Forty Years of Teaching Math, Computer Science and Engineering Science at a Community College- Part XIII- Linear Algebra

From 2001 until the time I retired I taught Linear Algebra every spring. In the 1970's Linear Algebra was a gateway to higher math for math majors and was taught in a very abstract fashion.  Through the years Linear Algebra became more applied, catering more to engineers and computer scientists.  A second course in Linear Algebra includes all the theory that was previously taught in the first course, and then some.  My course changed with the times.

I was pleasantly surprised in my last few years to have a fine bunch of computer science students. Some of them came into the class with a list of topics they wanted to learn. These bright students were well read in their field.  There was this barrier that they could not cross, and it was mostly Linear Algebra. Linear Algebra had emerged as a central course for AI in general, and specifically for machine learning.  Linear Algebra is also central for computer vision, computer graphics, gaming and robotics. Suffice it to say, Linear Algebra is a very important course, and its importance is growing as we speak. 

A simple problem in Linear Algebra is to take a bunch of points that represent a surface in 3D, multiply each point by an appropriate matrix, and surprise, the new set of points is the original surface rotated about a given axis.  Encoded in the rotational matrix is the axis of rotation and the number of degrees of the rotation. Humans see by viewing two 2D images - one rotated a fixed number of degrees from the other - and constructing a 3D image in our brain.  In Linear Algebra we can replicate this for a machine. 

Linear Algebra is also useful in just about every engineering course.  It is not required in engineering because there is already 150+ hours required by ABET.  Engineering students are faced with taking 153+ hours or learning the subject on the fly while they are taking 4 or 5 engineering courses in their junior year.  A handful of engineering students ended up in Linear Algebra, although they were not as curious about the subject matter, mostly because they were curious about how they would survive Dynamics, Mechanics of Materials, Circuits and Differential Equations, along with Linear Algebra.

In my next-to-last semester I had one particular student who, on the first day, asked me if we were going to learn how to factor matrices using QR Decomposition, and I think one other method.  There are several different types of factoring, all with specific uses, and multiple algorithms for each type of factorization.   

One use of factoring is to filter out noise.  With a sound file we can literally filter out background noise using linear algebra and some other math, and a specific factoring technique. In machine learning, we sometimes want to ignore extraneous variables, and isolate the important ones. These extraneous variables are called noise. Factoring matrices allows us to do this. We can factor a matrix of data into a rule matrix, and a noise matrix.  

As humans we make rules as we live in the world.  We drive for a while, and decide that 15 mph is a good speed to make a right turn.  We do not repeat an experiment - we take lots of little experiences and ignore what is not important, and make the rule, even if it is not a conscious rule.  The human mind is good at making such rules.  We go from facts to rules without even making a conscious effort.  And so it is with matrix factorization: we can take a handful of driving experiences, and calculate a 15 mph rule for right turns.  Human reasoning is replicated, although with different means.  I seriously doubt children are born with matrices in their brain. 

Scientists will isolate variables as much as they can, and do an experiment.  Epidemiologists cannot always isolate variables because they do studies in hindsight. Thus, the epidemiologist has to do more sophisticated math to isolate the variables after the fact.  And so it is with machine learning.  We want the machine to be able to learn as it "experiences" its environment.  Linear algebra helps us do that.  We can factor a matrix of experiences into the product of two matrices, where one matrix gives us the rule, while the other has the noise we can ignore. 

Anyway,  a student asked me about a specific kind of matrix factoring, so I told him I would oblige.  Weeks alter, he asked again, and I said not yet. I can't remember how many times it was brought up, but I stalled until the end of the semester. 

When I did finally show the student how to do QR factorization, the algorithm I used was easily and fully understood by the whole class, because various elements were based on all they had learned throughout the whole semester. During Week 1 of the class, I would have lost them 5 minutes in. By week 15 The class not only understood how to do the procedure, but they fully understood why the procedure worked, because of all the theory that was covered in the class.  A topic that was once nn impenetrable barrier was now a joy to learn!

