## Nytimes and algebra, again

9 Feb

Back in 2012, a professor named Andrew Hacker at Queens College in New York wrote an incendiary (to the math community) op-ed called “Is Algebra Necessary?”  I didn’t have a blog back then, but I did have a blog when a snarky and hilarious tweet appeared, and I posted about it/variables and algebra.  Tweet here:

This week, the NYT ran a short interview with Prof. Hacker, seemingly like a mild promo for his next book, “The Math Myth and Other STEM Delusions.”  A snarky and probably unfair summary of his previous books’ titles on sale at Amazon:  Blacks and Whites are separate and unequal in the US, Colleges suck, Politics from 1973, Women and Men are separate and unequal in the US, Rich and poor are separate and unequal in the US, Something maybe about gerrymandering?  My point is, this is an 86 year old man who likes to spin statistics about things people talk about the way Malcolm Gladwell likes to spin anecdata and make people talk about things, and he is also anti-math and pro-arithmetic.

Then I saw a video on facebook with over 4 million views of a woman explaining some “common core math” (see: old post on the wonderful thing that is common core standards) and how stupid she finds it.  But she surprisingly explains the steps carefully and it makes a lot of sense to me (though she skips why we add one of the 5s).  I actually love it: the kids can learn the concepts of why the answer is 30 rather than just a pure subtraction digit by digit shortcut algorithm that they can learn later.  Here’s the link; embedding isn’t working.

Throughout my time tutoring, teaching, and talking math, many, many students and adults have asked me “why do I need to know this?” and “how will this help me in the future?” and the conversations always seem to be two separate conversations.  “Math people” as we are sneeringly called by Hacker talk about something abstract [this is a link to an old but good blog post]: quantitative reasoning and logic skills, the ability to extract relevant information from paragraphs of data, visualization techniques, the ability to not be overwhelmed and taken in by misleading statistics and graphs.

Infamous unlabeled axes and generally “ethically wrong” graph from the Planned Parenthood hearing, from Americans United for Life website [quote from Politifact article]

Then there’s… not-math people?  Who want something more like this website which lists various jobs you use math in, and their median incomes.  Startling to me (I do not know where they get their numbers): they say biologists make medians of 44k, and mathematicians make 94k.  Anyways, mathematicians are used to abstract reasoning and use abstract terms as concrete ones (I can’t tell you how many times a week I say something like “Let’s use a concrete example like the plane” which is still a very abstract concept to many), which might explain the gap in this conversation.

I read an article this morning about the privatization of advanced math education and how rock and roll it is, but also extremely concerning in light of rising inequality.  Great article.  It gives me hope, especially this organization bringing advanced math to underserved communities.  I think that the ideal thing would be to have publicly funded school-year programs like UMTYMP available in as many places as possible, vs. having kids pay to attend summer camps like CTY, which offers some financial aid and also a gem of a paragraph on the financial aid FAQ site:

Families are also encouraged to seek funds from local agencies such as school districts, community service organizations, business associations, civic organizations and religious groups.

Note here that while I have TA’d at CTY summer camps before and had a blast, I never did them as a kid or even know about them.  I spent my summers playing as a middle school kid, and working or taking summer school as a high school kid.  (My high school summers: Health and Driver’s Ed classes, Boeing internship, working at Yoshinoya, working as a private tutor).  I really enjoyed them, but I think I also would’ve benefited from trying any of the various math/academic camps out there that neither I nor my parents knew about.  Then again, a bunch of my friends got sent to hagwon cram schools to memorize things and get great SAT scores during the summer, which sounds awful to me, so I counted myself as very privileged to be working a minimum or zero wage job instead.

I know the Common Core standards are young, but they’re also giving me hope that math is on the right track, and haters are gonna hate but kids are gonna learn and be able to do all those abstract things I said above.  I don’t have a lot to add to the conversation; this post was more to bring the Atlantic and NYTimes articles to your attention.

## Playtime with the hyperbolic plane

2 Feb

Update: Thanks to Anschel for noting that I messed up the statement of the last exercise.  It’s fixed now.  Thanks to Justin for noting that I messed up a square root.  Pythagorean theorem is hard, yo.

About a year and a half ago I explained what hyperbolic space is, specifically by contrasting it with Euclidean space and spherical space.  We’ve also run into hyperbolic groups a few times, which are groups whose Cayley graphs are somehow like hyperbolic space.  More precisely, a group is hyperbolic if, whenever you have a Cayley graph of that group, triangles are $\delta-$thin, which means the third side of any triangle is contained in a $\delta$ neighborhood of the other two sides.  It’s important that the same $\delta$ works for every triangle in the space.

