On not giving up

3 Dec

On my very first day of high school, my calculus teacher had me take a pre-test to make sure I belonged in the class.  I was the first freshman of that ridiculously excellent school’s history to be in calculus, which was entirely due to the INCREDIBLE program at the University of Minnesota, UMTYMP- if anyone you care about is a 10-12 year old in the greater Twin Cities area, I highly highly suggest checking out the program.  The next night my parents were extremely concerned about me, as I was in tears over my calculus homework.  I thought that I wasn’t good enough and that it was too hard for me, rather than that perhaps I was less prepared or mathematically mature than expected (see my post on whether we should do math at all for more thoughts in this direction).  I still ended up rocking both years of AP calculus, and doing okay at Cal State Fullerton, where I took a few more math courses during my remaining years of high school.

I made this picture all by myself

It’s been over a decade since my first math tears, and about three years since my last ones- I struggled so much over integrals over contours in my complex analysis course, and definitely had tears spring to my eyes when I finally lugged myself over to the math tutor (incidentally, I had some beer with him over the summer at a conference and he is awesome) to ask about one particular problem.  I was ridiculously heartened when he didn’t immediately spit out an answer, and told me that “the most important thing is to stay calm,” which kept me from nervous breakdowning at a total stranger.  When handing back exams to my calculus students, I’ve definitely noticed a few hastily wiped tears and debated on commenting and potentially embarrassing them, or letting it go and feeling like a callous ass for the rest of the day.  Now I tell them the story in the next paragraph.

A few months ago, after doing that mini-triathlon, I saw a groupon for Crossfit and thought I’d try out what I affectionately call the “cult.”  I’ve mentioned before that I’m incredibly weak, and I’ve definitely noticed this during my crossfit classes- I’m an okay runner, but in terms of strength I’m last, and definitely lag behind the pregnant woman (who is a beast).  Until yesterday I’ve been completely at peace with this, because I can tell I’m getting stronger and improving and feeling pretty good, even when the trainers have to set up separate stations for me because I can’t do a push up with good form.  At my last session we had a coach I hadn’t met before who started us all with the same strength, and gave us a few minutes to fiddle with it and add more weight as needed.  It is clear to me now that the burden was on me to speak up or simply do my thing and give myself less weight after trying out the initial condition, but I was too shy/ashamed to help myself do my best, and I ended up sabotaging myself and finishing my workout with many, many tears because I felt inadequate and incompetent.  I’m glad that I finished, but the coach had to lessen my weight partway through and I did one less round than the other women.

The moral is that we aren’t all born with the same strengths.  As my boyfriend said when comforting me that night, some of these women in this class have been playing sports since middle school, when I was doing Destination Imagination and Future Problem Solvers, or at least did athletics in high school, when I was playing clarinet in the marching band.  And that’s OK.  Those women will be lifting more than me, and I will be doing the best I can with what I have.  Not everyone in my calculus section is going to be an A student- they never learned algebra and are working two jobs to support themselves through college, so don’t have the time to master algebra and pass their other actual classes.  That’s OK.  What’s important is that they finish the workout and give it the best they have.  And tears are OK too, they happen to all of us.

HAPPY BIRTHDAY BLOG!

27 Nov

It’s been a year since I posted about that fruitcake!  Wow!

I would love to get this etsy card!  Also this is what showed up when I googled ‘birthday celebration women math’

My favorite baked goods of the year:

My favorite math-content posts of the year:

My favorite other posts of the year:

Not gonna lie, sometimes I look back at my blog and random posts and giggle to myself at the puns.  I just did that with the puree pun in this post.  Wish I could make a list of my favorite puns of the year but there are far too many.