I explained how pretty much anything else these students needed to know in Linear Algebra, at least applied to machine learning, etc., could likely be self taught and fully understood. The course I put together made it so.  It was a great meta-lesson, brought about by the students' curiosity. 

The above picture is from one of many short courses available for students entering various fields that require Linear Algebra.  I used to pass one or two of these out, allowing students to follow along as we developed the course. My course always covered about 95% of each of these short courses. I told students they were welcome to ask any question about Linear Algebra that pertained to any other field, if they chose.  Sometimes they would take me up on that offer, successfully.  Through the years I got all sorts of crazy questions. 

On a humorous note, I would always reserve the last day of class to "attack Canada." There was always a build up to this point, where I would promise to give them enough tools to launch an attack.  The students, of course, knew I was not serious.  It was very funny because it was such a preposterous idea. 

It is easy to formulate such a problem where we are adding soldiers by breeding, and subtracting them due to combat loss and natural deaths. Since it is an easy problem to visualize, it is a good problem. The usual solution requires solving a linear, first order system of differential equations. Using eigenvectors (part of Linear Algebra,) the whole solution can be solved very simply.  

Since our population is about 10 times that of Canada, we need to make Canadians great lovers and even better fighters to win a war.  We had a lot of fun with that!  

Eigenvectors are a central topic for all the various subjects listed above, and a subject that is often given little attention at universities. At the end of the semester we would bring to bear all the theory we learned, to give students a great understanding of such things. 

 

Forty Years of Teaching Math, Computer Science and Engineering Science at a Community College- Part XII- Physics

 

I wasn't at all surprised when Nick Jerla earned his Ph.D. in physics from SUNY Buffalo.  Nick is the person on the left of this photo. 

I first met Nick when he came to my office, asking for permission to take Linear Algebra, despite not having the prerequisites. Nick explained that he was trying to learn quantum mechanics, and he had run into a barrier with some terse linear algebra. I let him in.  Later he explained that he had failed 11th grade trig in high school.  I was skeptical of his abilities at that point.  Perhaps he was a dreamer who watched Good Will Hunting, and thought he was of the same caliber. 

In the actual Linear Algebra class Nick plowed through every topic, leaving no stone unturned. I knew at that point that he was something special. 

The last time I saw Nick was when he stopped by with a question about the 2-dimensional heat equation, and its application to a conduction problem on a disk. He had to solve one problem, and use the result to solve another. I explained what they wanted and he was good.  Nick then told me his transfer to U.B. was seamless.  His junior-level courses all picked up where we left off at NCCC.  That did not surprise me, either. 

The last chapter that I painstakingly added at the end of our calculus sequence develops the language of Maxwell's Equations, which govern the whole electro-magnetic universe. I developed my own problems that gave students a very deep understanding of various theorems in that chapter. I also added spherical coordinates to Calculus III, which are useful in quantum mechanics. In Differential Equations I added a plethora of applications of Newton's 2nd Law, including mechanical vibrations, and also circuits.  Various physics professors never seemed to explain these things well.  I must have "physics" written on my forehead, because through the years I answered more physics questions than I can count. Almost 40 years ago a student named Cheryl walked into my office and asked me a physics question.  Cheryl had pestered her physics professor and could not get to the bottom of some motion problem. That set in motion a series of questions that continued until my retirement. 

About 15 years ago my daughter took a C++ programming class at NCCC.  She was not a student at NCCC, so no one knew who she was. One day she was listening to a group of students behind her talking about physics.  The conversation went something like this.  Bill: if you have a physics question, ask Mr. T. Al: Yeah, he is real cool about it.  Really chill. Rachael: He can answer anything.  And he has a really simple way of explaining everything. 

One large problem I had Differential Equations students work on is J. J. Thompson's original determination of the ratio of the charge to the mass of an electron. In 1899 Thompson shot an electron beam into an electric and magnetic field, and it travelled in a cycloid path. That part of a cycloid looks somewhat like a quarter circle. Determining the ratio of e/m required solving a system of differential equations.  The students love this problem! It was an ingenious experiment, seeing how all the complex math played out. I also added some numerical methods that appear here and there throughout physics, including power series methods.  And then there were mixture problems, that perfectly matched the first junior-level Environmental Engineering course at U.B. Everything I added about physics applied to all the various branches of engineering, as well.  