Here the bottom side is contained in a neighborhood of the other two sides, and the triangle looks like it belongs in Star Trek

Here each side is contained in a small neighborhood of the other two sides, and it seems like the triangle is curving inward

Note that triangles in Euclidean space are way totally far from being $\delta-$hyperbolic.  For any big number n, you can make a triangle so that the third side is not contained in an n-neighborhood of the other two sides: just take a 2n horizontal segment and a 2n vertical segment to make an isoceles right triangle.  If is bigger than 2, then the midpoint of the hypotenuse is farther than away from the other two sides.  As usual, this long paragraph could be better done in a picture.

Soooo not hyperbolic: you can make arbitrarily fat triangles in Euclidean space.  Also, the purple line should have $\sqrt{2}}n as its length, not the square root of n.[/caption] I thought today we could just play around with hyperbolicity. I'm running a small reading group on geometric group theory with some grad students, and today we got sidetracked a few times by just basic thoughts about geodesics in the hyperbolic plane. We all thought they were interesting, so here I am trying to share it with you! There are lots of other definitions of hyperbolicity, but I like$latex \delta-\$thin triangles.  Oh I forgot to mention that a nneighborhood of a point/line/shape consists of all the points within n of that point/line/shape.  So, for instance, a 3-neighborhood of a point in Euclidean space is a circle.  But with a taxicab metric, that 3-neighborhood is a squarey circle.

[caption id="attachment_3081" align="alignnone" width="181"] Purple points are all distance three or less from red point

Anyways, I just put in that definition because it’s the first thing you’ll hear or see in a colloquium talk that involves the word “hyperbolic.”  Let’s play with the upper half plane model of hyperbolic space!  Here’s a repeat picture from that October 2014 post (wow that’s when baby was born!  He’s walking around and getting into trouble now, btw.).

Straight lines are ones that go straight up to infinity, and segments of half-circles whose diameters lie on the bottom line

The graph paper lines in this picture are misleading; they contrast hyperbolic geodesics with Euclidean ones.  So the gray lines are Euclidean geodesics, and the colored ones are hyperbolic.  All geodesics in this model are either straight lines perpendicular to the horizontal axis, or semicircles perpendicular to the horizontal axis.  All of the horizontal axis and everything that the straight up and down geodesics end at (sort of like a horizontal axis infinitely far away) represent infinity.

I’ll write down the metric in case you were wondering, but we won’t need it for what we’ll be doing: $ds^2=\frac{dx^2+dy^2}{y^2}$ [I took this formulation from wikipedia].  What this says is that the hyperbolic metric is a lot like the Euclidean one, except that the higher up you go on the y-axis, the less distance is covered (because of that 1/y factor).  More precisely, if you’re just looking at the straight line geodesics, the distance between two points at heights a<b is $ln(\frac{b}{a})$.

All the lines have the same length ln(2).  Blue: ln (8/4), green: ln (16/8)

The other fact we might want to know is that things that look like Euclidean dilations (stretching something like your pupil dilates from looking in a bright light to a dark room) are isometries in this model. You can see that in the picture above: the lines look like they’re stretching longer and longer in the Euclidean metric, but they’re actually all the same length.  Speaking of isometries, if you have any two geodesics (like a vertical line and a big old semi-circle somewhere else), you can find an isometry that sends one to the other.

First question: what do circles look like?  Whenever you have a metric space, it’s nice to know what neighborhoods look like, and the first thing you might want to consider are neighborhoods of points.  Turns out circles in this model look like circles in Euclidean space, but the centers aren’t where you think they are.  For instance, here’s a picture of circles with radius ln(2), which we saw in the straight lines above.

The center of each circle is at the top of its surprised mouth.  The next highest line segment shows that each vertical diameter is actually a diameter (twice the radius).

Notice that the centers of these circles hang a lot lower in the circle than they do in the Euclidean metric!  Isn’t playtime fun?!

Generally when I play with math I throw out a lot of garbage ideas, and then eventually one of them is somewhat right.  Other people apparently think for awhile before they put out an idea.  Anyways, here are some sketches of what I thought a 2-neighborhood of a vertical line might look like:

This is the most subtle joke I have ever put in this blog

Maybe you looked at these and were like “Yen that is nonsense what were you thinking?!”  Maybe you are my advisor or a practiced mathematician.  Let’s go through the nonsense-ness of each of these pictures:

The rightmost picture is a 2-neighborhood of the vertical line in Euclidean space.  We know hyperbolic space is pretty drastically different from Euclidean space, so we wouldn’t expect the neighborhoods to be so similar.  The middle and left pictures have similar shapes but different curviness, and yes we’d expect a hyperbolic neighborhood to look different so those are guesses based in some more intution.  However, let’s try to figure out the actual size of a neighborhood of a vertical line.  We can use our previous pictures, and switch to a ln(2) neighborhood.

