
title: Dropping out of Grad School
author: Colton Grainger
date: 20200620
status: emotional

## Summary
After 1.5 years in CU Boulder's math PhD program, I had "too many fish to fry" (a conflagration of conflicting commitments!), and signed papers to take an indefinite leave of absence.
I'm glad to have now discerned that, after all, I won't go back to the math department (as much as I would love to enroll in classes) on a teaching assistantship, because would rather "[work to be a winner, baby](https://mariedavidson.bandcamp.com/track/workit)" by breaking into the world as a "[tech professional](https://candor.co/)".
The following folks were instrumental in helping me realize that I could (and in fact should) pivot in my career trajectory: Agnès, Richard, Peter, Divya, Sam, JQ, Yu.
I don't really owe anyone an explanation, but since I might later be curious why I'm pivoting, I've compiled the following reverse chronological entries from a "working journal" I started in the style of Philip Guo, Issa Rice, and Nadia Egbhal between 0.5 and 2 years' time in grad school.
## 20200528
Have a phone interview today with [Jelli](https://www.crunchbase.com/organization/jelli).
Following the advice of , I'm preparing answers to the following ten "very basic interview questions that come up all the time", relative to my application for an entrylevel software engineering position at Jelli.
## 20200420
I moved to Boise, Idaho, my hometown, after [getting the bad idea](https://en.wikipedia.org/wiki/Mescaline) to leave Olympia and try to live in Tacoma.
## 20200331
Found out yesterday I didn't get the NSF
GRF for 2020 ([application documents](https://github.com/coltongrainger/fy20nsf)).
Reflecting on this news (rather early in the morning):
1. I think have been avoiding certain life tasks for want of superficial reward.
2. Had I gotten the GRF, I would've leveraged this funding to exacerbate power struggles in my "vertical" relationships (namely avoiding TA duties), rather than building horizontal relationships (what Alder describes as 'community feeling').
3. Now, since I am no longer tied to Boulder, I have freedom to choose where I want to live: and I want to live in Houston, TX.
Here're sections of texts I read to mull over my (vocational) tasks as distinct from the tasks of others.
### Tao Te Ching, lyric 9, translated by Aleister Crowley
(Originally quoted to me by Dave Spring 2014 after poorly passing Differential Equations.)
Fill not a vessel, lest it spill in carrying. Meddle not with a sharpened point
by feeling it constantly, or it will soon become blunted.
Gold and jade endanger the house of their possessor. Wealth and honors lead to
arrogance and envy, and bring ruin. Is they way famous and thy name becoming
distinguished? Withdraw, thy work once done, into obscurity; this is the way of
Heaven.
### Bhagavad Gita, verses 3.273.35, paraphrased from Edgarton Franklin
Material nature's Strands perform all actions. And one whose soul is deluded by ego imagines: 'I am the agent behind these actions.'
Yet one who knows the truth, O mighty Arjuna,  'The Strands act upon the Strands'  is not attached to actions.
Bewildered by material nature's Strands, many attach their Self to these Strands' actions. But those of complete knowledge cannot disturb these dull folks of incomplete knowledge.
So Arjuna, surrendering all your activities unto Me, fixing your mind on your highest self, being free from longing and selfishness, cast lethargy aside and fight!
Those who follow this doctrine of Mine, full of faith and not murmuring, are released from their karma bondage.
But those who  murmuring against it  do not follow my doctrine, are deluded in all their knowledge; know that these fools are lost.
One acts according to their own material nature  even the wise  as all beings follow their nature; what can repression accomplish?
Of every sense, upon the objects of that sense, longing and loathing are fixed. But one should not fall under their power, as both are foes.
Better one's own duty, (tho) imperfect, than another's duty well performed.
Better death while performing one’s own duty  another's duty brings danger.
### The Courage to Be Disliked, page 186, Ichiro Kishimi and Fumitame Koga
(Recommended to me by Scott this last Winter.)
Youth: But! When one is praised by another person, one becomes truly aware of
one's ability and regains one's courage. Please do not be stubborn about this
point  just acknowledge the necessity of giving praise.
Philosopher: No, I will not acknowledge that.
Youth: Why not?
Philosopher: The reason is clear. Being praised is what leads people to form the
belief that they have no ability.
Youth: What did you say?
Philosopher: Shall I repeat myself? The more one is praised by another, the more
one forms the belief that one has no ability. Please do your best to remember
this.
Youth: Do such foolish people even exist? It's got to be the other way around!
It is as a result of being praised that one becomes truly aware of one's
ability: isn't that obvious?
Philosopher: You are wrong. Even if you do derive joy from being praised, it is
the same as being dependent on relationships to your perceived superiors, and
implicitly conceding that you have no ability. Because giving praise is a
judgement that is passed by a person of ability onto a person without.
Youth: I just cannot agree with that.
Philosopher: When receiving praise becomes one's goal, one is choosing a way of
living that is in line with another person's system of values. Looking at your
life until now, aren't you tired of trying to live up to your superior's
expectations?
Youth: Um, well, I guess so.