I don't ever remember students complaining about Differential Equations being too difficult.  Students can accomplish some pretty amazing things, given the right circumstances.  Their confidence began with my confidence in them. 

I passed off my Differential Equations course to Tadeus Krupa back in 2013, when I got involved with teaching Engineering Science. Tad weaves everything together, as only he can do.  In the end he will start with 20 students, finish with 20, and the students will have received an excellent education, and are no worse for wear - all the while learning about 50% more content than when he and I took the class many years ago. 

Tadeus, by the way, almost did not get a job teaching at NCCC.  A shameless county legislator tried to put an unqualified candidate - a candidate who barely passed calculus - in his place when a search was done. Carolyn Goldberg, who was chairing the search, stood up to the county. That search was called off, under threat from the county. The very next year NCCC got a grant to replace a key faculty member, and the admin was going to spend the money on something else. Bulldog Tony Gullo called the admin out, and Tad was snuck into the department while the county legislature was looking the other way!  In the years since, the public has benefitted by having our graduates build rockets and stadium roofs, instead of receiving a substandard course taught by an unqualified instructor, with transfer students hanging on white knuckled, likely changing to a less quantitative curriculum.  Tad Krupa is unquestionably the best math teacher I have ever known, with no close second.

Very few people have the capacity and temperament to do what Nick did.  But, my point is that, for someone of his ability and interest,  it is possible to do what he did at NCCC, and to do it well.  Many more came before him, and did a similar thing according to their interest and ability. Nick was not a fluke.  We had countless students plug into all levels of STEM, successfully, and the math department played a pivotal role by removing many barriers, and propelling students forward to accomplish way beyond their wildest dreams. 

About 20 years ago I was invited to the wedding of Brian Milleville, who is now a math professor at ECC.  Brian teaches all their difficult courses, and does a magnificent job. One of his aunts asked how I knew Brian.  I told her I was his professor and advisor at NCCC.  She did not believe me at first.  She did not think it was even possible to take college math at NCCC. It was as if I stated that the Pope had become a Pentecostal.  I might just as well have stated that Sanborn really was Silicon Valley. 

When Brian got married he was in a Ph.D. program at Indiana University.  Brian had transferred from NCCC to U.B., and then was accepted into 6 Ph.D. programs for theoretical math.  He was ABD, but did not finish, instead taking a job at ECC and getting on with his life.

STEM at NCCC has been invisible to the public over the years.  Doc Kwitowski tried to advertise our programs and success stories during the Miller era, and was not allowed. It is one thing, after all, to give the public a brochure.  It is quite another to actually prove to the public that these programs work. In the 90's there was an NCCC commercial that was often played at area movie theaters. In that commercial a student making a clay pot was shown. I remember shrinking into my seat as fellow movie goers joked about going to NCCC to learn how to make clay pots. There is nothing wrong with fine arts, but during that era the public perception was that making clay pots was our forte, and that there was nothing more rigorous at NCCC than making clay pots. 

Dr. Cleveland would have gotten along with us, but she was not here long enough.  And Dr. Klyczek, well, it was no secret that all of our money went into advertising the NFCI.   Every time someone was hired at Delaware North there was a press release. 

At the time I did numerous searches on the NYS Department of Labor website, and the search term "Engineering" produced 500+ hits for a 25-mile radius of North Tonawanda, whereas search terms of "chef", "cook", etc. routinely returned about 10 hits.  Of the 10 or so hits, usually only one or two at most required a degree. 

In 2017 Kiplinger's ranked the top 10 undergraduate majors.  All but two were STEM fields, and the two that were not were health care-related, and required a lot of STEM classwork.  Kiplinger's also ranked the 10 worst, and the worst of the worst was Culinary. Their main reason was that very few culinary jobs require a college degree.  Kiplinger's recommended getting a business or accounting degree, and just working in a restaurant to get a handle on the business. 

