I think to be really understood, math needs to be applied. When I taught the calculus courses, I had the students work all the word problems. I collected the work and graded it. I would finish a term often two chapters ahead of some of my colleagues.
What is involved in solving word problems is translating from the written language to mathematical symbols, manipulating the symbols and then translating back to English or whatever language is in use.
My college advanced calculus course use the textbook âHigher mathematics for Physicists and Engineersâ. I spent hours working the assigned problems, but the math involved made sense to me.
Returning to the original posting a couple of quotes âŠ
âUndergraduate is about gaining an education, Graduate is about gaining a skillâ.
âIt ainât the name of the school but what you did while you were thereâ
âSince weâre going to have to completely retrain you anyway, what weâre looking for is someone who has demonstrated an ability to learn and has a demonstated multi year commitment to accompishing their goalsâ
Further, most people donât realize that most of the âTop Tier/Elte/Ivysâ consider themselves Liberal Arts Colleges and donât even offer Undergraduate degrees in Business, Law or Medicine although a heck of a lot of their graduates eventually go into these fields.
So my advice to a current Undergraduate would be, donât sweat the Major but instead focus on also taking the âmeatierâ courses (Statistics, Math, English Comp etc)⊠and earning the best grades possible.
1 Like
Caltechers who write well are exceptional. She showed her ability in courses. I suspect she showed her understanding in talking to the people whose work she was supposed to write up.
Caltech, and every school, for that matter, would love to have grad school applicants who showed up the first day ready to start their PhD research.
They give them; they donât admit people to pursue them. Many donât finish their PhD programs; some donât even pass their prelims. Giving them an MS on their way out the door does less
damage to their career prospects. Otherwise others will think they wasted their time.
I started off majoring in ChE (as they abbreviated it then). That wouldnât have happened 50 years ago. âThe graduate program in CCE [Chemistry and Chemical Engineering] provides students with the educational training and research experiences needed to achieve a PhD degree. (In special circumstances, a masterâs of science degree may be given.)â Graduate - Division of Chemistry and Chemical Engineering
Theyâre exceptional, but they exist. On the order of one in a million. I met one at Caltech.
Some do it without coursework.
Thatâs a minority of slave owners. But there were many slaves. From the 1860 census there were over 3 million slaves.
United States: black and slave population 1790-1880 | Statista
And if you didnât take that subject in undergrad then itâs damn near impossible.
So she did take classes? Didnât go directly from an English degree to PhD in Physics.
People who get masters degrees arenât doing it to be teachers or researchers. Itâs mainly for the work force. MS/MA is very useful in industry.
Exactly my point.
I know one guy who was accepted to Caltech for the PhD program. His background was BS in physics from Syracuse. He was a TA in one of my advanced Math classes at SU. Brilliant man. I donât see how anyone can get accepted to a PhD program in physics at Caltech without a damn good background in Physics and Math.
My daughter has her BS in chemistry from MIT and her MS in Chemical Engineering from Harvard. Her undergrad degree in Chemistry was perfect for a degree in Chem Engineering at Harvard.
Incorrect. I was offered admission in 1978 to pursue a masters in ChE at Caltech. That might not be the case now, but both the ChE and Physics departments have clear course requirements to get a PhD, many of which are math-related.
Some of the best students I had in my 44 year tenure teaching mathematics and computer science were also pursuing a major in music. It may be that the mathematics in music theory develops the mind for mathematics and computer science.
1 Like
It changed after 1971 then back by 2024? Have you conflated Caltech with Cal Poly?
I know admittees in Physics who took no courses at Caltech. I know one admittee in Math who came straight out of high school. ChE was more hide-bound and traditional, but I bet the student who showed enough could get admitted directly. I donât know any personally, but I left my interest in it freshman year.
Easy for the smart-enough.
I never said she did. I started off arguing that a degree in English doesnât condemn one to a life of literature.
Of course. I was just saying you donât have to get it in courses.
Hooray for you and your daughter. Congratulations to both. Whatâs she engineering today?
Are you kidding? They flew me out for an interview, I spent the night at the Athenaeum. I chose Stanford instead.
Iâm just going by the Caltech web site. It lists the Caltech course requirements to receive a phd for both departments. Have you checked?
Show me that person. Iâve worked with some extremely smart people with PhDâs and leaders in their fields in Physics and Math. None of them were smart enough.