Philosopher: First, do the separation of tasks. Then, while accepting each
other's difference, build equal horizontal relationships. Encouragement is the
approach that comes next.
Youth: So, concretely speaking, how does one go about this? One cannot praise,
and one cannot rebuke. What other words and choices are there?
## 20200317
Happy belated Pi Day! I have spent the last month or so learning how to "write idiomatic python programs" by studying notes from Jake Vanderplas [@Van16], Wes McKinney [@McK17], Michael Eichberg [@Eic18], John Guttag [@Gut16], and others [@Sha17]. Here's a bibliography.
### Project Development
A summary of [@Eic18].
> The goal [of these notes] is to enable you to systematically carry out small(er) commercial or opensource software projects.
> Basic knowledge of objectoriented programming concepts is necessary.
A summary of [@Sha17].
> Just write down what you think your process is and
what problems you seem to have. At this stage you might have no idea how you
work because you aren’t very experienced. To help you I’ve compiled a list of
questions:
>
>  Do you tend to make defective code with no idea why?
>  Do you keep piling code on top of code until there’s just a huge mess?
>  Do you get past the first implementation of your project and have no idea how to take it further?
>  Do you feel inferior or like a fraud who will get caught?
### "Idiomatic" Python
A summary of [@Gut16].
> When you have finished this book you should have [...] learned a systematic approach to *organizing, writing, and debugging mediumsized programs*.
A summary of [@Van16].
> *A Whirlwind Tour of Python* is a fastpaced introduction to *essential features [e.g., errors and exceptions, modules and packages]* of the Python language, aimed at researchers and developers who are already familiar with programming in another language.
A summary of [@McK17].
> This book is concerned with the nuts and bolts of *manipulating, processing, cleaning,
and crunching data in Python.* My goal is to offer a guide to the parts of the Python
programming language and its dataoriented library ecosystem and tools that will
equip you to become an effective data analyst.
### "Pythonic" SQL
From the introduction to [@Cop15].
> SQL is a powerful language for querying and manipulating data in a database,
> but sometimes it’s tough to integrate it with the rest of your application.
> You may have used string manipulation to generate queries to run over an
> ODBC interface, or used a DB API as a Python programmer. While those can be
> effective ways to handle data, they can make security and database changes
> very difficult.
>
> This book is about a very powerful and flexible Python library named
> SQLAlchemy that bridges the gap between relational databases and traditional
> programming. While SQLAlchemy allows you to “drop down” into raw SQL to
> execute your queries, it encourages higherlevel thinking through a more
> “Pythonic” and friendly approach to database queries and updates. It
> supplies the tools that let you map your application’s classes and objects
> to database tables once and then to “forget about it,” or to return to
> your model again and again to finetune performance.
>
> SQLAlchemy is powerful and flexible, but it can also be a little daunting.
> SQLAlchemy tutorials expose only a fraction of what’s available in this
> excellent library, and though the online documentation is extensive, it is
> often better as a reference than as a way to learn the library initially. This
> book is meant as a learning tool and a handy reference for when you’re in
> “implementation mode” and need an answer fast.
>
> This book is intended for those who want to learn more about how to use relational
databases in their Python programs, or have heard about SQLAlchemy and want
more information on it. To get the most out of this book, the reader should have
intermediate Python skills and at least moderate exposure to SQL databases. [...] If you are new to SQL and databases, check out *Learning SQL* by Alan
Beaulieu [@Bea20]. These will fill in any missing gaps as you work through this book.
## 20200205
MWE for the image archive.
## 20200121
In `ncar_pylib`, there's no module `MySQLdb` nor module `pymysql`. But SQLAlchemy can still connect via the connection string (c.f. )
```
mysql+mysqlconnector://:@[:]/
```
through `mysqlconnector`, which *is* available.
## 20200120
At least in `Btree` indexes and in group theory, a "transversal" refers to a unique set of "class" representatives.
```
[ad. L. transversus turned or directed across, pa. pple. of transvertĕre: see
transvert. Cf. F. transverse (16th c.).]
```
## 20200118
I found Philip's sample images on the SIParCS google drive and feel like a straight fool for not knowing they were there. I now have 7.4 GB of raw images to use as a test image database.
Moreover, I should also include the logbooks of the USS Jeanette.




Well, I'd at least better be able to connect to
```
rdadb.ucar.edu
```
but I can't even seem to do this with
```
globalprotect connect portal gp.ucar.edu
```
Erg! But there's hope, if I shell into Casper first (or maybe just use my work laptop) then I can access
```
mysql h rdadb.ucar.edu u p images
```
with no problem. Moreover
```
MySQL [images]> show grants for dssdb@localhost;
GRANT ALL PRIVILEGES ON `images`.* TO 'dssdb'@'localhost'
```
so that if I create the user `dssdb` on my local mysql server, and am able to inject metadata there, porting over to Casper shouldn't be too difficult.
I have through MLK day to do it. Yikes!