I ran engineering forums for a number of years, inviting numerous former students back to speak. At one such forum, we had an engineer who designed the roof for the world cup soccer stadium in South Africa, an electrical engineer who was the plant manager at American Brass in Tonawanda, a mechanical engineer who built the wind tunnel at Calspan (not a former student) and a mechanical engineer who now works at SpaceX.  

Later on we had a roboticist who worked on a new autonomous vehicle manufacturing facility at BMW/Clemson, the senior marketing manager at Micky Thompson, a mechanical engineer who designs hunting bows, an environmental engineer who works for the DEC, a senior engineer who works for National Fuel gas,  a pharmaco-kineticist who worked for Merck, a VP of Analytics at M&T Bank, an actuary who is the senior underwriter for Magellan Health Care and an electrical engineer who works at a nuclear power plant. 

The engineer who designed the world cup stadium roof went on to also design the roof for SOFI Stadium, and also the LA Clippers stadium. He spoke to our students numerous times. He is the leading expert in this country for rubber membrane roofing systems.  He said other companies try to get into that space, but hire him as a consultant after they botch things up. 

None of this was newsworthy, of course.  Public Relations would never advertise these events, despite all the blurbs I put together each year for a press release. I assume PR had their orders from on high. In the end I transitioned these events to just having former students come speak directly to our students, outside the purview of the public and our administration.   Every single former student I asked to come and speak did, with the exception of one industrial engineer who wanted to, but had a conflict. 

I made the best of it.  And my students prospered.  It was quite satisfying doing all this with little institutional support. 

Forty Years of Teaching Math, Computer Science and Engineering Science at a Community College- Part XI - Teaching 9th Grade Math in a Lutheran School, Part II

 

My involvement in the Lutheran schools was beneficial to the math department at NCCC.  In 1999 academic affairs would make a move to offer college courses for credit in area high schools. The department called on me over and over again, since I thoroughly knew what was going on with k-12 math. 

In the spring of 2002 there was a public debacle with the Math A/Math B high school math curriculum.  Math A was a 1.5-year course that was required for graduation from high school.  Formerly students could either pass a 9th grade math regents exam with mastery, or pass a lower-level RCT exam with mastery. By requiring all students to pass the Math A exam, NYS was increasing the standards across the board, or so said the propagandists. 

Numerous students could not pass the Math A exam in the middle of 10th grade, so it could be taken again, as many times as required. By the spring of 2002 there was a log jam of students who were on their last chance.  70% of the state failed that exam. A public outcry followed. In the end the state put a huge scale factor, or curve, on the exam. A raw score of about 30% was scaled up to a passing grade of 65.  And a significant portion of the exam was multiple choice!

A statewide committee of math educators was formed, and colleague Carolyn Goldberg was asked to be on the committee.  She asked me if I was interested, and I declined. By then my wife and I were busy driving our four kids around to various activities.  I did offer my advice to Carolyn, and she took me up on that offer numerous times. A handful of my ideas made their way into the NYS high school math curriculum. 

The story Carolyn told me was that the large committee started with Kindergarten and worked their way up. By the time they got to high school most of the committee had stepped down, which left Carolyn and a clueless college professor who maintained that geometry proofs is what turns students on to math. My recollection is that Carolyn did the bulk of the work in putting together the whole high school curriculum.  How did I help out?  As one example, the new SAT exam was just developed, and the initial NYS draft was missing some of the new content, so I wrote what was missing on a piece of scrap paper, and off Carolyn went to Albany that weekend with the missing content.  I also told her to make 9th grade math "Integrated Algebra" and not just a random integration of various strands, and so it was. 

The new math curriculum was a vast improvement over the Math A/Math B debacle.  High school math teachers uniformly agreed with that opinion. Eventually it was superseded by Common Core, which was good, although according to the Thomas B. Fordham Institute, Common Core actually lessened our standards in NY, but raised the standards in southern schools.  

