu
I was born and grew up in Bogotá, Colombia. I first got interested in combinatorics as an undergraduate at MIT, when I took a class similar to this one from Richard Stanley. He later became my Ph.D. advisor. I am now an associate professor at SFSU and an adjunct professor at Los Andes. In my research, I study objects in algebra, geometry, topology, and phylogenetics by understanding their combinatorial structure. I believe that everyone can enjoy mathematics; I try to do my part in building a mathematics community that welcomes all kinds of people, and benefits from it.

When I am not at work, you might find me exploring the SF Bay Area or Bogotá with my wife May-Li, on the fútbol field,
treasure hunting in little record stores, or sharing the love with La Pelanga collective. (www.lapelanga.com)

I'm from a wonderful city called Bucaramanga, and currently I'm a math graduate student. I like math, of course, but in my free time i like to read, watch, or hear any good story (called it a book, a series, a movie, a cartoon, etc), maybe I'll try to write something in the future (one of the writers for the TV Show 'Futurama' is a math PhD). I enjoy music a lot, from black metal to latin salsa I'm always looking for something different. My math interest are mainly algebra, geometry, and algorithms, all of them with a delicious combinatorial flavor.

felipe suárez . f.suarez482 en los andesI was born in Cartagena (Colombia) but I grew up in Bogota. I'm currently a fifth semester double major in Mathematics and Electronic Engineering at the Universidad de los Andes. My math interests are algebra, analysis, and topology. Other than math, I like to listen to and play classical music, watch movies and TV series, play chess, and, sometimes, working-out.

felipe vargas . lf.vargas797 en los andesI was born in Barrancabermeja, Colombia. I am studying mathematics at Universidad de los Andes, my math interest is number theory, i was motivated by different problems in math olympiads during high school. Also I practice voleyball and soccer and like play video games in my free time .

francisco barreras . fj.barreras512 en los andesMy math interests are Analysis, Game Theory and Mathematical Biology. Other interests: Neuroscience, cooperation, Economics, Chess, Social Dynamics and Politics.

george beck . george.beck en gmailI like to count and love to enumerate! I live in Comox on Vancouver Island up the coast from Columbia and SF... I should be retired by now but I continue to work for Wolfram Research as the technical editor for http://demonstrations.wolfram.com and the managing editor of http://mathematica-journal.com/. (There is a nice article on Ramsey numbers coming up by November 1 and some earlier combinatorics articles.) In the last century I did honours math at McGill and dropped out from a PhD in math at UBC. I taught as an instructor at the University of Toronto a couple of years and wrote http://calc101.com/. If you've read this far I have a reward if you teach graphing. I call it reverse graphing: draw a curve and have the students try to construct a function whose graph is that curve. (For example, abs(abs(x) - 1).) Brings experimentation into math; it was a big hit at UT.

hannah winkler . hwinkler en sfsuI was born in beautiful Petaluma, CA, and still live there today with my husband, John, and our two dogs. I'm into my second (and technically 1/2) year as a master's student at SFSU. My interests in math include algebraic combinatorics and discrete geometry, two areas that I just recently started to appreciate and become really excited about. Some of my interests outside of math are running, enjoying John's amazing meals (he's a cook), and just relaxing at home watching movies. I would say I'm equally scared and awesomely excited, because I think combinatorics (what little I know) is very fun and can be very satisfying, but also frustrating and really hard, because there can be so many ways to think about the same question.

hanner bastidas . hanner.bastidas en univalleI enjoy study mathematics, is one of my hobbys. I like specially themes at logic, algebra and topology. Now, I'm in my last undergraduate semesters at Univalle. My interest is provided in in applications of theoretical computer science. A few of my non-mathematical interests: biking, swimming, reading, climbing, hiking.

hayden liu . h.liu917 en los andesI was born on 29/11/92 (a palindrome!) in Bogota, where I'm currently double majoring in Mechanical Engineering and Mathematics (with a minor in education) at the Universidad de los Andes. Regarding my mathematical interests, I'm mostly into probability and statistics, numerical analysis, combinatorics, and other fields in applied math (cryptography anyone?). As for my engineering background, I'm interested in fluid dynamics and materials science, and am currently part of a robotics team. Other than academia, I love Japanese culture (which includes reading manga, watching anime, and folding origami - specially miniatures) and trying out new things (occasionally singing or writing).