```
bash4.2$ mysql h rdadb.ucar.edu u dssdb p V
mysql Ver 15.1 Distrib 5.5.56MariaDB, for Linux (x86_64) using readline 5.1
```
## 20200117
What do I need for yoga during the next couple of months? Christina lists:
1. An open mind and a commitment to learning.
2. A journal.
3. A notebook and pen.
4. A good mat, a mat towel.
5. Layers and clean clothing.
6. Eating utensils, snacks, packed lunches.
7. Consider dropping or reducing caffeine, sugar, smoking, social media, etc.
8. Extra support. We encourage other modalities (i.e. therapy, acupuncture, massage, etc.) to complement yoga.
9. A light heart.
## 20200113
### Bibliography
Here's a bibliography for some "[gymnastics](attached/1984iyengarymca.jpg)" that I'm getting into.
```
1966iyengarlightonyoga
2014hansennettersanatomycoloringbook
1997ellisclinicalanatomy
2002iyengarlightontheyogasutrasofpatanjali
2010freemanthemirrorofyoga
2009adeletheyamasandniyamasexploringyogaasethicalpractice
2000rothschildthebodyremembers
2004naparstekinvisibleheroes
2004vanderkolkthebodykeepsscore
2015roseuntangled
2017shermanalexieyoudonthavetosayyouloveme
2006tharpthecreativehabit
2012copethegreatworkofyourlife
2000rothschildthebodyrememberscasebook
2004alteryogainmodernindia
2005demicheliselizabethhistoryofmodernyoga
2010singletonyogabodytheoriginsofmodernposturepractice
2017mallinsonsingletontherootsofmodernyoga
2018cohentheupanishadsrouteledge
2016ithamarexploringthebhagavadgita
2000snyderreaderprosepoetryandtranslations
2010snyderthepracticeofthewild
2000desalvowritingasawayofhealing
2014snydermartinnobodyhomewritingbuddhismandlivinginplaces
```
## 20200110
[](http://blog.inechi.com/2019/11/2019.html)
From Inés Estrada, March 2019.
## 20200104
I might be motivated to work *for a particular person* rather than on *a specific project*.
This style of motivation is appropriate because I've given up on logging time for myself.
From my experience with kanban and without a cell phone over the last 3 months (since failing two prelims this Fall), I recognize I just shouldn't *actively* track myself when I'm "working on myself". (I have some *passive trackers*, e.g., time series data for my heartrate, my sleep, and my approximate location. But I don't have to remember do anything to collect this data, and I get to analyze it post hoc.)
At the same time, I *would like* to actively track myself, so I'm trying to be attentive (when I'm working) to *whom* I feel I am working for, rather than fretting to much about *what* I am doing.
 chores for myself
 rdai docs for Matt
 rdai database for Tom
 topology notes for Agnès
 algebra notes for Peter
 analysis notes for Sergei
## 20200101
From this summer with Sam.
## 20191128
Visited my folks in Idaho. Stopped going to classes once I got back to Boulder.
## 20191107
I am working as a student visitor for [DECS](https://web.archive.org/web/20191221123926/https://staff.ucar.edu/browse/orgs/DECS) at NCAR.
## 20191028
I present on the Research Data Archive's [image repository](https://github.com/coltongrainger/rdaimagearchive/) for the [CU STEMinar](https://web.archive.org/save/https://www.colorado.edu/csl/steminar/fall2019steminarschedule).
## 20190924
I present on [Lazard's](http://www.math.harvard.edu/~lurie/252xnotes/Lecture2.pdf) [theorem](http://www.math.harvard.edu/~lurie/252xnotes/Lecture3.pdf) for the [CU topology seminar](https://math.colorado.edu/seminars/?date=20190924).
## 20200901
Pretty sure I failed some prelims. Opps. Quit vaping.
## 20190825
I am teaching [Math 2510001 Introduction to Statistics](https://math2510.coltongrainger.com) this fall.
## 20190731
I present [Towards Categorical Metadata](https://www.youtube.com/watch?v=wURNDpfBS4Q) for SIParCS at NCAR.
## 20190704
Fourth of July BBQ with Janet and the SIParCS cohort. Janet and Ian left town to visit their folks, leaving me alone at 858 9th St for about a month.
## 20190604
Since I'm liable to forget, I'll describe my current "PIM schema" by cataloging
 my `$HOME` directory,
 what I have on paper, and
 software I subscribe to for managing projects.
### `$HOME`
I have a Lenovo T420, whose name is `lobster`. My home directory looks something like
```
colton@lobster:~$ tree L 1
.
├── art
├── blog
├── coltongrainger.bib
├── cv
├── Dropbox
├── fy
├── journal
├── lec
├── lit
├── mus
├── pho
├── raw
├── README.md
├── rec
├── rote
└── wiki
```
During "fiscal year 2019" (i.e., Jun 2018 to May 2019), I commonly worked commonly in
 `fy` (projects for the "fiscal year")
 `wiki` (materials for )
 `raw` (scanned handwritten notes, hence `raw`) and
 `rote` (tab separated files for mnemosyne).