Changed my mind this is the most subtle joke I’ve put in this blog please someone get it and appreciate it please please

Here I moved all our ln(2) circles so that their centers laid on the same line.  A neighborhood of a line is just the union of the neighborhoods of all of the points on that line, so if we just keep making ln(2) circles along the line we’ll end up with a neighborhood of the whole line.  So you can see that our actual neighborhood ended up being upside down from my middle picture above.  If this explanation didn’t make sense, here’s [half] a 2-neighborhood of a Euclidean line:

Note how the denser the circles, the closer their boundaries on the left get to becoming that straight line we see on the right.

Actually using Euclidean intuitions and then mixing them up a bit is a great way to play with the hyperbolic plane.  This next exercise was an actual exercise in the book but it is just so crazy I have to share it with you.  It’s just dramatically different from Euclidean space, just like the triangles were.

If you have a circle in the hyperbolic plane and project it to a geodesic segment that it doesn’t intersect (which means for any point on the circle, you find the closest point to it on the geodesic and draw a dot on the geodesic there), the projection is shorter than $ln(\frac{\sqrt{2}+1}{\sqrt{2}-1})$.  Here’s the picture in Euclidean space where this makes no sense:

Third place likes getting on the podium.  I meant, the vertical lines show the projections from the faces to the horizontal line, and you can see they can be as big as you want if you just make bigger and bigger circles.

And here’s a picture in hyperbolic space that might make you think this could possibly just maybe be true.  Any circle will eventually fit inside a big huge circle that looks like the blue one in the picture, so its projection would be shorter than the projection of the blue one.  That means you only have to worry about big huge circles in that particular position.  And by “big huge,” I mean “of (Euclidean) radius n“.

Remember, if we’re just looking at vertical lines, we know how to measure distance: it’s $ln(\frac{a}{b})$.  So if you can show that the small orange circle hits the vertical line at $\sqrt{2}n-n$ and the big orange circle hits it at $\sqrt{2}n+n$, you’ll have proved the contraction property.  Try using Euclidean geometry, and think about how we did the triangles case.

That was fun for me I hope it was fun for you!

26 Jan

This is, as far as I can tell, a great way to succeed in math academia.  But I’m only partway through the process and I’m not married to the idea of being in mathademia (I’m married to my spouse!).  Side story: some years back a professor was surprisingly denied tenure at a university where his wife’s family lived nearby.  He and his wife (and kids) then moved to a different country so he could be a tenured math professor there [it’s a good job].  I do not identify with this story.  I do identify with this: when I was a kid my mom would annually schlep us three kids to California from Minnesota for all two weeks of her allotted vacation time.

Outline of mathademia [I did not know all this til grad school]: you spend 4 years in undergrad somewhere that you want to go/live, then 5-6 years getting a Ph.D. somewhere you learn to enjoy going to/living (though no one cares how long you spend in grad school; I know one professor who took a six year break before going on), then 1-3 years doing a postdoc somewhere you often don’t want to live/go to, then possibly more of those postdocs until you get a tenure-track job somewhere that you better want to live.  After 6-7 years in your tenure track job, you either get tenure and will live there forever, or not and will have to go find somewhere else.  It’s all fairly civilized and organized.  Also, it gets more and more selective the further you go: I regularly hear about people applying to 80 jobs and getting 2-3 interviews and one offer.  Also, if you are romantically involved with someone else in academia, good luck with the two-body problem; almost every academic couple I know has had years of long-distance dating or marriage.

1. Go to college.  While there (4 year liberal arts school or a university that offers PhDs both seem fine), major in math and take as many math courses as you can.  If possible, take graduate courses in math as an undergraduate.  If none are available, ask to take a reading course with a professor or a graduate student [for instance, several schools have grad-undergrad student reading programs like UT, UMD, UCHicago, Rutgers, UConnBerkeley, MIT, Yale,  and more all the time].  For studying abroad, consider Budapest.  I did it and it was great!  I’m still in touch with friends from BSM and there are several in my field.
2. While in college, do research.  Ask a professor for advice on doing a senior thesis project.  During your junior and/or sophomore summer, DO AN REU and get a little money to go to math research camp for a few weeks and hopefully get a peek into the publishing world.
3. GO TO OFFICE HOURS.
4. Also, study for the Math GRE during that same summer if not earlier.  Even if you’re a math hotshot it’s a hard test and you should study for it.  It’s only offered three times a year.  Note: some grad programs don’t require this.  Take the regular GRE too but there’s probably no need to study for it.
5. Take the Putnam.  Do any extracurricular math activities you can.
6. If you followed steps 1 and 2 you should be able to get some strong letters of recommendation for applying to grad school.  So, apply to grad school.  There’s lots of advice out there about this.  Also, while you’re applying to grad school, APPLY TO THE NSF GRFP and possibly NDSEG as well.  Note: this step is a lot of work!

