In September, 1948, while living in New York City, I began studies, as a physics major, at Columbia University under "The G. I. Bill". It was not my decision to become a physics major. Columbia University then and now has the best Journalism School in the country. I wanted to start as an Emglish major and go into the Journalism School when possible. I hoped to become a science writer, an ambition I'd had since 16, from reading the writings of H. G. Wells.
But I'd been an Army Air Corps weather observer and weather forecaster for approximately 5 years, before, during and after World War II ("The Big War", as Archie says). So, the supervisor at the Veterans Adminstration (who had to sign my papers for Government Support) said I must enter as a meteorological major. However, Columbia no longer had this major (put in during the War). The nearest place where I could be accepted for this major was Cornell University, Ithaca, NY. After arguments and delay, the supervisor agreed that I should not have to move to go to college. But picked physics as the "next best".
I had almost no formal training in mathematics and should not have been accepted for Physics.
My first Advisor was an English Instructor who put me in "College Algebra" and "First Semester Calculus". Why? Because these classes were open.
But "Calculus" was ridiculous for I'd had no Trigonometry and no Analytic Geometry. The professor was a mad Russian, Ervard Kogbetliantz, who invented Three-Dimensional Chess (now so popular on computers). He was appalled at my background and passed me out of pity, urging me to take Trig and Analytic Geometry before going on.
Trig was not available. I'm completely self-taught in Trigonometry, which was the first Course I had to teach upon becoming an Instructor. But I took the Analytic Geometry before going on to "Second Semester Calculus".
In my four years at Columbia, I never had an Advisor in my Major -- rather an Egnlish Instructor, a Professor of Chemical Engineering, and Professor of Astronomy. The latter allowed me to get into a lot of trouble. (I've often said that becoming a Parent and Teacher was easier for me than most. I just remembered what was done with me -- and DID THE OPPOSITE!)
I must tell you about another problem, which affected all Veterans at Columbia. At this time, there was an age restriction for entering Columbia College. You must be under 25 years of ago. Now, the average age of Veterans at the end of the War was 25 or 26. So, eager to get that "G. I." money, the "suits" turned a Night School -- The School of General Studies -- into a degree school, so we Veterans had to enter it. We had only a partial faculty, most of whom had no offices where we could consult with them. (We met them on Campus park benches.) And we had no Dean on Campus for the next four years -- he was in Great Britian.
And many SGS majors, particularly those in Physics, had a special problem. We had to take First Year courses designed only for SGS, then we were dumped in with Columbia College students in the second year. BUT THEY HAD HAD A DIFFERENT PREPARATION!!! In particular -- and relevant to my title subject -- they had "Calculus with Vectors", but WE SGS students DID NOT. Yet we had to use VECTORS in the "Mechanics" and "Electricity and Magnetism" Courses. So we had to teach ourselves "Calculus with Vectors" to keep up. Result: three-fourths of us failed the First Semester of each Course, and had to repeat.
I forgot to mention that we had no resident President. The month I entered Columbia, its President, Dwight Einsenhower, left to become Commander of the new NATO Forces in Europe. So Columbia was run by a "junta" of "suits", which is why things remained so sloppy. (When, years later, Columbia students rioted, I was sad at the event, but not surprised. The story of this riot was told in The Strawberry Statement by James S. Kuhnen. The film had a background score with songs by Crosby, Stills, and Nash.)
The biggest obstacles for Columbia physics majors were two graduate courses you had to take if you wanted a Master's degree. The FAILURE RATE in these two courses was so high, that "smart" undergrads took these in their Fourth Year, took "Incomplete", then did them over in their First Year of Graduate Studies.
One was a Physics Laboratory Course, which resorted to a trick perhaps unique in the country. The instruments were checked periodically, but usually NOT RECALIBRATED if "a little off". So, you'd better not get GOOD RESULTS, which would be evidence of "fudging". This was so nerve-wracking that 90% of the large number of attendees failed to turn in their reports and received "Incomplete". I did the same. But, after receiving a B.S. in Physics (with the equivalent of a Major in Mathematics and a Minor in Chemistry), I transferred to New York University, majoring in mathematics. (I received 30 credits in Physics, and 32 in Math from Columbia.) So I never passed the Lab Course. A friend stayed there and PASSED after taking the Year's Course three times -- which was "better than the average".
The other "killer" Physics Course was "Analytical Dynamics", heavy on math, particularly Vector Analysis. The Course was only given (always by the same Professor, who shall be nameless) in the Spring Semester for 6 Credits -- 2 hours a day, 5 days a week.
The Course was always given in a particular Amphitheater, holding 100+ students, with 9 sliding Blackboards down front.
There was a tough and confusing text book, A Treatise on the Analytical Dynamics of Particles and Rigit Bodies, by E. T. Whittaker. Professor Nameless had written a 100-page book of "Notes" to study, and a 100-page book of "Problems".
BUT THAT WASN'T ALL!!! Grad students advised us to get to the Class, in the Amphitheater, an hour ahead of time. Three Assistants would enter with notes and cover the 9 blackboards with information, which was erased before Professor Nameless entered the room to lecture. And THAT INFORMATION NEVER APPEARED IN THE COURSE AGAIN. Some poor snooks never could figure out where some of that info came from!
The failure rate was also 90%. So, you took it as an Undergrad, taking "Incomplete". Sat in again the next Spring. Failed. Then tried it again the following Spring. I also escaped that by transferring to NYU.