Sunday, July 31, 2016

How would you compare the UALR math/stat dept with math/stat depts at other univs that you may have attended?

I've gone to three different schools.  TCC, tarleton, and ualr.  My favorite was TCC.  I took college algebra, trigonometry, calculus 1, and calculus 2 there.  I don't really blame TCC for misrepresenting math because they don't offer a math degree.  Retroactively, I wish that the beginning math classes had just been advanced calculus or real analysis or whatever, but at the time I liked the math classes at TCC and the math teachers I had (David Gustafson and Cynthia Albee and someone else whose name I don't remember) were super available and super helpful and Gustafson in particular made the subject even more interesting than I already found it at the time.

I didn't want to go to tarleton, so that colors all of my experiences there.  But anyway, the teachers were generally not as available or interested in helping me and they didn't explain stuff as well as the teachers at TCC did and I didn't understand a lot of the stuff in calculus 3 and differential equations and some other classes and I hated them, although some of the classes were interesting despite the lack of good teachers, including discrete math and number theory.

I didn't really want to go to UALR either.  Linear algebra was easy and interesting despite having a terrible teacher.  I finally understood what a vector was in that class.  Math software was fine, but not actually a math class.  College geometry was pretty stupid. Applied statistics 1 was stuff I already knew mostly, and I crapped my way through applied statistics 2 without actually learning anything.  I really hated math history, even though I want to emphasize I was extremely interesting the subject, the teacher of the class was such an annoying piece of crap I couldn't stand it.  Advanced calculus was totally opaque to me the first time I took it and when I went to the teacher for help, I left more confused and dropped the class half way through.  The second time I took it I did better in it, but I failed the class for unrelated personal reasons. The first time I took the senior seminar, I didn't know how to do any of the homework and I think I horribly failed the MFT and I didn't have a good research project and I just ended up giving up because I hated everything.

I can't really pick one out of UALR and tarleton as the better one. They're both kind of crappy.  And TCC was good.  When it comes to like, my experience in the classes I mean.  When it comes to preparing you to like be a mathematician they probably all suck equally.

How would you compare the UALR math/stats dept with other UALR academic depts with which you have had contact?

The departments I recall experiences with at UALR
writing & rhetoric
computer science
information science
information assurance

maybe others I've missed, whatever.
the main ones are math/stat, cs, and disls.

I had sucked at "writing" ever since 7th grade and failed/dropped composition classes three times at Tarleton, and then I took composition 1 and 2 at UALR and those were really good experiences except for during composition 1 i sprained  my ankle and missed the last two weeks of school and so I didn't get to get my last paper revised so ended up only getting a B in that class even though I had an A up to that point and probably would have gotten an A if not for my sprained ankle and I'm annoyed at the teacher for not emailing me back feedback on my last paper and letting me revise it before giving me my final grade, but other than that she was a good helper with the writing of the papers and I was actually proud of several of the papers that I wrote in that class, and the same is true for composition 2, although that class was harder and i got a B in it and actually think I deserved at most a B, and I had an incomplete in that class because I wasn't able to complete the assignments by the deadlines but I was working on them continuously and always going to the teacher's office for help and she was always really helpful and one time she listened to me rant for like 20 minutes about how I felt like I would never be able to get a job.

So summary of that that math teacher might actually want to hear:

********  I've taken two classes in writing & rhetoric, composition 1 and composition 2.  I had taken similar classes at Tarleton and dropped them 3 times because they were too hard and those teachers said that I was really bad at writing and should take a remedial writing class.  But then later the composition teachers at UALR were really helpful and said I was actually pretty good at writing, and I got B's in both of those classes.  My one complaint is that in composition 1, I had an A until the last assignment, and I was injured and couldn't come to class and the teacher refused to give me feedback on my paper via email, so I wasn't able to revise it, so that brought my grade down to a B.  Composition 2 was harder and I needed extra time on all the assignments and got an incomplete and went to the teacher's office for help almost every day, and she was apparently happy to help me and give me extra time.  ************

I've taken one class in philosophy that I completed and one that I ended up dropping.  The one I completed was intro to logic, and the class material was really easy and stuff I had already learned before in high school, so I got an A in it, but the teacher (who was a PhD student at the time) was a terrible jerk.  The other class was ethics & society, and I dropped it because the teacher was insufferable.