1. Maybe you took some time between undergrad and grad school.  In that case, you’d better brush up on your math!  Some people have success in looking at their old notes/books/homework.  You could also check out these books: All the Math You Missed, Mathematician’s Survival Guide.
2. If you’re a woman, consider doing this incredible summer brush up program that I did.  It’s great.
3. Take 15 minutes and do this exercise.  First, quickly write down a list of five things that you value (for me: food, family, learning, math, creativity/writing).  Then choose one of the things and take five full minutes (time yourself) to write about why you value that thing.  Do so for two other things too.  I did this my first semester of graduate school with my roommate based on an article I can’t find anymore, but roughly was this one.  The point is that affirming your values and sense of identity can help you cope with graduate school.
4. Figure out a physical exercise that you enjoy doing enough to actually do it.  If you’re already a gym rat or sports person, great.  If not, may I suggest Couch 2 5K.  Other things I’ve seen grad students do: rock climbing, cross country skiing, ballroom dancing, triathlons, marathons, swimming, yoga.  Physical activity really helps with the mental strain of first year of grad school.

1. Swim in your own lane.  First and second year it’s easy to compare to other students who are in your same classes/have better or worse preparation than you.  After that it gets a lot harder and a lot more tempting to compare with your cohort.  Try to avoid this.
2. Finish prelims/qualifying exams as quickly as possible, so you can focus on research = primary goal of graduate school.  This is how I studied for prelims: took the courses if applicable, downloaded all the previous exams (generally available on the department website), did one or two exams a week and checked answers with a study group once a week.  Study group = invaluable for problems that you aren’t sure how to solve.  Made a binder of all exams and all solutions (neatly written up) to reread at my leisure before exam.
3. Talk to other graduate students, especially older ones.  Many programs have a big sib/little sib program for first years.  Exploit this.  Grad students know so many things that aren’t on the internet (which professors are good to TA for, shortcuts between classroom buildings, who wants what for exams or reading courses, what seminars to attend, who to ask for help).
4. Publish if possible.  Find collaborators and publish results.  This is far easier said than done.
5. Read read read.  Trawl arxiv every day (takes a few minutes) just to prime some words into your head/see who’s who in your field.  Read.  Reading math is HARD.  You need to do a lot of it in mathademia so you should try to learn how you do it best.  I take extensive notes while reading, others don’t.
6. Give talks.  Every program has somewhere you can give a talk (1st/2nd year seminar, grad student colloquium, junior topic seminars) and you should give at least one before you start doing job talks.  It’s terrifying and then gets better the more you do.
7. Go to seminars!  Every professor who has given me advice has said this to me.  I am not great about it but I think I have sleep apnea/mild narcolepsy.  My advisor is always falling asleep in talks too, which makes me feel better, but then he wakes up and asks intelligent questions which makes me feel worse.
8. Take care of yourself.  Mental health days are legit.  Get physical exercise.  Eat well.  DO YOUR LAUNDRY, for all of our sakes.
9. Go to at least one conference so people know you.  Follow your advisor around and have her introduce you to people in your field.  Try to give some talks at conferences.
10. Applying to jobs is pretty much a full-time extremely stressful job.  So that fall semester of your last year of grad school, don’t expect to get a lot of math done.
11. Write for the future version of yourself who doesn’t understand past you’s cryptic notation.  Write write write.  This is the ultimate goal of graduate school, to write a thesis.

Post doc

1. Write write write.  Publish publish publish.  Collaborate.
2. Make sure people care about your work, somehow (attend conferences, give talks???)
3. ????

Tenure track job

1. Write write write.  Publish publish publish.
2. From my perspective, be superhumanly amazing and incredible.

Tenure

1. Profit from your hard work!  Keep working hard because if you made it this far, you really love math and your work.  I’ve heard many professors say “why would I retire?” but I also know that teaching is draining.

ALTERNATE TRACK, STARTING IN GRAD SCHOOL

1. Become a really good TA, and try to instruct your own courses.  Become conversant in things like flipped classrooms, IBL, clickers, and various pedagogy.  Consider doing math circle, DRP mentorship, tutoring.
2. Write an incredible teaching statement, and personalize your cover letter to each teaching school you’re applying to.  Convince them that you love teaching.  Teach the letter reader something they didn’t know/think about before.  See notes I took from a talk by the president of the MAA:
3. Be an awesome teacher, and continue to do research on the side (depending on your position).

Note that I had a lot more advice for undergraduates than I did for after where I am now (I didn’t follow all that undergraduate advice either).  I also have no metrics really of “success” besides getting tenure, which is not for everyone.  I feel very successful life-wise with my family and blog and triathlons, but as to professional success I am pretty emo.  This blog post is about professional success==tenure.  Or you could be a badass and become a freelance mathematician or a mathematical writer  or anything else you want to be!  You’re getting a Ph.D. in math; the world is your oyster!