The previous two years (modulo a few details) look like
```
colton@lobster:~$ tree L 1 fy/18
fy/18
├── 201709jobapps
├── 20180416offerlettercuboulder.pdf
├── 20180427picklebricapplication.txt
├── 20180618tutoring
├── bulma0.7.1
├── codingwithkids
├── cogrwebpage
├── coq
├── datamanagementplan
├── diagnostic
├── dishwashing
├── eo
├── fscssinterviews
├── fscssprivate
├── fscsswiki
├── fscsswork
├── gradapps
├── gradfunding
├── grapapps.bak
├── hakyll
├── leadinglesson
├── logos
├── mentoring
├── mnepscript
├── notedown
├── num
├── odes
├── PreTeXtmathbook
├── prob
├── py
├── PythonDataScienceHandbook
├── rcf
├── spokenword
└── textemplates
```
and
```
colton@lobster:~$ tree L 1 fy/19
fy/19
├── 201806alg1top1ana1.pdf
├── 201806until201902.pdf
├── 201903topologyseminars.pdf
├── 20190511top2omnibus.pdf
├── alg1
├── alg2
├── clothing
├── cu3d
├── diffgeo1
├── dircolorssolarized
├── examples
├── internships
├── mitschriebwiki
├── napkinoutline
├── neuralnetwork
├── orientation
├── prelims
├── prob1
├── projectideas
├── recordsandoldtodo
├── ripser
├── RISE
├── safe
├── slowpitch
├── soml
├── stylefiles
├── summerreview
├── ta
├── TDAstats
├── top1
├── top2
├── triposcourseguides
├── unicode.sh
├── vimtexfold
└── yst
```
About 75% of repositories I have on github (for lack of a better name) are prefixed with, e.g., `fy00`, to indicate that they are locally saved under, e.g., `$HOME/fy/00/`.
I only have digital directories under `fy` back to (about) 20092010, when I was spending quite a bit of time after school with "kdawg wangalicous" and the policy debate topic was
> Resolved: The United States federal government should substantially increase social services for persons living in poverty in the United States.
```
colton@lobster:~/fy/10$ tree
.
├── 2009apologytodavidson.txt
├── 2009GDINietzscheK.pdf
├── 2009GDIObjectivism.pdf
├── 2009UTNIFCarceralArchipelagoK.pdf
├── 2009UTNIFMarxismK.pdf
├── 2009UTNIFStandpointEpistemologyCritique.pdf
├── 2010ecopandabehemoth.pptx
├── 2010ganatosnaryslenderscript.txt
└── 2010meinlieblingsplatz.txt
```
This coming year looks like
```
colton@lobster:~$ tree L 1 fy/20
fy/20
├── aiwatch
├── analysis
├── appliedanalysis
├── nsfgrf
├── pandas
├── rdaimagearchive
├── siparcs
└── topologyprelim
```
Last year, I used my dropbox to sync notes (written in Notability on my tablet) and pdfs.
```
colton@lobster:~$ tree L 1 Dropbox/
Dropbox/
├── Crypted
├── Downloads
├── export
├── import
└── todo.txt
```
This year, I plan to keep pdfs in google drive and designate dropbox as my download folder. (I have an SD card for torrent files >2GB.)
### Paper
I am abandoning *taking notes* on my tablet, because the generated pdfs were large (~100MB) and I realized that Notability was just another (however sleek) WYSIWYG editor in which I wasted my time and was often frustrated with formatting. The alternatives look like
 notes in `latex` or `markdown` on my laptop
 notes in a (chronological) series of 13x21 cm, unruled, [cahier journals](https://web.archive.org/web/20190516162841/https://us.moleskine.com/cahierjournalbrown/p0408)
 notes on paper, scanned as dated pdfs to `raw`
I may scan the cahier journals pages (as done by mpacer here ). Primarily however, in leaving the tablet for paper, I'm following :
> ... I have specificity for writing implements on par with my vim configuration. I use a very specific kind of notepadunruled, cheap, abundant, lowweight stockand similarly specific notebookssmall, unruled. I can never use paper or a notebook that I feel is too fancy to house my unendingly bad ideas and egregious mistakes. The only good paper is paper for which, when you throw it on the ground and grab a new sheet to start over, you don't feel bad. Lined paper is hell. I prefer 0.9 mm lead mechanical pencils, though more often than not a 0.7 mm Bic is what I have handy.
At the same time, I will keep *books* and lecture notes that are *polished and proofread* on my tablet, to save weight and leave room in my backpack for plenty of snacks.
### Software
Tersely, I subscribe to use the following software.
 trello
 for a single todo list,
 and a single reading list.
 pinboard
 zotero
 github
Each week, I put ~15 links in pinboard, ~30 cards in trello, and ~3 citations in zotero.
I abandoned emacs orgmode for my TODO list because
 I didn't find any use for clocking my time,
 my use was too ephemeral to properly learn orgmode's chording,
 I suffered through 2 weeks of "emacs configuration bankruptcy" in May 2018
 I couldn't stand to edit my TODO.org file on my phone.
I listen to music off my phone (connected to a Marshall Woburn Bluetooth speaker) via
 google play music, or
 the hype machine.
## 20190419
Here's a viscerally boring design problem.