I took one ASL class and despite the fact that I was motivated, I didn't understand a lot of it and I got a B in the class, so I blame their attempt at "natural" learning.  That means they try to teach you the language by just "exposing" you to it and not teaching you the grammar.  I don't learn that way and in fact most adults do not learn that way.

I've taken one class in the english department, vocabulary building.  It was a joke.  We didn't use most of the class time and when we were in class we spent most of that time listening to one particular student ramble about his opinions on current events.  The class was easy but I didn't learn anything, and I didn't even finish the final because while I was working on it, the teacher said she wanted to go home so I should just stop and she would give me an A anyway.

I took two speech classes, one was the like basic speech class that was required for the core requirements, and the other was a class called interviewing.  I took an intro speech class at tarleton and it was really hard and the teacher was really aloof and unhelpful and I dropped the class.  I was nervous about taking the speech class at UALR because I was bad at writing, and this was before I took the composition classes.  I did have some trouble with the speech class, but it was a lot better than when I tried it at tarleton and the teacher was helpful and willing to spend time helping me, and I ended up getting a B in that class.  Because of that success I decided to explore the speech department further and I took interviewing, but the class ended up just not being to my taste and I dropped it.

I took the intro information assurance class and it was garbage and I learned nothing and I think I got an A in it.

I think I've taken two information science classes that were required for the CS degree and they were both ok.

DISLS:  I've taken spanish 4 (which doesn't exist anymore, the semester I took it was the last semester they offered it I think), spanish grammar, spanish phonetics, and a spanish linguistics seminar.  I also took and dropped because they were terrible:  spanish conversation, spanish communications interpretive, and spanish communications interpersonal.  The grammar, phonetics, and linguistics classes were ones that were taught by my mom.  She is the only good spanish teacher I've ever had and she is in the top 2 of good teachers I've ever had in my whole life, the other one being Dr Minsker of the computer science dept.  I'm not alone in thinking my mom is a good teacher.  I've heard lots of other people say she's the best etc and she always gets good evaluations.  The other teachers generally sucked balls, although some were worse than others.  When I dropped classes it was because the teachers were terrible.  I knew more about spanish grammar than they did, and the spanish 4 teacher pronounced things wrong all the time, like horribly ridiculously wrong.  Also their theory behind the required classes was stupid.  They were told by some accrediting agency that they were supposed to involve presentational, interpersonal, and interpretive skills in their program, so they made separate classes called "spanish communications presentational", "... interpersonal", and "... interpretive", and they wanted all three of them to be required for the major, but because someone failed at paperwork, they didn't manage to get the presentational one required.  They didn't make the grammar class required, so they tried to sprinkle grammar lessons throughout all the other classes, including spanish conversation, and that's how they ended up with people who didn't know shit about grammar trying to teach it.

I also took and completed french 1 and 2 and took and dropped french 3.  French 1 and 2 were fine, although the french teachers didn't know a lot about grammar and were hostile to my learning style of grammatical analysis.  When I took french 3, that semester the french teachers had decided to do away with "pencil and paper tests", so the tests were just another student or the teacher asking you a question and then the teacher subjectively rated your answer on fluency and pronunciation and a couple other categories I don't remember.  On the first test I got marked down on fluency because I paused to *think about my answer* to a personal question, and that was the last straw for me and I dropped the class.  They also continued to eschew the teaching of grammar, which is the same problem the ASL classes had, that they wanted to teach the language in the "natural" way that babies learn despite the fact that the vast majority of adults cannot acquire a second language that way.

I also took one german class and it was fine.

A general problem with language degrees is that they don't actually help you attain fluency in the language.  But they imply to potential students that, for example, you can use your spanish degree to become a spanish interpreter.

I've taken a bunch of computer science classes.  I have two major complaints about it.  One, they assume a lot of pre-requisite knowledge of the students that's not covered in any of their classes.  Two, there's one particular teacher who's so incredibly atrociously stupid that I don't even know how he manages to be alive, and on top of that he's an asshole, and the department made a terrible unforgivable mistake in hiring him and giving him tenure (if they have, i think they have, i'll look it up).