Also!  Writing this blog has been very fun and rewarding and one of the best parts is when undergraduates or beginning grad students or other people write to me to ask for advice or just say hey.  I love hearing from you!  I’m on email (yenergy), twitter (yenergy), and instagram (yenergyyy) so hit me up!

## KRINGLE

19 Jan

I was walking through Trader Joe’s the other week and saw a flat package wrapped in opaque wax paper labeled “Almond Kringle.  From Wisconsin!  Limited Quantities available!”  You may know that I love almond everything.  Side story: I love the almond soap they have on Amtrak trains.  A lot.  So much that I tweeted once about how much I love it and where could I find some?  And Amtrak tweeted back to me, and I ended up getting a bottle of soap that doesn’t have a flat bottom (it screws in to the train) so I can’t use it unless I empty the soap into another container.  And it was great.

Also, I’m from Minnesota, so if I run into something in Texas that says “from the midwest!” I’ll buy it (also I am a sucker).  And “Limited quantities available,” because I am a sucker, means that I’ll buy it.  All the ingredients were in place for me to get this magical, amazing delicious experience (I’m not the only one who feels this way).  After getting home and taking a bite of the oval shaped pastry that came out of the mystery bag, I laughed and couldn’t stop laughing for five minutes.  My husband had a bite, and then we both texted all the people we knew from Wisconsin and told them that while we loved them, they are not the best thing to come from Wisconsin.

After we polished off our TJ’s Kringle in three days (it’s a bit over a pound, and contains at least one pound of butter), I decided to try to make my own.  The official recipe will have you use just over a pound of butter and take three days to make all the layers.  But there are plenty of homemade ones out there that do not take three days or tons of rolling, and that’s what I did.  You can stuff kringles with anything, but the TJ’s one was filled with marzipan (yum) and I did a coconut and almond filling for mine.  Many recipes were just butterscotch (butter + sugar).

I also was still in a bit of a funk when I decided to impulse make the kringle, so no ingredient photos.  The dough and recipe is super simple, but this was my first time making a filled pastry so I did a bad job (who knew you have to actually close it all the way, or the filling all falls out?!)

Dough or dough not, there is no try

The dough was just cutting butter into flour, then adding in yogurt (the recipe called for sour cream, but I use yogurt as a substitute for most white goops like mayo, sour cream, and sometimes butter/margarine/shortening).   The dough is VERY STICKY.

Though if you want a doughnut this is not the recipe for you

Wrap it up in plastic wrap and stick it in the fridge for a while (all day is great, or overnight).  Meanwhile you can put together the filling, which is another cup of butter beaten with brown sugar and shredded coconut and almond pieces.  I put my coconut in a dry pan on the stove for a few minutes, until lightly brown and toasty.  I also used sweetened shredded coconut, unsweetened flaked would also be fine.

Happy MLK Day! You could also think of social justice once a week all day, perhaps AllMond ays?

Now you split the dough into two halves, and leave one in the fridge while you roll out the other on a very floured surface (remember, sticky) until very, very thin.  Far thinner than expected for a person who’s never made a filled pastry before.

I had some friends over while I made this kringle and we were watching Clueless and at this point I kept saying I was ‘rollin with my homies.’ Actually this isn’t true because I don’t have friends to watch Clueless with while baking.

Filling goes in one long line down the middle.  If you want to make two separate danishes, like lines, then stop before the ends so you can tuck down the top.  I put my two halves together so spread the filling pretty far to the ends.

If baking was Hollywood we’d celebrate avant garde fil(ling)makers

The recipe called for some fancy cutting and braiding, but didn’t have pictures.  I attempted this on the first half and then all the filling went out through the holes.  So, good luck to you if you decide to go the braided danish route- check for seals in your dough!  Instead, I recommend just folding the two sides over and making a less beautiful but more structurally sound tube of dough.

Kringles at TJ’s come from O&H bakery in Racine, Wisconsin. The other option besides the O is an H shape. This is not true.

See all the holes in my kringle above?  Don’t do that.  But do make two tubes and tuck them together to make the beautiful wreath shape of the kringle.  Bake at 375 until golden brown and it smells SO GOOD and it’s SO GOOD.  Even if it doesn’t turn out beautiful.

Easy coconut-almond kringle, adapted from Taste of Home

2 c flour

1 lb (4 sticks) butter

1 c full-fat plain yogurt (or sour cream)

1 c brown sugar

2 c sliced almonds

2 c shredded coconut, toasted

Cut 1 c (2 sticks) butter into the flour, until you have pea-sized chunks or smaller of butter.  Mix in the yogurt well, until you have very sticky dough.  Cover in plastic wrap and refrigerate all day or overnight or at least a few hours.

Beat the brown sugar with the remaining cup of butter.  Toast the almonds and coconut by putting each in a dry pan over medium heat for a few minutes, stirring lightly a few times, until they smell yummy and look lightly brown/toasty.  Mix the almonds and coconut (or whatever filling of nuts/fruits you want here) in with the butter and brown sugar mix.