jorge alberto olarte . ja.olarte1299 en los andesI'm Jorge Alberto Olarte, born in Bogota, model '92. I am in my last undegraduate year here at Los Andes. I like Algebra, Combinatorics and Topology. Besides math I enjoy watching soccer (que viva Santa Fe!), hearing music and playing videogames.

josé bastidas . jd.bastidas251 en los andesI'm coursing my master's program at Universidad de los Andes, and I've been living in Bogotá for five years now. My principal mathematical interests are commutative algebra and algebraic geometry, but I'm also looking forward to add combinatorics to this list after the course. I'm always listening music and in my free time I enjoy watching some series and movies.

juan camilo carranza . jc.carranza1617 en los andesI was born and raised in Bogotá. I am studying Electronic Engineering and Mathematics in Los Andes University. My main mathematical interests are number theory and real analysis. Some of my other interests are: playing football, table tennis and chess.

juan sebastián osuna . js.osuna120 en los andesI'm from Bogotá, Colombia. I'm a Systems and Computer Engineer in my last semeter of Mathematics and senior year of Physics at Universidad de los Andes. My math interests are in Geometry, Computational Topology, Statistics and Applications in Computer Science. Outside formal maths I'm also interested in Machine Learning and Artificial Intelligence in general, programming, Tech start ups and video games.

julián romero . ja.romero913 en los andesHi guys! I'm a grad student from Los Andes currently interested in Combinatorial Optimization, but I also like some of Stochastics and Statistics. I love Prog-(metal,rock...) music - I must say I'm a music nerd (like the guy on The Needle Drop YouTube channel- Oh... I almost look the same like this guy). I play guitar and synth on a band called "Oneiric Trend" (??) and I DO count slowly...

kyla quillin . hellokyla en gmailMath-wise I like thinking about topology and combinatorics most, and I'd like to further explore their intersection. I appreciate the elegance of many combinatorial arguments, and I'm excited to pursue that here. I wish my brain were simply 'open' (in the spirit of Erdos), but itŐs honestly 'clopen,' and I'm working on it. For me the grounding of yoga complements the abstraction of math. I wish to travel the world by bicycle. I like to share (tea, meals, chocolate, math, ideas, hope).

maría alejandra bravo . ma.bravo641 en los andesMy name is María Alejandra and I'm Colombian. I study math and biomedical engineering at Universidad de los Andes. I'm interested in applied math, combinatory and analysis. I am hoping to learn how combinatory can be used to solve biomedical problems. Beside this I love cooking, playing tennis, learning French, oil painting and number pi.

matthew kim . m.cadier.kim en gmailThis is my third semester in the MA in Mathematics program at SFSU. As an undergraduate I majored in philosophy, however in my senior year I began studying the history of science, then logic. This eventually led me to algebra, geometry computer science etc. Because of my relatively recent entry into mathematics, I only have very vague ideas about what interests me. The general trend nevertheless has been towards discrete geometry and combinatorics. I also like conifers and would be very interested in hearing about the cone bearing plants of South America.

nicolás peña . ne.pena1587 en los andesI am interested in theoretical computer science (especially complexity theory), algorithms, model theory, applied logic, combinatorics, and optimization. I like playing in the computer, programming, and reading.

nina cerutti . nina.cerutti en gmailMy name is Nina and I am going into my third year at SFSU. I got my BA in Mathematics at CSU Stanislaus in 2011 and immediately joined SFSU's awesome math department the following Fall. I am currently working towards my thesis in the field of graph theory under Dr. Matt Beck. I particularly love graph coloring and it's applications, as well as signed and mixed graphs. Overall, I love combinatorics! When I am not in class, I am working as a mathematician with my partner teacher, Marcus Hung, at June Jordan School for Equity for the (CM)^2 fellowship program. I am also part of SF Math Circle (an after school program for high school and middle school students to explore abstract mathematics). On my spare time, I love to read, cook, and explore what the city of San Francisco has to offer.