I've taken a handful of math and stat classes at UALR.  linear algebra, applied stats 1 and 2, college geometry, math software.  and i've taken others and dropped or failed them, for one ore more of the following reasons.  One, I hate math.  Two, the class was too hard.  Three, the teacher wasn't helpful or didn't make themself available to help me.  Four, the teacher was an insufferable idiot/asshole.  So here are my three main complaints about the math department.  One, the essence of math is misrepresented in lower-level math classes.  Two, Kosmatov is a jerk.  Three, the guy who teaches math history is fucking god damned annoying and an asshole idiot.

^ I need to add more to that paragraph about how I think math should be taught differently for math majors.

Monday, July 11, 2016

preliminary notes on imperfect, conditional, and future

The imperfect has 3 irregulars.  For the regular ones the endings are

aba      ábamos
abas    abais
aba      aban

ía      íamos
ías    íais
ía      ían

The stem is formed by dropping the ar/er/ir from the infinitive.

There are no stem changes.

Now the irregulars.  Ver, ir, ser.

Ver is not very irregular.  It's only irregularity is that the stem is ve- instead of just v-.

veía      veíamos
veías     veíais
veía      veían

Ir is not very irregular either. Just insert a B in the endings and that's the whole word.

iba      íbamos
ibas    ibais
iba      iban

And then ser.  Ser is weird.

era      éramos
eras    erais
era      eran

It's not THAT different from the others, except that it starts with er- instead of ab- or i-.

Now the conditional.  The conditional endings are the same as the endings for the -er/-ir verbs in the imperfect.

ía      íamos
ías    íais
ía      ían

Those are the endings for ALL the verbs in the conditional.

For regular verbs, the stem is the entire infinitive, for example hablar-

hablaría      hablaríamos
hablarías    hablaríais
hablaría      hablarían

For irregular verbs, like I said the endings are the same, but the stem is altered slightly.  Here's a list of some of the infinitives and their irregular stems.

hacer har-
tener tendr-

For example

saber sabr-
sabría      sabríamos
sabrías     sabríais
sabría      sabrían

And now the future indicative.  The stem is the same as the conditional.  It's the entire infinitive for the regular ones and it's the same altered form of the infinitive for the irregulars.  Add these endings:

é      emos
ás     éis
á      án

hablaré      hablaremos
hablarás    hablaréis
hablará      hablarán

Sunday, July 10, 2016

preliminary notes on present subjunctive

present subjunctive is based on the yo form of the present indicative.

There are six irregulars.  They're irregular because they are the six verbs where the yo form of the present indicative doesn't end in an -o.  for regulars you get the stem for the present subjunctive by dropping the o from the yo form of the present indicative, but for these six irregulars you have to memorize them separately.

Here they are, infinitives, yo form of the present indicative, and the stem for the present subjunctive

haber  he      hay-
saber  sé       sep-
ir        voy     vay-
ser      soy     se-
dar     doy     d-
estar   estoy  est-

Then add the endings, which are the same as for the regular verbs, except estar is weird.

ar verbs
-e     -emos
-es   -éis
-e     -en

er/ir verbs
-a     -amos
-as   -áis
-a     -an

haya, hayas, haya, hayamos, hayáis, hayan
sepa, sepas, sepa, sepamos, sepáis, sepan
vaya, vayas, vaya, vayamos, vayáis, vayan
sea, seas, sea, seamos, seáis, sean
dé, des, dé, demos, deis, den

and estar
esté, estés, esté, estemos, estéis, estén

Estar is weird because it's stressed on the last syllable in the boot, which is unusual, like I think it's the only verb that does that?  It's probably because it comes from latin stare, and then you drop the final -e and get "star", but then spanish has a rule about S's so you have to put an e before it for pronunciation, so it's estar.  Anyway, the endings for estar in the present subjunctive are regular except for the stress pattern.

dar is actually regular in the forms of the present subjunctive.  The only reason it's considered irregular is that the yo form of the present indicative doesn't end in an o, so it technically doesn't fit the rule of dropping the o to get the stem for the present subjunctive.  You have to drop the -oy.

ser is almost regular, the only problems being that you have to drop the -oy from the yo form of the present indicative instead of just the -o, like dar, and also that the present subjunctive has an extra "e" hanging out in its stem, whereas if it were regular the stem would just be s- like how the stem for dar is d-.

ver and haber are weird, idk where their present subjunctive forms come from.