Split the chilled dough into two halves.  Preheat oven to 375.  Roll out dough very thin into a rough rectangle, then put one half of the filling in one straight line down the middle of the dough.  Either cut and braid the outsides in, or fold them over.  Do so with both halves, then push the halves together into an oval shape on a baking sheet.

Bake for 25 minutes, until lightly browned.

## Pineapple upside-down cake, using box mix

11 Jan

I’m alive!  My fingers and palm are tingling a bit as I type this, because I contracted a particularly virulent strain of hand, foot, and mouth disease from my baby (it’s not as bad as it sounds).  Yesterday I had a 103.1 fever, and last week he had a 103.1 fever.  I took him to the ER, I gave myself a Tylenol and a nap.  It’s been mildly hectic.  As I’ve said before, I’m so impressed with stay-at-home parents and I don’t know how anyone gets anything done with their kids (like, for instance, a Ph.D. thesis).  Baby had a mild fever the day before his crazy one, so I kept him home with me.  We went to the store, and I thought hey, it’s never too early to introduce kids to the things you love to do, so let’s bake a cake!

I’ve blogged before about a super easy pineapple upside down cake, but that required some amount of measuring so I decided to just go with a box cake.  Semi-homemade all the way, snobbery be damned!

If Rooney Mara and Al Pacino got together and decided to combine last names, would they be the Maracinos?  Also that would be gross because she is 30 and he is 75 and unrelatedly he is 5’7″.

The topping is the same as for the easy-peasy amazing cinnamon buns I’ve done over and over again: put a stick of butter in a pyrex in a cold oven, and turn it on.  You could definitely do this with only half a stick of butter instead; I just had a frozen stick so used the whole thing.

Meanwhile, drain the pineapple rings and you’ll get just under a cup of pineapple juice.  This is great, you use it to make the cake, following the box instructions and subbing juice for water.  Also I’m not so great at following instructions, so I used yogurt instead of butter (I got the “butter recipe” box).

Do you ever worry you won’t measure up?

That even with all the eggstras you’ve added to the world, the whisks involved with you weren’t worth the benefits?

I mentioned that I didn’t feel like measuring, so I didn’t, but you probably know how big half a cup is, and can eyeball about that much of full fat yogurt.  (Remember, we’re using yogurt to replace butter so we need the fat).

It’s important to remember that we were all once babes in the woods, and also it doesn’t matter how effective/efficient you are, but that you made an effort.

If you were starting with half a stick of unfrozen butter, it’s probably melted by now.  If like me you had a stick of frozen butter slowly melting in your oven, you have some time now to play patty cake or clean up or sit.  Whatever floats your boat.

Once the butter is all melted, take it out of the oven and sprinkle brown sugar all over it, then lay down the pineapple rings and sprinkle maraschino cherries everywhere they’ll fit.  Pour on the batter.  I put in about half the batter, then sprinkled it with coconut, and added the other half to cover the coconut.

Sometimes you feel like you’re a ringer, but you’re just cherry-picking examples where you don’t fit in.  (Incidentally I’ve been using the sports idiom “ringer” wrong my whole life I thought it was a great person you save for the end who will win the game what’s the word for that?)

Cakes are like onions; they have layers! (Shrek joke, does that date me?)

Bake it for 40-45 minutes, let it cool for a bit, and then invert it onto a plate.  Honestly the hardest part of this cake is finding something to invert the cake onto.  I ended up picking up the whole thing and putting it back into the Pyrex after, for storage.

Everything will be okay, just turn that brown upside down!

Even if you miss, there’ll always be an imprint of your attempts at success (I located the sticky pineapple ring and put it back on the cake, btw).

Pineapple upside down cake, adapted from Betty Crocker

1/4 c (half a stick) of butter

1/2 c brown sugar

1 can pineapple slices in juice

1 small jar maraschino cherries

1 box yellow cake mix

3 eggs

1/2 c full fat yogurt

1 c sweetened flaked coconut

Put the butter in a 13 by 9 dish, and put it in the oven.  Turn to 350.

Meanwhile, mix the eggs, juice from the pineapple, cake mix, and yogurt until almost totally smooth.  This is a good place for kids to help!

Once the butter is melted, sprinkle the brown sugar evenly over it, then lay in the pineapple slices and put in the maraschino cherries wherever they’ll fit (take off the stems).

Pour half the cake batter oven the topping, then sprinkle the coconut all over it.  Pour the rest of the cake batter over.

Bake for 40 minutes or until brown.  Let cool for 10-15 minutes, then run a knife all along the edge and invert onto a plate.  Eat.

17 Dec

I had a draft of this post but then a woman posted a thing on her blog that blows this out of the water so please read her post.  She exploded on the math scene a few weeks ago with her incredible amazing readable Ph.D. thesis which is my new goal in life and I think this is an achievable goal.  Here’s a short post about that amazing incredible thesis.