  
lecture notes  laptop or notebook
reading scribbles  iPad or scratch
problem sets  laptop or iPad
## 20190408
My bibliography has gotten out of control. Leo told me to stop shopping around. But how?
> Ask for advice?
## 20190323
Took a hiatus from updates to focus on coursework.
Trivial news: I've transitioned my notes and reading material to [Notability](https://www.gingerlabs.com/) for the iPad. As a result, most of my workflow is once again offline.
By working from an iPad, however, I am happily meeting some immediate goals. These include:
 reading broadly for prelims,
 integrating my lecture notes with my reading notes, and
 frequently grinding through exercises.
## 20190201
  
alg2  free modules, feedback on written work, e.g., avoid vague notation such as "Let $\phi \in \mathrm{Hom}$" [@DF04 ch. 10.3]
diffgeo1  manifolds with boundary, defining smooth maps, equivalent characterizations of smoothness [@Lee03, pp. 2435]
top2  relative chain complexes, pairs of topological spaces, tensor product review, cohomology with coefficients in $G$ [@Bre03, section IV.5]
## 20190131
TAing. Not much math.
## 20190130
  
alg2  subobjects, direct sums, freely generated modules [@DF04 ch. 10.3]
diffgeo1  smooth manifold chart lemma, Grassmannians [@Lee03, pp. 2122]
top2  presentations from problem sets; handling edge cases for the first homology group
Presentations were a bit nerveracking when I realized that I had too heavyhandedly abelianized an infinite product. (See .) Ulrich and I found a counter example where $[\prod G_i, \prod G_i] \subsetneq \prod [G_i, G_i]$. I was then incensed to straighten out *which* (co)products exist in *which* concrete categories I'm usually working in.
## 20190129
 Revised some module theoretic arguments for Green into twocolumn proofs.
 Caught up on basic (topological) properties of manifolds.
 Prepared for [presentations](https://github.com/coltongrainger/fy19top2/blob/master/20190130introhomology.pdf) in top2.
I was glad to attend the organizational meeting for the [topology seminar](https://sites.google.com/view/cutopology/spring2019?authuser=0). From Beaudry's introduction:
> This semester, we will cover some of the topics in homotopy theory that make an appearance in the work of Freed–Hopkins–Teleman on topological phases of matter. This seminar will be parallel to the Mathematical Physics seminar (Wednesdays from 34 pm in MATH 350) but will be for the most part independent. This seminar will be about topology: To understand the connections to physics, you’ll have to read on your own or go the other seminar. We have an ambitious schedule (see plan). It’s not a bad idea to read up a bit on the topics before the talks since we’ll be covering material fast.
The [mathphysics](https://math.colorado.edu/seminars/) seminar is coorganized with Prof [Hermele](https://spot.colorado.edu/~hermele/), whose research is in theoretical condensed matter physics.
## 20190128
  
alg2  finitely generated modules [@DF04, ch. 10.3]
diffgeo1  smooth structures, transition maps [@Lee03, pp. 1016]; spheres, level sets [@Lee03, pp. 1723]
top2  exact sequences of chain complexes, the [Bockstein homomorphism](https://en.wikipedia.org/wiki/Bockstein_homomorphism)
## 20190127
Notes from Clelland. Basic examples of smooth manifolds. Finished modules problem set from [@DF04, ch. 10.2].
## 20190126
Notes from Green on modules.
## 20190125
Lectures. In top2, Beaudry mentioned that "if we didn't like that game" [forcing maps defined out of the cycle group $Z_1(X)$ to descend to the quotient $H_1(X)$] "then we would like it soon because we were about to play it *hard.*" Lol.
In the afternoon, I set up definitions for functor categories and generally the category of quivers (directed graphs).
Talked a bit with Ulrich about duality and Gelfand–Naimark, which motivated me to try and rope the content in alg2 and diffgeo1 closer together. (Ulrich also suggested that I push to do homological algebra sooner than later.)
## 20190124
In prob1, we defined random variables and set up results to guarantee the existence of a random variable that's equal in distribution to whatever probability measure we have chosen. Also defined cdfs, pdfs, and pmfs, with reference to the Lebesgue decomposition theorem.
I spent the rest of the day TAing. I decided to [abandon](https://prooflogger.quamash.net) prooflogger since only a third of the sections had anything to do with it. I was brought to my senses by Ulrich, after he mentioned that he only attended recitations in Trondheim to drop off homework.
## 20190123
Lectures.
 In top2, we set out to prove Hurewicz's theorem.
 In alg2, we defined module homomorphisms and started to construct some sort of chain of $F[x]$modules.
 In diffgeo1, we stated topological properties of manifolds [@Lee03, pages 59] and exhibited spheres, products, and projective spaces as manifolds with charts.
## 20190122
I spent the day solidifying my argument for [the smooth chain rule in Banach spaces](https://quamash.net/diffgeo1#banachspacesandthesmoothchainrule). Also finished [@DF04, section 10.1].
## 20190121
Went through Lang's introduction [@Lan99, ch. 1] to topological vector spaces.
## 20190120
I translated Folland's "first look" at functional relations into intuition for the dimension and symmetric properties of repeated Fréchet derivatives.