From 1996 to 2012 I taught 4-8 students per year in a Lutheran school, which was more than half of each 8th grade class. Both St. John and St. Peter had no admission standards, unlike elite private schools.  Their student population was roughly half from the congregation and half from without. In terms of native ability, students formed a pretty good cross section of the population. There were two differences worth mentioning.  (1) Special needs students were rare, and could get better services in the public school.  (2) Lutheran schools were likely to have students with parents who were more involved with their children's education.   So, comparisons with the public schools are difficult. 

I had a listing of all my students and what happened to them later, but that list was lost.  None the less, over half of my students went to college for a very quantitative STEM curriculum. Most of the STEM students majored in engineering (more than 2/3 of them). Of the whole lot, only one failed to graduate from college in the field in which they started. That surprised even myself. These difficult STEM fields have around 80% attrition, nationwide. 

Looking back I expected my students to do well in high school and beyond. Why?  Everything I taught them significantly amplified how much they learned in 10th-12th grade math, physics and chemistry.  And various branches of engineering are applied physics and applied math.  It was not obvious how to do this.  But, doing this was not as difficult as you may think.  It is easy, if you know how.  

Forty Years of Teaching Math, Computer Science and Engineering Science at a Community College- Part XI - Teaching 9th Grade Math in a Lutheran School, Part I

 

By the fall of 1995 I was resigned to the fact that innovation at NCCC would be limited to revising our existing courses. The Miller-Kwitowski feud showed no sign of subsiding, and it would continue for four more years.  And no one else in the math department was interested in innovating anything related to engineering and the physical sciences, which I was.  The senior members were all on their way out, and would retire shortly. 

Also in the fall of 1995, Beverly Craig,  the first grade teacher at St. Peter Lutheran, North Ridge, mentioned to me that her son Ken Craig was teaching 9th grade math to 8th graders at St. Matthew Lutheran in NT.  I asked why we didn't have that at North Ridge. 

In a matter of hours I would volunteer to teach this class at North Ridge. My youngest, Jeremiah, was born that fall, so I offered to teach the course beginning in January after Christmas. I also was only available M-W-F, so we would meet three afternoons per week for a little more than 1 hour, after which I would drive my kids home from school.

I explained to the parents that I could not make any promises under the circumstances, but that at least each student would get a head start on 9th grade math when they went on to high school.

When I started in January I was in for a few surprises.  The valedictorian from the previous year was struggling with math, and eventually would drop out of Regents-level classes at Starpoint. Why?  K-4 at North Ridge were outstanding.  The 5th-6th grade teacher was too busy working on his next career to be of much use to his students.  And, the 7th grade teacher hated math. A parent named Rhonda told me the kids hardly had any math at all in 7th grade. Their teacher would save math for the end of the day, and usually would not get to it. 

The above text was supplied to me by Wilson High School.  It is a great text.  Unfortunately, it is about 1,000 pages, and working through the text, page by page, was unworkable.

One night in January I went for a long run, and came up with a plan. The plan involved lots of mental math, plenty of worksheets of my own construction, and a constant stream of algebra in large chunks.  The worksheets would develop some powerful intuitions in pre-algebra and set the stage for a deep, conceptual understanding of the most abstract elements of the course.  The book was very useful for algebra word problems and two well-written chapters on logic. 

The students were stoked. I assigned lots of homework and the students did every assignment, faithfully. 

In 22 short weeks, with 66 class periods, the class went from a 5th-6th grade math level to the end of 9th grade.  One girl named Elizabeth earned a perfect 100 on her 9th grade math Regents exam, and went on to be a biochemist. Another earned a 98, missing one multiple choice question.  Lisa would win a math award at Fredonia, and is now a high school math teacher.  The next three students scored 84, 82 and 81. Chad earned an 82 and went to NU for business, and now runs his own insurance agency in North Carolina. 