pedro fernández . pedroel13 en hotmailI am a student at the Universidad Distrital majoring in Math. I have been doing undergraduate research since 2010, getting some articles published joint with any of their teachers. I wish to continue my graduate education in the U.S.A. I am very happy to study mathematics. I am interested in representations of Algebras, Number Theory, Combinatorics and its Applications. My website is: http://comunidad.udistrital.edu.co/pffernandeze/

rafael montoya . r.montoya100 en los andesMy name is Rafael Montoya. I am (first year) in the master degree program in Mathematics in Universidad de los Andes. I am from a Manizales, a small city in Colombia's coffee region. My interests in mathematics are probabitlity and statistics. I also like real and functional analysis. My interests outside math are cooking (I'm also studying to be a chef), biking and I want to learn some climbing.

santiago cerón . s.ceron1495 en los andesHello! My name is Santiago. I live in Bogota, Colombia and I'm currently doing my 7th undergrad semester at Universidad de los Andes. Though I am not married with any branch of maths just yet, I like subjects related to computer sciences a lot. I am interested in teaching as well. Outside of math, I really enjoy programming, travelling and cooking (although I can barely cook anything), and I will never say no to some temaki sushi (specially with the right company). I am also a BIG nerd, my main hobby being computer gaming/ esports.

sarah marquis . sarahmarie.marquis25 en gmailI grew up in Lyon, France, before moving to Boston in 2001. I later attended Tufts, graduated last year and moved to San Francisco with two college friends. At Tufts, I had the liberty to take a number of different classes before picking a major. I realized after my first year that math classes were the most interesting to me, so I pursued a Bachelor's in abstract math. I am now thinking about grad school, but am not certain what I want to do with math, which is why I have not applied yet. My other passion is volleyball, and I played multiple times a week for years until I got injured last year.

sebastián auly . juanseauly en gmailMy name is Juan Sebastián Auly, I was born in Cartagena and I majored in Mathematics at Los Andes. I'm applying to the Master's at SFSU (Spring 2014). I am interested in algebra, number theory and lately I've become interested in combinatorics. My nonmathematical interests include soccer (following Manchester United and playing as well), drawing comics and reading... well, almost everything I can find, but mostly fiction, sociology and philosophy.

servando pineda . spineda6239 en gmailHello math enthusiasts my name is Servando. I was born in Mexico, but was basically raised here in the Bay Area. I am second year graduate student at SFSU finishing up my thesis. My research combines Polytopes, Algebra, Probability Theory and Combinatorics beautifully. Aside from pure mathematics I am also very passionate about math education and using mathematics as a tool to help empower the Latino community. Outside of mathematics all together I enjoy reading books and graphic novels. I plan to someday do my own graphic novel surrounding my life. I have "read" certain graphic novel whose pictures are just as powerful as words. Check out Thomas Ott. Lastly I'm also an avid salsero and use it to relieve my graduate school stress =P.

tahir anjum . tanjum en yahoo
I was born and raised in the bay area, primarily in Hayward, CA. Upon graduating from high school in 2005, I entered San Francisco State University. After remaining undeclared for three years, I decided to study mathematics, and graduated with my bachelor's in mathematics in Spring of 2011. I am now a graduate student in the masters program of mathematics, starting my third year.

Outside of school, I usually spend time with my family and friends. I also read a lot, primarily epic fantasy novels. I play games of many types, such as video games, sports, dominoes, board games, and card games (I just love games!). My favorite band is Iron Maiden, favorite number is thirty-seven, favorite color is blue, and favorite movie is Pulp Fiction. I am always up for new adventures, so if you have any recommendations, feel free!

I'm a graduate student at Los Andes (Bogotá). When I'm not studying I like to hang out with my girlfriend (and our cute little dog, Martina, the black one on the picture), play with my dog (Sami, the other one on the picture), play guitar, write songs, ride my bike, watch some movie or talk, I really enjoy talking. Just know I'm about to send some applications to, if someone wants me, begin graduate studies on the next fall. I really enjoy math and everything related with math, I like analysis, geometry, algebra (I don't know statistics but I really admire them) and right know I'm learning some nice stuff about geometry of operators. However, my current research interests are mathematical biology and epidemiology. Combinatorics is somehow new for me, so I'm really exited about this course.