To encourage you to read that thesis (please do read it, no matter what level of math you are especially if you are math-phobic), here is an excerpt:

I like to imagine abstraction (abstractly ha ha ha) as pulling the strings on a marionette. The marionette, being “real life,” is easily accessible. Everyone understands the marionette whether it’s walking or dancing or fighting. We can see it and it makes sense. But watch instead the hands of the puppeteers. Can you look at the hand movements of the puppeteers and know what the marionette is doing? A puppeteer walks up to you and says “I’m really excited about figuring out Fermat’s Last Thumb Bend!” You say, “huh?” The puppeteer responds, “Oh, well, it’s simply a matter of realizing that the main thumb joint has several properties that distinguish it from…” You’re already starting to fantasize about the Zombie Apocalypse.

Don’t you want to read it now?  And also be the author’s best friend?  That’s my reaction anyway.  If the thesis is too long, at least read the first post linked, here’s a quote.  This has been shared by so many of my Facebook friends and in my math communities and the post clearly struck a chord.

My experience discussing math with mathematicians is that I get dragged into a perspective that includes a hierarchy of knowledge that says some information is trivial, some ideas are “stupid”; that declares what is basic knowledge, and presents open incredulity in the face of dissent.

Anyways, here’s my original post that I drafted some time ago.  Though I might add that after I was mildly eviscerated by some professors during the question part after a talk I gave (so I’m still up at board and audience is still sitting and there were like 30 people at least there), one student came up to me and said “don’t let the haters get to you.”  It’s the best thing anyone has ever said to me after a talk, and now we’re friends, and maybe it’s a coincidence and maybe it’s not that he’s black (I can count on one hand the number of black male mathematicians I’ve interacted with, and I only know black female mathematicians from that awesome EDGE program).

I think all graduate students feel inadequate at some points, and also isolated in that feeling, which leads to imposter syndrome [this is a really good link].  A few weeks ago, I had lunch with a prominent mathematician (A) who said that all us women at UT looked happy, and in contrast she remembered grad school being extremely difficult.  Another professor remembered that when they were in grad school, A had seemed happy too.  We all look and seem fine, but we aren’t constantly happy, and that’s okay, especially if we recognize that we aren’t isolated in this sadness.

Anyways, me time!  We’ve got a paper from that awesome summer research program in the galleys, and I’ve written a zeroth, error-ridden draft of a project that I’ve been working on for just under a year.  My blog is 3 and I occasionally get compliments on it, my baby is 1 and I often get compliments on him, and I’m finally sleeping through almost every night.  My brain is back from its pregnancy/new baby/sleep-deprived state, my spouse is incredibly supportive and also supports us financially, so I have much less to worry about than many people.  I have my health.  I enjoy tremendous privilege.  And look at this bibimbap I made for dinner!

I included all that awesomeness to highlight how, even when life is going great and so Instagrammable, you can still feel crappy.  We just have one life so it’s hard to compare with others.  For instance, by the time she was my age, my mom had left her country on a boat and with it everything she’d ever had or known, and stayed in a Korean refugee camp for months, and moved to freezing Minnesota from tropical Vietnam, and worked every possible job, and had a two year old and a husband and had built a life despite having a stroke shortly after coming here.  My mom’s a tough cookie.  I hope someday my kid can say that about me, because right now I feel more like a soft but also inexplicably burnt piece of dough.

What are the anxieties plaguing me?  Oh, the usual, which I’m sure lots of grad students feel sometimes:

• I’m not good enough at math.  I’ll never be smart enough/fast enough/good enough to solve real problems.
• Nobody cares about my research; it’s trivial and stupid.  And when I do figure out things they are trivial and stupid, and I’d spent months following the stupid path and not seeing the trivial conclusion.
• I’ll never finish.  Everything will always be wrong, and when I do write things down see bullet points 1 and 2.
• I’m a bad person.  I should be contributing to society and doing good instead of sitting all day banging my head against the chalkboard.
• I don’t deserve x,y,z (fill in with your favorites, my go-tos are my supportive husband, sympathy and slack because I have a baby, a day off because I don’t get anything done on my days on)

Anyways, I’m feeling better nowadays.  When I started grad school, a professor told me “Don’t let your highs get too high or your lows get too low,” which is good advice.  My favorite grad school advice: “Swim in your own lane.”  That sort of deals with almost all the anxieties in five words.  But I’m not trying to offer solutions to those anxieties, just that they exist and I feel them sometimes and maybe so do you, and that’s okay.  Even mathematicians are mere mortals.

Here’s a hilarious picture of my sweet baby to wrap up this post!