THANK YOU very much for reading, whoever you are!  It’s been a fun year and should continue being fun as I go further in my Ph.D. journey.  Oh a few weeks ago I got my candidacy letter (and promptly put it up on instagram).  Coming up in the next year: a better layout for this blog (it drives me nuts!), more baking, more math, more non-baking cooking, starting with my mom’s thit kho (Vietnamese braised pork) recipe!  Tomorrow I’m going to be baking a turducken in my cousin’s oven; it’ll be the first time my family’s eaten my turducken.  Wish me luck, and happy Thanksgiving =)

Lemon-sage olive oil cake

23 Nov

This cake is remarkably polarizing.  My roommate pretty much hates it, while my officemate has said that it’s “my new favorite anything.”  The tangy bits of lemon zest play well with the super moist, slightly peppery/savory olive oil flavor, and the sage ties it all together.  Definitely not your typical over-sweet hyper-decadent cake, but I love it!  And it’s pretty easy to put together (though I still don’t have much zest for zesting).  Also it’s better if you leave it for a day or two, a la fruitcake.

I spent a while saying ‘ah love’ and ‘i love’ and ‘ah live’ and couldn’t come up with a pun. I guess OLIVE with that.

You’re supposed to use a springform pan, and parchment paper, and greasing with this cake, but I have only the last of those three things.  So I greased a cake pan with a generous pour of olive oil, and got to work on the wet ingredients: sugar, yogurt, olive oil, and eggs.

Once a dude had this problem where he accidentally crossed all his ‘l’s so people thought they were ‘t’s. He even did this when typing. So he didn’t have much luck with online dating, as he thought he was saying hey to some fine lookin’ young ladies and they thought he just kept saying “YO GURT’ at them.  Boy thinks I should get rid of this caption.

Oil oil, toil and trouble…

Hand burn and egg yolks bubble! Wouldn’t it have been so great if the witches in Macbeth ended up baking a cake and giving it to everyone alive at the end? Knowing them though, everyone would’ve immediately died.

You also get to make lemon flour!  Zest your lemon directly into the flour.  I think the more zest the better- about two lemons worth is very nice.  Don’t forget baking powder.

Sometimes I just get bowled over by how grate lemons are!

DON’T LOOK WE’RE NAKED!  Maybe that’s why pink lemonade is that way: they zest the lemons, so they blush.  Definitely the reason, Yen.

Then “finely” chop up your sage.  I say “finely” because I’m not very good at cutting things up but one day I will take a knife skills course at Kendall, really!

I’m not sure how wise it is to leave such big pieces here. Oh well, it’s still sage!

Mix your sage into your wet ingredients, and then mix in the dry ingredients.  Pour into your pan and bake!

Mmm is an entire cake a good sized POURtion?

Bake that sucker until a toothpick comes out clean (maybe 25 minutes, maybe more).  I took a picture of my toothpick test, then put it back in the oven for another 5 minutes.

If a toothpick falls in a cake, does anyone choke on it? Yes, probably.

I’m pretty picky when it comes to this test: there shouldn’t be more than like 3 crumbs attached to the pick, at most.

These next two steps are what make this cake SO GREAT.  Squeeze the juice of a lemon and a half into a bowl, and add 1/4 c powdered sugar, whisk that syrup so well.  It’ll be pretty lemony.  Then prick your cake all over with a fork…

It can be forkin’ hard to come up with so many puns/to not break a cake when poking it

And use a spoon to carefully spread the syrup all over the cake.

If Tom Cruise was in my kitchen we’d definitely be dancing around in button up shirts and socks, and then I’d set him to this whisky business

You can try to put the syrup onto the cake by bending the spoon with your mind… or you can just spoon it on

Then (this is hard) you have to walk away from the cake.  If you put on the icing too early, it’ll melt into nothingness as happened with my second attempt at the cake.  So leave it for like half an hour, go play candy crush and lose all your lives or something.  Then come back and ice it!  Squeeze the remaining half lemon of juice into a bowl with much more powdered sugar, and go wild!

My bathroom is right next to my kitchen, so if Miley were here if she was waiting in line for it I’d suggest she help me with this white powder instead

Looks like play-doh, but it’s more like yay-doh! yay delicious icing i mean.

Ice it, and cut a piece and give it to your mom for first taste.  If she’s anything like my mom she’ll love it.

Sometimes I’m so happy I just think man, I sing of this cake!