the present subjunctive of saber is based on an old form of the yo form of the present indicative:  sepo.  There's like one other verb that still has an irregular yo form of the present indicative like that and that is caber (quepo).  since the yo form of the present indicative of caber IS currently quepo, the present subjunctive of caber is not irregular, it's just based directly on quepo.  Saber is irregular because it's based on sepo, but the modern yo form of the present indicative of saber is sé.

and like i said for all the regular ones you drop the o from the yo form of the present indicative and add the endings listed above, but that's not all!  There are stem-changes to think about.

member how some stem changes appear in the boot and some appear only in the short-boot?  If a verb is stem-changing in the present indicative but only in the short-boot, then the stem-change does NOT appear in the present subjunctive.  So you just add the endings and you're done.

If the stem-change appears in the yo form of the present indicative, then it will appear in the BOOT of the present subjunctive.

And then you have to check to see if it's an ar, er, or ir verb.  If it's an ar or er verb, you're done. If it's an ir verb, then a *reduced stem-change* appears in the NOT-BOOT, ie the nosotrxs and vosotrxs forms.  The reduced stem-change is e -> i and o -> u.  (That means if the verb's stem-change was e -> i to begin with then all six forms end up with the same e -> i stem-change.  There's no such thing as an o -> u stem change so that's not an issue.  If it was i -> ie, then the reduced stem-change looks exactly like a lack of a stem-change.  That's rare but does occur.  And there is such a thing as u -> ue stem-change, but there's only one verb that does that and it's not an -ir verb, so it's not an issue here either.)

So I think that's all.

preliminary notes on infinitives and verb conjugation

infinitives end in -ar, -er, or -ir.

verbs are conjugated in six different "people".
1st singular, 1st plural
2nd singular, 2nd plural
3rd singular, 3rd plural

the nosotrxs form of a verb always ends in -mos.  always.  in every tense, mood, etc, whatever.
the uds/ellxs form always always always ends in an n.  -an, -en, or -on.
the vosotrxs form always ends in -is.  -ais, -eis, or -is.
the ud/ellx form always ends in a vowel, either a or e.
the tú form almost always ends in an s.  as or es.  the exception is the preterist, which ends in aste or iste.
the yo form is usually the same as the ud/ella/él form.  two exceptions, the preterite and the present indicative.  in the preterite, it ends in e or i.  in the present indicative, it usually ends in -o, with only six exceptions.

different forms or conjugations or whatever are
present indicative
present subjunctive
past indicative preterite
past indicative imperfect
past subjunctive
future indicative
future subjunctive (archaic, but awesome so I use it anyway)
past participle
present participle

preliminary notes on spanish spelling

I'm not going to go into all the details about patterns in spanish spelling, only the parts you need to know in order to conjugate verbs and decline other words.

to make the /k/ sound, you need either "c" or "qu" (or sometimes "k", but that's only in some borrowed words and not relevant to this).  If it's before an e or an i, you  need "qu", otherwise "c".  This comes up in verb conjugation in for example the word "buscar".  In the preterite, it's "busqué".  It's pronounced like "buskar" and "buské", a /k/ sound in both cases, but you can't spell "buské" with a "c" because c before e or i goes /s/, so that one has to be a "qu", busqué; and you can't have "qu" anywhere *except* before an e or an i because spanish says so (totally arbitrarily, french for example doesn't follow the rule), so it has to be a "c", buscar.

to make the /g/ sound before an e or an i, you have to insert a "u", because in "ge" or "gi" the "g" is pronounced like a j.  So instead you write "gue" or "gui" and the u is silent.  This comes up in "pagar".  The preterite is "pagué".  <- silent "u".

If a g is before an e or an i, and then the conjugation makes the g be followed by something else (o, a), then you have to change the g to a j to maintain the pronunciation.  eg proteger.  the yo form of the present indicative is protejo.

Spanish says a z can't come before an e or an i (except in some borrowed words) so sometimes a z has to change to a c.  For example, the plural of luz is luces.

Sidenote, if you want to write /gwe/ or /gwi/, you can by putting umlauts on the u, güe, güi.  Words with the ü are very rare.