## Biscuits and Gravy, super easy

16 Dec

About a year ago two of my friends held a Southern dinner party, where a bunch of displaced Southerners brought comfort food.  It was just as delicious as it sounds, with greens, fried chicken, fried green tomatoes, okra, pies, shrimp and grits… and biscuits and gravy.  I’ve always loved biscuits and gravy and I associate this heavy breakfast with long road trips through the flyover states as we trekked from Minnesota to Texas or California in our minivan, stopping at diners with big signs that said “RESTAURANT” or “EATS.”  So at this dinner party I asked the people who brought the awesome gravy for their recipe, and it was so simple that I memorized it and have made it several times since.  It’s literally “1, 2, 3, lots.”  Then for biscuit recipes I’ve done my friend’s secret family recipe as well as one from allrecipes that I’ve made several times (because it’s on the internet and my friend’s is written in a book).

Biscuits and gravy is great because once you pop the biscuits in the oven, you have just enough time to make gravy and everything is hot and ready at the same time.  So let’s start with the biscuits.

Not to be confused with bisque-it’s a smooth creamy soup often made with seafood. These are small rolls of unyeasted bread

Several years ago I went on a huge biscuit kick, the first time I lived in an apartment with a kitchen (not a dorm).  My dear friend/roommate (now non-coincidentally a math educator) and I made so many biscuits and so much homemade jam within a few months.  It was just as wonderful as it sounds.  If you are young I highly recommend eating a ridiculous amount of carbs for a short while, because your metabolism and stomach will likely not be so great in the future [I am young but I do not think I could eat half a pan of biscuits by myself in one sitting anymore].  Anyways, biscuits are really easy!  Mix flour with a few other things (salt, baking powder, sugar), cut in your fat (shortening and/or butter), and then mix in your liquid (milk or buttermilk or vegan substitute) until sticky dough is formed.

Cloudy with a chance of meatballs? Not quite, there are biscuits in the forkast today

Throw some (1/4 cup) flour on a clean counter or table, and lightly knead the dough until it’s smooth (not smooth and elastic like yeasty bread dough, just not lumpy).

My husband really doesn’t appreciate my puns. Oh well, you can’t always get what you want. But if you try sometimes, you just might find you get what you knead. Here, I’m kneading biscuits.

Then pat or roll it out, and cut it out with a glass dipped in flour.  Roll the scraps together and cut out more.  I always end up with one funky biscuit, the last one made of tiny pieces sadly patted together into an approximation of a circle.

That last biscuit is always teased, and he always responds “cut it out, guys” and they respond “that’s what we did but what are you?”

Then toss those beauties into the oven on an ungreased baking sheet, and get ready for gravy!

The recipe said it makes 9 but I’m not good at uniformity. It makes me too ten-se.

You need one pound of breakfast sausage (I like Jimmy Dean’s sage sausage), two tablespoons of flour, three cups of milk, and far more pepper than you think is reasonable.  Brown the sausage…

Making breakfast for the family before everyone is up definitely gave me brownie points

Then sprinkle it with the two tablespoons of flour and stir until the meat is evenly covered with flour; by then the flour should be browned too.  Pour in the three cups of milk.

I tried to milk this good deed for all it’s worth

Now it looks like greasy sausage floating in milk, but bring it to a simmer and let it simmer for awhile, stirring, until it’s thick and turned into gravy.  Then add way more pepper than seems necessary.

Even if I mess up, my family still eats it and loves me. It’s all gravy.

Those biscuits should be wrapping up in a few minutes.  To serve, split a biscuit and put it on a plate, then drown it in gravy.  I actually went back to sleep after making this and my family ate it without me (this is what happens when you have a baby who doesn’t understand time zones) and merely dabbed with gravy.  Nope, drown it!

Biscuits and gravy (biscuits adapted from allrecipes, gravy from folklore)

2 c flour +more for dusting

1 TB white sugar

1 TB baking powder

1 tsp salt

1/3 c butter

1 c buttermilk

Preheat oven to 425.  Whisk together the flour, sugar, baking powder, and salt, then cut in the butter until crumbly.  Slowly stir in the milk until it’s doughy and pulls away from side of bowl.

Turn dough onto a floured surface and knead (they say 15-20 times; 10 is fine) lightly, then roll out to 1 inch thickness and cut rounds with a glass dipped in flour.  Place on an ungreased baking sheet, and bake 13-15 minutes.

Meanwhile…

1 lb sausage (I’ve enjoyed Jimmy Dean’s maple as well as hot, and I hear good things about sage)

2 TB flour

3 c milk

black pepper

Brown the sausage in a large saucepan or medium sized pot over medium heat, crumbling/breaking it up into chunks using a wooden spoon.  Sprinkle with the flour and mix well until flour is browned, then pour in the milk.  Turn up the heat and bring to a boil, stirring occasionally, then lower heat and let simmer until thick/coats the spoon.  Stir in lots of fresh ground black pepper (like 2 tsp or more).  Serve on the biscuits, which should be done by now!