Go ahead, take the (w)edge off with a piece of cake

Lemon-olive oil sage cake, from Blue Kitchen

1-1/2 cups all-purpose flour

2 teaspoons baking powder

Pinch of salt
2 lemons

1/2 cup plain yogurt (full fat!  Do it!)
1 cup sugar
3 large eggs
1/2 cup olive oil

2 teaspoons fresh sage

1 c powdered sugar

First, oil your pan- if you have a springform, do your springform thing.  If you’re like me, just throw a gob of olive oil in your pan and smoosh it around.  Preheat oven to 350 (that’s how fast this cake comes together, I’m telling you to preheat now).

Next: mix the yogurt, sugar, eggs, oil, and chopped sage.

Then: zest the lemons into the flour and mix well with the baking powder.

Mix the two bowls of stuff, and bake for 25 minutes.  Check with a toothpick.  Mine took 30 minutes.  Let cool (about 10 minutes)

Mix juice of 1.5 lemons and 1/4 c powdered sugar.  Prick cake all over with a fork, then spoon the syrup slowly over it.  Try to get everywhere.  It’s so good.

Wait.  Go do something else.  At least half an hour.

Mix the remaining .5 lemon’s worth of juice with 3/4 c powdered sugar.  Really squeeze those lemons to get the last few drops if your icing is too thick.  Ice the cake.  Eat the cake.  It’s not a lie.

Open problem in geometric group theory

16 Nov

Update: Per Jeremy’s comments, I’ve updated the end of this post to be more clear and less inaccurate/blatantly untrue.  Thanks Jkun!

The other day in my topics in geometric group theory course, my professor described an open problem which I thought was pretty cool and relatively easy to explain.

First, if you haven’t (which you probably haven’t), check out the “groups” section in my post about Cayley graphs, which was really just about groups.  I just need you to know what the group of integers is $\mathbb{Z}$.

Now we’re going to talk about generators.  Again, mathematicians do a pretty good job of using reasonable words to name mathematical terms: generators of a group are elements of the group that “generate” that group- just like our parents created our generation (aww yeah), the integers “1″ generates all of the integers.  So 2 = 1+1, 17 = 1+ 1+ … +1, -23 = (-1)+ (-1)+ … + (-1).  There’s a bit of terminology that I slipped in there without pointing it out: I used -1 as well as +1 to build all the integers, but I only said that 1 generated everything.  Technically it’s that 1 and -1 generate all the integers, but since -1 is “negative one,” or the inverse of 1, I’ll just say that 1 generates the integers, leaving it implicit that we also include the inverse.

I could also choose more generators.  So, for instance, “1″ and “2″.  Why would I do this when I can already write everything in terms of 1?  Because it’s faster sometimes to write things in terms of 2.  For instance, 6 = 1+ 1+ 1+ 1+ 1+ 1, but 6= 2+2+2.  I only need three generators to express 6 if I use 2 as a generator, but I need six if I only have 1.  One thing that geometers care about is distance.  So if I just use “1″ as my generators, the distance from 0 to 6 is 6.  But I use “2″ as a generator, the distance from 0 to 6 is 3, because I only needed to use three generators to get to 6.

Six blue arrows, only three red arrows

OK so that’s generators, and why we care about them (distances, a.k.a. metrics).  We’re going to switch gears for a minute and then I’ll describe the open problem (it hinges on using different generators for the integers).

Next topic, much scarier sounding word that isn’t actually that scary: quasi-isometry.  Let’s deal with “isometry” first, and “quasi” later.  An isometry is a function from one space to another that preserves distances.  So if x and y are distance 3 apart in the first space, then f(x) and f(y) are still distance 3 apart in the second space.  A few examples: translating $x\mapsto x+1$ on the real number line is an isometry, since if $x-y = d$, then $f(x) - f(y) = (x+1)-(y+1) = x-y = d$.  Multiplying $x\mapsto 3x$ isn’t an isometry: for instance, 1 and 4 are distance 3 apart on the real line, but 3*1 =3 and 3*4=12 are distance 12-3=9 apart.  So this map didn’t preserve distance, and so it isn’t an isometry.  In symbols, the equation for an isometry is $d(x,y) = d(f(x),f(y))$, and we want this to be true for all possible choices of x and y.