I think that's all.

preliminary notes on present indicative conjugation

regular ar endings
o     amos
as    áis
a     an

regular er endings
o     emos
es    éis
e     en

regular ir endings
o     imos
es    ís
e     en

The accent marks on the vosotrxs forms are short-hand for the fact that the word would be stressed on that syllable.  If it's a single-syllable word, it may not actually have the accent mark.  The only way it would then is if it has to be distinguished from a homonym that doesn't get sentence-level stress.

There's also stem changes.  Possible stem changes are
e -> i
e -> ie
i -> ie (very rare)
o -> ue (if the ue is at the beginning of the word, you have to put an h before it)
u -> ue (very rare)

ie would also have to have an h before it at the beginning of the word, but I think all such words already have an h at the beginning of them in the infinitive.

stem changes appear in the boot or short-boot.  Boot is yo, tú, ella, ellas.  Short-boot is all those except yo.  If the stem-change only appears in the short-boot, it's because the yo form is irregular.

Then there's some other weird irregular forms that you have to memorize.  meh, not gonna go into all that.

There are six verbs where the yo form doesn't end in an o.  Only six.

preliminary notes on diphthongs and antidiphthongs

a diphthong is made of a vowel and a semi-vowel.  The semi-vowels in spanish are i and u.  When they are being semi-vowels they're like y and w.  When an i or a u comes next to an a, e, or o, it's by default a semi-vowel.


ai is pronounced like ay
ei is pronounced like ey
oi is pronounced like oy

ia is pronounced like ya
ie is pronounced like ye
io is pronounced like yo

au is pronounced like aw (like the english word "ow" actually)
eu is pronounced like ew (not a typical english vowel sound, nothing to compare to)
ou is pronounced like ow (as in "owe")

ua is pronounced like wa
ue is pronounced like we
uo is pronounced like wo

When i and u are together, the first one is the semi-vowel and the second one is the vowel.

iu is pronounced like yu
ui is pronouncd like wi

note the word "muy".  It's spelled with a y, not an i, which seems to indicate that the u should be the vowel and the y should be the semi-vowel, but some people pronounce is like "mwi", rhyming with the word "fui" which is pronounce like "fwi".

If you have one of these letter combinations but they DON'T form a diphthong, that's called an antidiphthong, and if the vowel that would have been the semi-vowel is instead the stressed vowel of the word, then it needs an accent mark.  (It's possible but rare to have an antidiphthong where the would-be semi-vowel is not the stressed vowel of the word.  In that case it does not get an accent mark, but the word might end up with an accent mark on its stressed vowel for some other reason.)

países is paheeses, not payses
leíste not leyste
oíste not oyste

día has an accent mark because it's deeah, not "dya".
vacíe is not "vacye"
confío is not "confyo"

raúl not rawl
reúne not rewne
can't find examples of oú


preliminary notes on accent marks

Accent marks in spanish

A word can have at most one accent mark.  either zero or one.  that's it.

the ~ on the ñ is not an accent mark.  that's part of the letter.  so a word can have any number of ~'s and one accent mark or zero accent marks.

the accent marks always go up to the right. áéíóúÁÉÍÓÚ

If a word has an accent mark, the accent mark is always on the stressed vowel of the word.  A word has one stressed syllable and a syllable has one vowel that is its nucleus.  If the word has an accent mark, it goes over that vowel.

How to determine if a word has an accent mark.
it has to meet at least one of the following

1.  it's a one-syllable word that gets sentence-level stress that has at least one homonym that doesn't get sentence-level stress.  so like "sé" gets an accent mark and "se" doesn't because sé is a verb and se is a pronoun.  The parts of speech that get sentence-level stress are nouns, verbs, adjective, adverbs, i think that's all, need to get confirmation on this.

2.  it's a "question word" that needs to be distinguished from its corresponding relative pronoun or whatever.  so like if "qué" means "what", it gets an accent mark, but if it means "that", it doesn't.  when "cómo" means "how", it gets an accent mark, but when it means "as", it doesn't.  bizarro exception is the phrase "lo que" which is treated as one word separate from "qué" so it never gets an accent mark.

3.  it contains an antidiptongo.  uh, I will just make a separate entry explaining diphthongs and antidiphthongs.

4.  it breaks the assumed stress pattern.  Words that end in a vowel, n, or s are assumed to be stressed on the second-to-last syllable, so if they are stressed on any other syllable, there needs to be an accent mark over the stressed vowel.  Words that end in any other letter are assumed to be stressed on the last syllable, so if they are stressed on any other syllable, there needs to be an accent mark on the stressed vowel.