I surveyed proofs for inverse function theorems and implicit function theorems [@Fol02, ch. 3.1], [@HH15, ch. 2.10], [@Lee03, no. C.34].
## 20190119
Worked through the motivating historical calculus in Massey's [Singular Homology Theory](https://www.springer.com/us/book/9781468492330) [@Mas80, chapter 1]. (Massey develops homology theory with $n$cubes rather than simpliceswhy? To have oriented $n$cubes available as integrands? Does some argument/limiting process fail when working with an infinitesmally thickening mesh of simplices?)
I struggled with notation for repeated applications of the Fréchet derivative. Got distracted in considering repeated linear transformations as vectors spaces themselves in the category of topological vector spaces. Skimmed related results in I.3 of Lang's [Fundamentals of Differential Geometry](https://www.springer.com/us/book/9780387985930) [@Lan99, chapter 1].
In Folland, I gladly found two problems that matched gaps in my knowledge: one to do with Lagrange multipliers and the spectral theorem, the other to do with setting up a meaningful definition of higher Fréchet derivatives.
> Let $A$ be a symmetric $n \times n$ matrix, and let $f(\vec{x}) = (A \vec x) \cdot \vec x$ for $\vec x \in \mathbf{R}^n$. Show that the maximum and minimum of $f$ on the unit sphere $\{ \vec x : \lvert\vec x\rvert = 1\}$ are the largest and smallest eigenvalues of $A$. [@Fol02, number 2.9.19]
> Suppose $f \colon \mathbf{R}^n \to \mathbf{R}$ is of class $C^2$; then $\nabla f$ is a $C^1$ mapping from $\mathbf{R}^n$ to itself. Show that $D(\nabla f)$ is the Hessian matrix of $f$. [@Fol02, number 2.10.6]
## 20190118
Lectures.
 Alg2: In the category of modules, we defined homomorphisms, kernels, quotients, and began to state a series of familiar isomorphism theorems [@DF04, chapter 10.2].
 Diffgeo1: Stated the implicit function theorem [@Lee03, chapter C], and defined a topological manifold [@Lee03, chapter 1].
 Top2: Reasoned about long exact/nonexact sequences of abelian groups.
I found out that I conditionally passed the algebra prelim, and so, made a haphazard sketch of work to do.
term  workload
  
He18  Algebra 1, Topology 1, StatOptML (algebra prelim)
Fr19  Algebra 2, Topology 2, DiffGeo1 (topology prelim)
So19  SIParCS, CU MRE, NSF apps
He19  Algebra (Green, Wise, CasalainaMartin), Analysis 1, Numerics (Bradley, Meiss, Becker, Raf)
Fr20  Analysis 2, Complex Analysis, Algebraic Topology (Pflaum, Beaudry)
So20  Talbot, more NSF apps, teaching
He20  topic proposal, advisors in MATH/APPM/CS
(I have 90% confidence that I will stave off probability until next year.)
(Update: Maybe quantum physics with Hermele next year?)
## 20190117
Mostly teaching, then munging surveys I had put out to the calculus sections. I went to the first meeting for a reading course in probability/measure theory. (I then had about 0.3 confidence I would drop.)
I reviewed the chain rule in Folland's [Advanced Calculus](http://www.math.ucla.edu/~iacoley/32H.pdf) [@Fol99, chapter 2.3], and derivatives in several variables as linear transformations in Hubbard's [A Unified Approach](http://matrixeditions.com/5thUnifiedApproach.html) [@HH15, chapter 1.71.9].
## 20190116
Lectures again, worked to flesh out definitions for modules and simplices. Made progress in defining *two* functors:
 $\Delta (  )\colon \mathsf{Top} \to \mathsf{Ch}$ (by moving from graded abelian groups to chain complexes), and
 the correspondence 'tween $F[x]$modules and $F$vector spaces $V$ with a chosen endomorphism $V \to V$.
## 20190115
Attended offices hours for top2. Asked how to distinguish the monodromy action from action of the group of deck transformations. Got permission to stop reviewing top1 (woot!) and pass onto homology.
Thought about morphisms of vector spaces from a categorical perspective. Skimmed Breezer's [FCLA](http://linear.ups.edu/html/fcla.html) (elementary matrices as transformations, 4 subspaces, similar and diagonal matrices). Worked through examples (especially notation) in PCM I.3.4. Slowly began to understand why one would want eigenvector bases to study subspaces "stable" under linear transformation.
Also spent an upsetting amount of time configuring pandoc on my laptop and server. Gross. I don't even see how the software is held together. Way beyond me.
## 20190114
Started lecture notes for [Topology 2](https://quamash.net/top2) (top2), [Differential Geometry 1](https://quamash.net/diffgeo1) (diffgeo1), and [Algebra 2](https://quamash.net/alg2) (alg2). Linearity is 4sure the unifying theme of the week. Notably, diffgeo1 made a whirlwind tour of Appendix B in Lee's *Introduction to Smooth Manifolds*.
## 20190113
I previewed syllabi and reading for the next 2 weeks.