I would continue teaching this class, voluntarily, until 2012 - for three years at St. Peter, and later at St. John in Wheatfield. Sometime later Academic Affairs would tell me that this venture is not considered Community Service, and that I should take it off my resume that was used for promotion.  I took my resume back, and did rewrite it.  I explained how my neighbor and good friend Clyde Burmaster was a Methodist, and considered Ransomville United Methodist Church as part of the community.  Clyde was a Niagara County Legislator. I also mentioned that my good friend Shirley Urtel was Chairwoman of the Finance Committee of the County Legislature, and how her committee appropriated over 8 million dollars for NCCC.  Shirley was a member of St. Peter, her two children were enrolled in the school, and her daughter was involved with equestrian activities at the same barn as my daughter.  I knew Shirley very well, and I mentioned that she surely felt that St. Peter was part of the community.  My kids are still friends with Shirley's, to this day. 

More to come.......

Forty Years of Teaching Math, Computer Science and Engineering Science at a Community College- Part X - More Art

On Christmas Eve, 1981, I went in to the math department at SUNY Buffalo to get my paycheck. I earned $110 per week for roughly 10 hours of work. I taught 4 hours of recitation, did 2 hours in their math lab and had 4 office hours. It was a nice gig, considering I paid no tuition as well. 

In the commons were John Isbell and Stephen Schanuel, working some problem on the blackboard. It was 4:30 in the afternoon.  I would later pick my mom up, a recent widow, and take her to Church. Both Dr.Isbell and Dr. Schanuel were brilliant mathematicians. Their work is easy to find.  Along with F. William Levere, the three of them were part of a hiring binge in the 60's, where the push was to make U.B. the Berkeley of the east.  

Eventually these two would have a falling out, with one calling the other an "ineducable idiot."  Also later on, two other professors would get drunk at a party and come to blows over the definition of infinity. There are a lot of divisions in the foundations of math - constructivists, intuitionists, etc. -  with people staking their claims and willing to go to war over them. 

I would go on to really enjoy spending 16 hours per day, or more, doing theoretical math. I am sure Art did at one time as well. None the less, that image of these two geniuses going at it, while life passed them by, remained vivid in my mind.  There was a whole world of celebration going on a very short distance from Diefendorf Hall, down Main Street in Buffalo.  Stores were decorated, people were shopping, children were anticipating, and the taverns were full of Christmas cheer.  Yet, this was all these mathematicians had.  Right or wrong, I believed at the time that these professors' whole life had shrunk to a point, on which danced a few math problems that were of no more cosmic significance than the page of theorems about angels the Scholastics had proved, and that Erasmus spoke disparagingly  about in his seminal 1511 work, In Praise of Folly. 

G. K. Chesterton, in his magnificent work Orthodoxy, pointed out that it is always the logician who goes mad, and almost never the poet or the artist. Chesterton got that right. He went on to say that logicians (and mathematicians) live in a really small world, unlike the artists, who live in a much larger and wonderful world.  Logic does draw you in, with the prospect of certainty.  In the end the world of certainty is a very small one, indeed, and logicians often cannot escape that small confined space. I managed to escape. 

One professor I worked for in the department would lose their mind, and end up in a homeless shelter.  Another committed suicide a few short years after she taught me logic.  At the time I wondered if math made these people lose their minds, or if math attracted people who lost their minds.  Abstract math can be very isolating, especially when, if you are at the top of the field, there may be only a handful of people who fully understand and appreciate what it is you are doing.  Mathematicians can also be very arrogant.  It is not good for the soul to look down your nose at humanity, and especially the least among us.  

Art Hadley had a better life than these mathematicians. At one time he owned a Cessna.  And those who knew Art would agree that he often lived life to the fullest. 

It would not surprise me at all if by some metric, Art Hadley was brighter than both Dr. Isbell and Dr. Schanuel.  I also thought that if I did what Dr. Isbell and Dr. Schanuel did for 40 years, I might be a whole lot better at it than them - that is, if I did not go mad in the meantime.  Dr. Scott Williams, himself a well know topologist, told me I was by far the best graduate student he had in 20 years. 