5.  spanish is "regulated" by a stupid "academy" and they "decided" that this isn't true anymore, but you will probably still see it sometimes:  the words este(os)/a(s), ese(os)/a(s), aquel(los)/la(s) can be pronouns or adjectives and the "old" way is to give them an accent mark when they are being pronouns.

So to figure out if a word needs an accent mark.
1.  Is it a one-syllable word?  If so then check if it's one of those that gets an accent mark to distinguish it from a "tiny" homonym.
2.  Is it a question word that needs to be distinguished from a homonymy relative pronoun?  Then it gets an accent mark probably i think i need to look into this.
3.  Is it one of those three demonstrative pronouns?  Then you can put an accent mark on it if you want but it's not required anymore.
4.  If the word has more than one syllable apply this rule.  If it's not a llana word that ends in a vowel n or s, or an aguda word that ends in any other letter, then it gets an accent mark.
5.  If it contains an antidiptongo where the would-be deslisada is the stressed vowel of the word, then it gets an accent mark.

They don't have to be done in order.

preliminary notes on spanish pronunciation

a like the stereotypical "say ah" sound.
b, v these are pronounced the same, either like a b or like a "v" made with both lips instead of lips and teeth.  which pronunciation is used depends on the letter that follows.
c (before e or i), s, z these all make the same sound, like english s.
c before any other letter, k, q same as the english k sound except less aspirated, spanish is generally less aspirated.
ch same as english except aspiration
d like the "th" in the english word "the", either the occlusive or fricative version.  which pronunciation depends on the letter that follows.
e either closed "sharp" e like you start to say the word "ape" and get cut off before you finish the vowel, or open e like in english "let", depends on surrounding letters, not a big deal.
f same except aspiration
g (before e or i), j, x (sometimes) these make the same sound, it's the same point of articulation as a k, but it's fricative.  sounds kind of like hissing.
g before any other letter is either the same english or a fricative version of that, depending on the following letter.
h silent. it's there because it used to be an F that then changed in pronunciation to an H and then became silent.  eg spanish hacer comes from latin facere.
i, y, pronounced the same, either like english long e or like english y, depending on surrounding letters and stress.
l normally alveolar but they assimilate to d's and maybe something else i'm forgetting.
ll always the english y sound.
m same
n alveolar except it assimilates to following consonants
ñ palatal n, which causes the "y" sound with it.
o closed like in english "for" or open but idfk how to differentiate this pronunciation so don't worry about it.
p same cept aspiration
r, rr flap your tongue against the alveolar ridge like the t/d in "little ladder", for single r it's usually just one flap, for rr, it's repeated a few times, and sometimes the r is pronounced like rr (eg at the beginning of a word, idk all the cases).
t with the tip of your tongue touching the top back of your teeth.  it comes out sounding slightly more th-y than the english t.
u, w like the i and y, these are either english u like the oo in "boot" or the english w sound, depending on surrounding letters and stress, except that "oo" will never be spelled with a "w" and w only appears in some borrowed words anyway so mostly forget about it.
x either ks or just s, or rarely like spanish j

Saturday, July 2, 2016

List and rank any significant weaknesses that you might see in the UALR Mathematics/Statistics Department

Don't worry, it's not just you, it's all of UALR, well, all of the classes I've taken, no I'm sorry, I do recall a few good classes.  Comp 1 and Comp 2 and spanish phonetics and spanish grammar were good. :D My mom was the teacher of the spanish classes.  Anyway.  Anyway.  It's fucking stupid that you have this stupid capstone class and require original research out of people going for bachelor's degrees.  And college in general sucks.  It's a stupid way to attempt to learn things.  Lectures are stupid.  Be khan academy.  with teachers on call.

What do you consider to be strengths of the UALR Mathematics & Statistics Department? (rank in order of relative strength)

Nothing.  Zero.  You suck.  I hate you.  FML.  I wish I had never gone to college at all.  Meh, community college was OK.

Have you developed the ability to work both independently (individually) and collaboratively (group work) on mathematical problems? State an example of each.