 Homology in Hatcher, Bredon, and May;
 Modules in Dummit & Foote;
 Linear Algebra/Calculus review in Lee.
I also setup , a catalog of 3Dprinted models, for the MARC.
## 20190112
Errands. Odds & ends from last semester's `todo.org`. I had a lengthy, meandering conversation with two older grad students (TK & Carly) about faculty transitions at CU in the last 6 years. I realized how convenient was for summarizing rank/career changes. Not much math.
## 20190111
More teacher training. Finished my [SIParCS application](https://github.com/coltongrainger/internships/blob/master/statements/siparcsclimatemodels.md). Mnemosyne.
## 20190110
Attended teacher training. Finished transcribing an [interview with Leah Buechley](https://github.com/coltongrainger/neuralnetwork/blob/master/posts/20180910leahbuechley.md). Setup duplicity with google cloud platform. Defragmented my gmail archive.
## 20190109
Took the topology prelim. Answered 3 of 6 questions in pointset and algebraic topology.
 separation properties
 applications of Seifert vanKampen
 homotopy groups of real projective space
Talked to TK: what to review for differential geometry?
 multilinear forms up to the definition of a tensor product
 implicit and inverse function theorems
## 20190108
More chores, etc. I installed KeePassX.
## 20190107
As a chore and measure of progress, I attempted the algebra prelim.
 I struggled to understand possible group actions of $Q_8$ on $\{1, \ldots, n\}$. In a dilemma, I wrote out a treacherously long table of conjugacy classes for $S_n$, $n = 4, \ldots, 7$ and made a confusing argument about normal subgroups as unions of conjugacy classes.
 Afterwards, Andre and I discovered a oneliner to show "$Q_8 \le S_n$" is absurd for these cases.
> When $Q_8$ acts on $I_n$ for $n < 8$, the stabilizer of any point in $I_n$ contains $1$, whence $1$ is in the kernel of the action.
 Also afterwards, when I needed to determine which primes in $\mathbf{Z}$ were also Gaussian primes, I found myself impressed with Weissstein's [MathWorld](https://en.wikipedia.org/wiki/MathWorld).
 I expect the Slack channel Chris and I were using to study will soon be defunct.
 To shift gears for topology, I passed over a survey: [PCM IV.10](http://catdir.loc.gov/catdir/toc/ecip0818/2008020450.html).
## 20190106
Chris and I ran through Micky's group theory notes. I discovered Zassenhaus' [The Theory of Groups](https://books.google.com/books?id=_lOycgz7bQYC) and skimmed through chapter IV on $p$groups and Sylow $p$groups.
To destress before the prelim, I browsed the OED for historical uses of `morphism`, `quaternion`, `group`, `ring`, `field`. (I found Zassenhaus under `quaternions`.)
## 20190105
I continued to atomicize mnemosyne cards by expanding "naive" procedural topics from the GRE. I went through a proof of Sylow's theorems and thought about the conjugation and left translation action of a group $G$ on its $p$groups.
## 20190104
Chris and I sat for a timed [practice exam](https://github.com/coltongrainger/fy19alg1/blob/master/20190104algebraseppractice.md), adapted from Ed Dummit's 2014 [algebra summer enhancement program](https://sites.google.com/a/wisc.edu/mathintranet/home/quals). I feel silly taking the exam before I know what I'm doing, but
 there's a timeline, and
 our dept chair emphasizes ["trusting oneself"](http://math.colorado.edu/~kstange/gradstudy.pdf) to seek out "new challenges and novel contexts".
Her accompanying advice is, of course, to "doubt oneself" and "build what you know", which I look forward to reverting to after next week.
I compiled Micky Steinberg's [2014 group theory notes](https://www.math.wisc.edu/~micky/grouptheory.pdf) into a [lighthearted practice exam](https://github.com/coltongrainger/fy19alg1/blob/master/20190105algebramickypractice.md) for tomorrow.
## 20190103
Chris talked me through problems 13 on CU's [Jan 2008 algebra prelim](https://github.com/coltongrainger/prelims/blob/master/20080115cualgebraprelim.pdf), which I didn't understand. For prob 2, we needed to make a recursive argument to find a nontrivial abelian normal subgroup of prime power order in a finite solvable group. Ian also mentioned this problem (with enthusiasm) before break, so I might revisit it.
I started reviewing from [Hubbard](http://matrixeditions.com/5thUnifiedApproach.html), following the [week 1](https://canvas.harvard.edu/courses/45219/pages/weeklyschedule) schedule for Paul Bamberg's [Math 23a](https://canvas.harvard.edu/courses/45219/files/6701269/download?verifier=Yvcu1AARsTzhWbCTmjtM2cT0BWA4sCCxBS3VftOE&wrap=1). (The supplemental materials for math 23a are great, and I think I'll exhaust most of my free time before Jan 14 going over these.)
Lastly, I went through exercises in I.1 Fields from Halmos's [Finite Dimensional Vector Spaces](https://www.springer.com/us/book/9780387900933), which is admittedly out of date. I'm going through Halmos, however, because
 I found a hardcopy in the math dept's reading room, and
 I was impressed when I skimmed [Halmos's and Steenrod's](https://news.ycombinator.com/item?id=16829440) 1973 *How to Write Mathematics*.