Name one. Just one.
Some people do.
For a masterâs degree? The language in the 1971 catalogue is identical to that in the 2024 website. I canât believe it changed in 1978. You may have thought it was a masterâs degree but they thought it was for a PhD. Or were you some guy in industry they wanted to work with on a project?
Yes.
Stephen Wolfram.
I was clear, they understood. I must be one of your special people.
While a lot of what he learned was self taught - he still received structured instruction in Math and Physics. So he wasnât an English Major who decided to get a PhD in physics and just read books on Physics to meet the prerequisites.
I think you meant they donât require any coursework in anything to be admitted to a phd program. They do require graduate level coursework to receive a phd. At least thatâs what the Caltech physics and ChE department web pages says.
Who said he âjust read books?â Iâve learned plenty of complicated things without âstructured instruction.â (But sureâŠit wasnât math and physics, so I guess thatâs just âspecial.â) Why do you think it needs to be formal classroom instruction that lands on a transcript? Being self-taught is a thing.
@bing, you are clearly misinformed about the facts of the cause of the Civil War. It was about slavery, 100%. BUT, what was changed in the history books was that is wasnât about the morality of slavery but the economics of slavery. The myth of it being a moral issue did come up well after the war.
The fact is that the long summers and mild winters in the south made slavery economically viable. The short summers and long cold winters did not make slavery economically practical. I could write a book on why this is so, but that has already been done. One reference would be âThe Maple Sugar Storyâ by Helen and Scott Nearing. Very few in the north were morally opposed to slavery, but the economics of using slaves gave the south an advantage in the market place.
Slavery had been an issue since the Revolutionary War. It has ben said that the Civil War was actually the last battle of the Revolutionary War.
It is true that Blacks did own slaves, BUT that is taken out of context. When slaves were freed, many started successful businesses and would use their wealth, meager as it may have been, to buy their family members. Because freed slaves would often be kidnapped back into slavery, the freed slaves did not free their family members because as long as someone had the deed on them, it was more difficult for the kidnappers to sell them into slavery in another location and easier to recover them if that did happen.
You are correct that only a few whites owned slaves. Those who did own slaves were primarily from aristocracy of England. They got the big land grants from the King of England, paid for by their families. Mostly they were the second born sons. Only the first born sons inherited the estates in England as that was the law. It prevented the estates from being broken up.
The large plantations were difficult for the poor white farmers to compete against. The Planters (what the plantation owners were called) could use their advantages of size and slaves to undercut the value of the goods produced on the family farms. If you were one of the 98% of southeners who didnât own slaves, life was very harsh. Around the time of the Civil War, the Confederate Flag was NOT beneficial to them, in fact it was a sign of suppression. If the truth about that flagâs effect on their ancestors, most Southerners today wouldnât be so quick to embrace it.
Not to belabor the issue but professor Gallagher from the u of Virginia is the renowned expert. He has even a number of YouTube presentations and has been teaching the subject for decades.
For the north the issue was keeping the union together. Slavery was never on the minds of most of the volunteers and Lincoln until way later.
With the republican President though the south was afraid of the system being dismantled as a cultural thing and a states rights issue. Thanks to South Carolina, slavery was still permitted in the constitution and Lincoln could not stop it until it was amended in 1865. S Carolina was first to secede and then the others followed.
Torqueville had some interesting comments about the north and south as it related to industriousness and labor and nothing to do with climate. Sowell also makes interesting observations on the lack of industry in the south, particularly the lack of developing the iron mine in Alabama, the production of cheese, the care of livestock and so on. Slavery was seen as a bane to development in the south, not climate but culture. Not to mention ring worm from not wearing shoes.
But sure there were abolishonists in both the north and south and those that could care less. But there is no way the north could have gotten the volunteers and the production over the slavery issue. It was about keeping the union together.
Good strawman argument. Never said you canât learn new and even complicated subjects on your own. Show where I said that. Learning the prerequisites in Physics and Math on your own with a starting point of English degree is not the same. Not even close. I donât know about you but every physics (and other science(s) class - about 50% of the grade was lab. Helped a student get a better understanding of what they were being taught.
So youâve learned all your Physics and Math without going to any classroom?
IDK. Youâve been implying all along that formal course work / formal prereqs are needed. Even like two sentences later.
And then again:
And I donât have much going for math and physics. Never claimed to.