Isometries are great, but sometimes life is a little bit fuzzier than perfectly preserving distances.  We wanted a word to describe functions that were almost isometries, and in math land, that would be quasi-isometry.  Using an equation, we have that f is a quasi-isometry if there are constant numbers k and C so that $\frac{1}{k}d(f(x),f(y))-C \leq d(x,y) \leq k d(f(x),f(y))+C$.  So it’s an isometry up to some multiplicative and additive constants.  Examples and non examples: all isometries are quasi-isometries, we just let k=1 and C=0.  That multiplication map from earlier is a quasi-isometry with k=3 and C=0: $d(f(x),f(y)) = d(3x,3y) = |3x-3y| = 3|x-y| = 3d(x,y)$.  Here’s something that’s not a quasi-isometry: $x\mapsto e^x$.  The exponential map grows faster than the multiplicative constant can hold it down.

And now that you know what the integers, generators, and quasi-isometries are, I can describe this open problem.

Remember that $2^0 =1, 2^1=2, 2^2= 4, 2^3 = 8,\ldots$ and $3^0 =1, 3^1=3, 3^2=9, 3^3=27,\ldots$.  This is the question: is the integers generated by $\{2^n\}$ quasi-isometric to the integers generated by $\{3^n\}$?  For instance, we know that $9=3^2$, so 9 has length 1 in the second set (since $3^2$ is a generator), but $9=2^3 + 2^0$, so 9 has length 2 in the first set.  You can play around with any integer and write it as a sum of powers of 2 and of 3, and try to see if there’s a relationship between the lengths (i.e. the length of 45 is 23 in the 2-set, and is only 15 in the 3-set).  To reiterate, the length of a number in the first set is the minimum number of powers of two you need to add up to it- so although $9 = 2 ^1 + 2^2 + 2^0+2^1$, the length of 9 in the first set isn’t 4, but just 2, which is the minimum number.  Similarly, in the second set its the minimum number of powers of three you need.

Fact: If we only look at a finite set of generators, the sets are quasi-isometric.  The tricky part is when we have infinitely many generators, as they get farther and farther apart.

Now you understand something that no one knows the answer to yet!  Isn’t that cool??? This is math!

Candied almonds

10 Nov

These are very fast and quite tasty.  You just throw raw almonds + sugar in a pot, let it boil, and then roast them for awhile.  I messed up a bit and made almond brittle, essentially, but it was still really tasty.

I wonder if Doc and Marty had to carry a lot of stuff with them in a murse or something in that movie… it’d be a bag to the future

Measure out the brown sugar, and let it boil in a pot with the salt, cinnamon, and some water.

I see the light! It’s the least important word on the bag!

This view makes the tsp of cinnamon look HUGE. Good to keep spice in perspective: otherwise you’ll just have a messed up privet and who wants that plant?

You may worry, but don’t.  It’s a little bit energetic, the boiling, but everything will be okay, just stir in the almonds.

Double double toil and trouble, fire burn and pot of sugar bubble

OK everyone in the pool! All (m) in!

I just sat here and watched, ranking the almonds. You could say I was SATuRATING

Also I didn’t read the recipe and apparently I was supposed to stir these constantly.  Oh well!  Cook until the liquid is absorbed/evaporated.

If Doc and Marty brought this along, it’d be a hot tub time machine for the almonds.

Then dump them out onto a silpat or a sheet of parchment paper (NOT DIRECTLY ON THE BAKING SHEET), and spread those guys out.

This one almond has no equal… because every other one is better. OOH ROASTED!

Bake for 10-15 minutes.  I sprinkled them with salt before throwing them in.

Brittle me this: are almonds all they’re cracked up to be?