## 20190102
Distracted today: I setup yst to compile yaml data into a [CV](https://coltongrainger.com/cv), as per Dom Moritz's . Dom's jobhunting stress thoroughly dosed me (by proxy) with timeline stress, and, incidentally, I spent the day "signalling".
## 20190101
I revised cards on introductory measure theory, also group actions. I continued through a backlog of reviews I owed mnemosyne from last semester.
(Oddly as well, I flicked through photos from 2018 back to the beginning of 2016, when I was skiing a bit and preparing to graduate. From my undergraduate coursework, maybe I'm only interested to mnemofy notes from electricity and magnetism? from ordinary differential equations?)
## 20191231
I spent some time convincing myself that "chunking mathematical concepts" would be more rewarding "completing prerequisites in a satisfactory order" after reading Michael Nielsen's [essay on anki](http://augmentingcognition.com/ltm.html). I reactivated [mnemosyne cards](https://quamash.net/mathsGRE) I had made studying for the math GRE.
While revising cards I had starred for typos, I began to recognize I'd been trying to chunk concepts that were too complex for a first pass. (I found a particularly bad batch of measure theory cardsshould delete these or just atomicize them?)
## 20181230
I finished , which I hope Lee will allow me to force some of the calculus sections to use. [Here](https://quamash.net/math1300#participation) is an outline I'd give students. I aim to game students into presenting proofs to each other and providing constructive oral feedback.
## 20181229
I thought about social support networks while travelling from Idaho back to Boulder, e.g., [the cohort effect](http://www.pgbovine.net/PGVlog252cohorteffects.htm).
## 20181227
Following , , and I'm starting a working journal with a broad scope: early graduate school in the mathematics department at CU Boulder.
This journal supersedes my now obsolete [blog](https://blog.coltongrainger.com).
I haven't gotten permission to emulate any one of the above authors, so I'm sort of planning to write in a manner that oscillates between each's style. In spite of the common medium (~daily entries) it seems each author's motivation is tangential to the other two's: writing for exploration, for transparency, for reflection.
I imagine I will be keeping this journal
 to narrate what I've been working on in a chronological fashion,
 to give myself encouragement by tracking progress through my coursework,
 to urge myself on (as in skiracing, where we'd often yell at each other "up up up!").
I think it would be appropriate to include characteristic quotes, which motivate this journal.
Nadia Eghbal ([notes](https://nadiaeghbal.com/notes/))
> 11/26/18
>
> Realizing that I love to be alone, like in a physically lowstimulation environment, but I still think of myself as socially oriented even in that context. I still like texting/FaceTiming friends. And: I only want to be alone to work on ideas that I eventually take back to others. Like, if I were just writing for the sake of writing and not publishing it out, I’d probably get pretty bored and antsy
> 11/26/18
>
> Amplification vs. exploration: Usually I say that I prefer writing to talks/interviews bc I can think better through writing over speaking. But I think another big reason is bc people often want you to talk about stuff you’ve already done, which is not that interesting to me. Whereas with blog posts, it’s my blog, I don’t really care if you read it or not, I’m just putting stuff out there and hopefully connecting with a few ppl who feel the same way. To me, writing is pushing to the edges, exploring the limits of my identity and what I’m comfortable sharing in public. Whereas any other form of communicating ideas feels performative: I’m rehashing things I already know, and that you know me for. Also why I had to get off Medium (bc it made blogging feel performative)
Issa Rice ([a note on scope of updates](https://issarice.wordpress.com/2018/12/01/anoteonscopeofupdates/))
> As I stated at the beginning, this blog came about because I wanted to make available information about “what I’m up to” in cases where “what I’m up to” doesn’t naturally lead to public updates. So I think it’s not so important to record things on here when the same information can be obtained through other sources (i.e. my public activity on other websites).
>
> However, I also want to have some kind of conceptual coherence about this blog. And since the overlap between “my activity that doesn’t naturally lead to public updates but where I would like to make public updates available” and “my AI safety learning” is nearly perfect, I think I will track the former by writing about the latter.
Philip Guo ([vlog transcript, talking about his journal](https://youtu.be/M2pGiBrwNs?t=272))
> anyways so when I started my postdoc I thought of this idea I don't know how I thought of it but I thought this idea that I would just keep a running diary of anything that I've encountered that to workrelated that I felt like writing down. so it was very simple. I created a text file. this is my first one (reading it) this is really funny I'm just reading this. this is July 2013, my first month as a postdoc.
>
> > July 2013 I'm going to start a rough weekly work diary reflecting on my thoughts about life as a young academic. I need to focus more on how I feel rather than what I did since it's easy to later reconstruct what I did from other artifacts but it's hard to recreate old feelings. this diary is gonna be quite rough and I don't want to hold myself to a strict writing schedule. let's keep this fairly freeform and lowkey.
>
> once again in parentheses I said: focus on how I feel rather than just what I did