No.  But one time in probability & statistics at tarleton, I had to do group work.  We had to do something about the monty hall problem.  The other people didn't believe me.  I retrieved a copy of The curious incident of the dog in the nighttime, which is the book I learned it from, and I showed them the diagram, and then we set up an experiment and it came out just the way the diagram predicted.  Individually?  Um, I took the SAT and the ACT.  I've taken tests in most of my math classes.  Obvs I've solved stupid math problems independently.  5+5=10.  There's an example.  I just did it.  Ugh.  I built a shelf once.  That involved math.  I did it alone.  I mean, I did the math alone.  Someone else cut the boards.

How do you approach writing proofs?

If it's one I haven't seen before and therefore just already know how to do, then I guess my method is to write whatever I ramblingly think about it and compare to examples from the class to see how much detail the teacher wants.  Like do I have to prove commutativity or something like that.

What is problem solving? How do you approach problem solving?

Sorry, am I suddenly in that shitty class with bayrak?  What is problem solving?  It's solving a fucking problem.  Do you need a definition of the words?

according to google problem solving is "the process of finding solutions to difficult or complex issues."

Problem is "a matter or situation regarded as unwelcome or harmful and needing to be dealt with and overcome." or "an inquiry starting from given conditions to investigate or demonstrate a fact, result, or law."

to solve is "find an answer to, explanation for, or means of effectively dealing with (a problem or mystery)."

Anyway.  Problem solving is solving a problem.  Finding a solution to a problem.  In math, finding THE solution.

How do I approach problem solving?  IDFK.  Um. I ask google.  Or I look in the relevant math book if I have one.  Solving engineering problems I think comes down to experience.  Maybe.  How did I think of repairing the blinds with tape?  I don't remember.  I remember about the coaster holder.  I first thought of a rubber band but I thought it would be too easy for them to roll over it.  I thought it needed something taller but then it would have to be looser to make room for the coasters and I thought of the headband thing.  I needed experience to even think of rubber bands and headbands.  I also needed supplies.  I don't remember exactly how the phone case came to me either.  Sometimes I have to think and sometimes things just pop into my head.

I don't really remember solving math problems but I remember that I did, and I remember thinking that I relied on experience.  I tried things that had worked on similar problems before.  Or I just tried random things if nothing seemed to fit, until it led somewhere familiar.  If it takes too long, where "too long" is subjective, look it up, and after a while give up.

Do you feel competent to read mathematical proofs that are technically involved?

Probably not.  I don't really know.

What are you going to be doing after graduation? Do you feel mathematically prepared?

In answer to the second question, no.  I know more math than most of the people I know, and I felt like I was making a little progress with advanced calculus and I am finally starting to understand taylor series after watching the khan academy videos about it, but I feel like what I know is a vanishingly small fraction of what there is to know and that I'm probably wrong about everything I think I know.

To the first question:  I want to study to go on jeopardy, I want to write a spanish textbook and/or app or something, I want to learn more languages, I want to become a better engineer.  The only thing I can imagine ever wanting to do with math is teaching crappy math to other people who are never going to do anything with it.

Please give me your favorite mathematical insight or discovery. Have you discovered any connections between different areas of mathematics?

This is a question I have to answer for my shitty shit shit garbage math class.  My grade depends on this somehow.  I don't know what the criteria are.  Fuck all of this.  Fuck the teacher.  Fuck ualr.  Fuck college.

I do not have a favorite mathematical insight.  I hate all of math.  I used to like it.  Well, no, I liked what I was told was math.  How am I supposed to remember everything and pick a favorite?  That's fucking stupid.  Obviously the thing I'm most interested in at the moment is the thing I chose to do for my stupid "research project".  But it's not really special.  I've realized other things too.  Like if you are given a finite number of points on a graph then there's an infinite number of functions that fit those points.  Ugh, I remember liking math, I remember liking things and being happily amazed by things, but it's been too long, I can't remember anything else.  I don't even know what different areas of math are.  What math have I studied?  algebra geometry trigonometry calculus differential equations statistics probability number theory discrete math college geometry idfk what else.  Algebra is used in all of it, statistics is nonsense to me, trigonometry calculus and differential equations are all the same thing, geometry is algebra with stupid shapes, probability is algebra, whatever, the only really weird thing was college geometry.  It made use of arithmetic?  I guess?  I don't even really remember.

What will I tell the teacher?  What is my favorite math whatever?