Let that cool (I let them sit out overnight), and then break up the brittle.  If you cooked them long enough and stirred them which I did not, they’ll probably end up looking more like the original blogger’s:

Candied almonds from Barbara Bakes:

• 1 cup brown sugar
• 1/4 cup water
• 1 tablespoon cinnamon
• Pinch of salt (I like lots of it!)
• 2 cups almonds

Boil brown sugar, water, cinnamon, salt.  Once boiling, stir in the almonds.  Stir constantly until liquid is evaporated (5-10 minutes).  Spread out onto a baking sheet lined with something (foil, parchment, silpat, anything!), and bake at 350 for 10-15 minutes.

Sunday brunch- dill and caramelized onion mini-souffles

3 Nov

I am ridiculously, incredibly lucky and blessed in many many parts of my life, and some of those are a) I live in Chicago! and b) I have an awesome boyfriend who likes spending stupid amounts of money on restaurants (whereas I spend relatively stupid amounts of money on ingredients like chia seed and flax and agar agar).  So last week we grabbed a chance to eat the Bocuse d’Or menu at Next, which was ridiculous and exciting and a five hour extravaganza and the best experience of about 4-8 hours of my life (close second is the Twilight movie marathon I did before the midnight showing of the fourth movie).  There’s literally a trailer for our meal: http://youtu.be/hSnhoOwoG_s.  Here’s some random review talking about how great it was.

Packs mighty flavor for such a shrimp of a dish (it’s maybe 2 inches in diameter). Photo by Michel Gebert, click for link to the site for more pictures.

This was one of my favorite dishes of the night, a teeny tiny savory souffle made with strong flavors of shrimp and fennel, with teeny juicy prawns tucked at the bottom.

I’m far from a molecular gastronomist or a great chef, but I’m a pretty decent cook and more importantly, I like food a lot.  Enough to experiment, to revel in the tasty and successful and to woman up and choke down the less tasty and less successful (well, besides that vegan key lime avocado pie I made with fermented avocado).  Whenever we go out to eat I like to make a mental note of the flavor combinations or of unusual things that go together- this is why I put raisins on my Indian curries or apples in my Vietnamese spring rolls.  So, inspired by this savory shrimp souffle, I thought I’d make mini savory souffles for brunch.  I opened my fridge and found a quarter of an onion, eggs, almond milk, half a bunch of dill and some cheddar cheese.  We seriously needed to go grocery shopping.

AL(l) I need in the MOND(e) is right here

The basic steps for this souffle is much like the sweet souffle that I apparently haven’t posted yet.  Make a roux, add the milk until it’s thick, and in all the other things, bake.  Serve immediately before it depuffs!

But, but, but her piece was bigger! Why did you melt mine???

I agree, to just melt her like that without asking is just ROUX-de

The thing that took longest here was grating all of the cheese.  This would be better with better cheese but I had a Costco block so that’s what I used.  I also caramelized some onions to put on the bottom of the souffles, like how Next had the little prawns on the bottom (prawns?  shrimp?  what are they called?)

Are these puns too cheesy?

All yolks aside, souffles are serious business

Not a care in the world… that’s not true; there’s at least one: these CAREmelized onions

So they tell you to beat the egg white until stiff, but I didn’t want to take the beater out of the box and wash it etc.  So I just whisked that egg white for 2-3 minutes and I got it pretty foamy/kept it’s shape-ish.  Whatever.  Egg whites can become like 8 times bigger and this one probably got twice as big, which is pretty good for hand whisking.

I barely got the whole bowl in this picture… maybe I should pick a whiter frame.

Enter the fold, my child. And be… incorporated?

This really was surprisingly easy.  Then just put the onions in your greased ramekins, pour the egg mix on top, and bake until done!

These make me tear up they’re so cute

Dill and Caramelized Onion mini-souffles, adapted from food.com:

4 TB butter

1/4 onion

1/3 c flour

1 c milk

3 eggs

2 TB fresh dill

1/2 c grated cheese

Preheat the oven to 400.  It takes awhile which is why this step is up here.

Dice the onion and throw in a pan with a little bit of oil on medium.  Stir occasionally while doing below.