Now, after 44 years, teaching at a community college worked out well for me. I certainly have no regrets.  There was a whole lot more to life than math. And many of the people who I trust the most, and respect  the most, and enjoy hanging out with the most, are the poets, the musicians and blue collar workers. All of these fine individuals know a lot about life. Teaching at a community college kept me in touch with humanity. 

More to come......

Forty Years of Teaching Math, Computer Science and Engineering Science at a Community College- Part IX - Tony Gullo

Tony Gullo came to NCCC in 1967, having a B.A. and M.A. in physical anthropology. From my student days all I remember is the name. Sometime later Tony told me of his involvement from the early days. His list was long, and from my recollection, Tony Gullo was omnipresent in college-wide affairs in the early stages of development of Nabisco Tech.

Certain things are a given when a college is formed. Other things are elective, like accreditations, union contracts, management domains, etc., and land wherever the people involved define the shape of things to come. Many of those elective things were formed inside Tony Gullo's brain and carried out by his will. 

I knew Tony as my Faculty Association President, from fall of 1985 to spring of 2006, when Tony retired.  In the fall of 1985, younger faculty were being impoverished by past circumstances that were beyond faculty control, and particularly beyond Tony's control.  By 2006 we had a faculty contract that was fair for all. It was not a perfect contract, but it was a herculean effort that took place, and was no doubt the best that anyone could have carried out.  In my case, that contract allowed me to support a family of 6 on one income and to earn an honest living doing what I truly enjoy.  My salary was on par with k-12 educators in the area, and that did not happen because of the good will of the county. 

Over 20 years ago I was the Chairman of the Board of Christian Education at St. John Lutheran School in Wheatfield. We went through a National Lutheran School accreditation at the time.  The benchmark for expenditures was that at least 70% of revenue was to be spent directly on instruction. If expenditures fell below 70%, our accreditation would not be renewed. Community colleges have similar benchmarks, nationally at about 40% and California having a state guideline of 50%.

The lower figure for CC's is to be expected. For one, most Lutheran schools are provided a building rent free, with capital expenditures being underwritten by a sponsoring congregation. And, CC's maintain a strong support staff that includes counselors and librarians, and more expenditures on lab/tech equipment than the average elementary school. 

Tony steadfastly made sure that funding from tuition, state and county was appropriately spent on faculty/instruction.  I don't have any hard figures from that era, but a good educated guess would be 40-50% being spent on instruction, perhaps more at times.  

Not too long ago, maybe 2018 or so,  one of our trustees complained that 30% of our budget was being spent on instruction. The complaint was that 30% is too high!  The true figure is probably below 30%, since many capital projects seem to be funded outside the budget. And, the senior faculty prosper while the new faculty do not. The gap is wide and growing, unimpeded. 

What the current state of affairs would be had Tony stayed on for another 20 years is anyone's guess, but the fact is that when Tony was on the job, money landed squarely where it was supposed to. I would guess there was constant pressure to do otherwise. 

My Lutheran theology tells me that all are sinful, and corrupt to a certain degree, but Tony's actions would seen to contradict that point. He was seemingly incorruptible, in steadfastly carrying out his duties as union boss.  There were a few disturbances in the early days of the Faculty Association, but they were quickly put down, and the honest edifice of union leadership allowed the whole faculty to prosper. He was surrounded by a few other bulldogs, who were as honest as the day is long - in particular Bryce McMichael and Randy Schultz - two  men who I thoroughly respect. 

Forty Years of Teaching Math, Computer Science and Engineering Science at a Community College- Part VIII - Arthur Hadley

 

There are certain difficult concepts in math that are fully comprehended by few. Calculus is difficult enough, but the field of Real Analysis is theoretical calculus, and Topology is theoretical Real Analysis. And there are further abstractions.

None of this was beyond the reach of Arthur Hadley. Art came to NCCC in the late 60's.  The exact date eludes me as I gave away all my old yearbooks, so I'll go with 1967.  Art is on my very short list of brilliant people I have known. 