Melt the butter in a pot, then whisk in the flour to form a roux.  Once that’s mixed (see above picture; it can be sorta clumpy), pour in the milk and whisk hard so there’s no clumps.  Bring to a boil, stirring constantly, and simmer for a few minutes (<5) until the milk is thickened.

Turn off heat under the milk.  If you haven’t already, grate your cheese, chop the dill, separate your eggs, grease your ramekins (I cut the recipe in half and made 4 mini ramekins).  If the onions are done to your liking, put them in the ramekins.  If not, keep cooking them.

Stir the cheese, dill, and egg yolks into the sauce.  Beat the egg whites until stiff or until you’re bored of doing so, and fold it in, a little bit at a time.  Then divide the mixture into the ramekins and bake for 15-20 minutes, or until they look lightly golden brown on top and have poufed.

Surprisingly emotional reaction to being a woman in math

28 Oct

I wrote this a few weeks ago, just after that quick link post.  I was pretty emotional at the time, and I’ll just leave it unedited to give a sense of how I felt:

I just had a meeting with two professors and four graduate students, all male, in which we discussed that nytimes article.  I’ve spoken about this article and my personal experiences plenty over the past week, but I got choked up and found it hard to talk without tearing up when I tried to say something about how women need that bit of encouragement (I wrote in my last post the thought on internalizing vs. externalizing) and how much more it means to women.  It wasn’t a hostile environment; I know all the guys there personally and they’re all pro-feminism/obviously care about teaching, but I still had this psychosomatic reaction to representing the experiences of all women to this group of men who never got this particular little monster plugged into their psyches.

This particular little monster is the one that says boys save the day and overcome obstacles and girls get rescued, even when they try to save the day.  Or the one that sees the handwriting on the exam and braces itself for a bad proof.  The one that thinks you’re more like Amy and not like Penny at all (from Big Bang Theory, a show I actively hate for reasons I’ll go into later if ever), but that wants to be “normal.”  It’s the monster that says you don’t know what you’re talking about and you don’t know what’s going on so why even try.

OK so that’s what I wrote a few weeks ago and it’s just been sitting here since then.  Shortly thereafter I received a kind email from one of the professors:

Thanks very much for sharing your thoughts and feelings in the ESP meeting today. I recognize that the subject and the issues mean a lot to you.

And, with a bit of time, I recognized what had happened and I emailed him back:

Thanks for the note.  I’ve actually been talking about the issue a lot since the article came out in many different situations, so I was rather surprised when I got a bit choked up in the ESP meeting as I’m quite opinionated/vocal generally about it.  Upon reflection I believe that I felt like I was speaking on behalf of all women in a room full of men, a responsibility that I wasn’t prepared for.  It’s like having a discussion about race in a room with one person of color.  It’s a little weird.

So that’s the state of things.  When I’m a super-minority (as in the only person with a particular characteristic in an otherwise homogenous situation), I feel a burden of responsibility to represent whatever that minority is: woman, mathematician, non-white person.  One way to deal with this is to shut it down and not deal with it, but that’s impossible if, for instance, you find yourself in the situation I was in.  Another way is to embrace stereotypes: in undergraduate, I was the one of two math people in my residential college (~400 people) for my years there [one guy graduated and then a girl came in the next year], and I would often joke about being the math nerd and push up my glasses in an effort to make those around me more comfortable (my friends would often joke about being dumb at math or hopeless etc.  See previous post.)

Anyway that’s a thing that happened.  I did do something productive out of it, which was go through all of the graduate students in my department and figure out how many women were in pure/applied math out of the total number of students per incoming year.  And by I did this I mean I did my year and this year’s students, and asked my generous friends to spend 15 minutes doing it for their years-information is hard to find and parse!  There’s some ambiguity because when students leave they disappear from our website so we can’t tell if they’re in math or stats (our departments are together).

Here are our numbers:

Entering class   # women/ total # PM-AM  Percentage%
2013   2/17   12%
2012   3/19   16%
2011   3/23   13%
2010   3-6/25-28  12%-21%
2009   4/10-12  30%-40%