Art came here from a Ph.D. program in theoretical math at SUNY Albany.  Art finished a couple years of his Ph.D. and could easily have finished the Ph.D., but told me the pay was better at NCCC than at SUNY Albany, and he enjoyed the culture and freedom that he had here. 

I knew Art well when I started in 1985.  I talked to him whenever I would stop by and he was interested in my progress, well into graduate school. Art was also my Calculus II teacher at NCCC in the spring of 1978 at night. Of course, I noticed immediately how intelligent he was. Every Calculus II class was followed by an optional lab in M-Building, also known as the Marlboro Inn. There was always plenty of beer involved, followed by a few games of pool. I lived down the street from M-Building so I could walk home from Calculus Lab.  

I really did live an idyllic life that year. Every day was a new adventure of learning - everything from Aristotle to Newton - and I had the freedom of an adult, had a good set of friends and all this happened in my hometown.  Most important of all, I was getting a much better education than my peers who had left town for "a real college".  My friends were going into debt and I always had plenty of cash to spend. Ironically, but not surprisingly, I was the only one in my circle of friends who graduated in 4 years.  I also was accepted into 3 Ph.D. programs for theoretical math, each with a full tuition scholarship and a generous assistantship. 

We also had a number of interesting speakers at NCCC, including Alan Zweibel, who was one of the original writers from SNL and a UB grad.  Cross Country was also going well.  Coach Jim Mezhir knew how to get us runners to respond, and he was the best coach I ever had. The whole XC team was close, with lots of comradery, and we all got along very well.  The following fall we would win our conference and finish near the front in some major invitationals. 

When I arrived in the fall of 1985,  during one of my first encounters with Art, he said, " I'll bet I scored higher on my GRE math than you did." I had my transcripts and GRE scores in a manila folder, which I happened to have handy, and showed him my perfect 800.  Art had scored 780, and had never met anyone with a higher score. He got such a kick out of that episode. Each year Art would return to our annual Ken Raymond Math Award ceremony, where I was always the MC, and Art would tell that story with a chuckle. 

Art was always a good friend and offered a lot of valuable career advice, all of which turned out to be sound. 

In my 4th, 5th and 6th year of teaching at NCCC I took over the main sequence in Computer Science - Programming Logic I & II, and Data Structures.  In doing so I updated the language from Pascal to Modula-2, and developed all my own projects, aligning students' work with ACM and IEEE standards. Freshman enrollment increased from 13 to 39. To keep current I learned  four more languages, including non-imperative (AI) languages of Prolog and LISP.  

To learn Modula-2 I developed a program where a user opened windows with various financial formulas.  In each window the user could enter 3 variables and solve for the 4th. Then the program could be prompted to print out a lesson on how to do the work with pencil and paper.  On top of that I built a macro language so the user could write a program to use the opened financial functions to build solutions to more complicated financial problems.  And, I developed a debugger for the macro programming  language.  This was all done on an MS-DOS platform, before Windows was widely used.  The next step would have been to generalize this program into other areas of applied math. It really was innovative, and I believe no one has done anything like this since. 

I had engaged my comp. sci. students, having them work on worthwhile projects.  SUNY Buffalo had students solve the Eight Queens problem, so I assigned the more difficult problem of the Knights Tour. Two transferred to U.B. and worked on their hand writing recognition project for the USPS. Another student named Jesse developed a relational database. And a Chinese student named Tom Wang did all our classes in one year, and then did another year at RIT, finishing his 4-year comp. sci. degree. in 2 years  I still have a gift Tom gave me. Tom already had a Ph.D. in physics from University of Beijing.  

When it came time for a promotion, Academic Affairs told me I was "not doing enough for the college".  I was not sure what "the college" was.  Perhaps there was another college that no one told me about.  This system did take some getting used to.  

Art gave me a lot pf practical advice during this period that kept my head screwed on straight.  Art very bluntly mentioned that what I teach does not matter, and how I teach it does not matter either. It is what happens outside the classroom, and how many favors I can do for the admin. 

During that era our remedial math and English teachers reached full professor in 11 or 12 years, while I took 20. It was not a level playing field. Why?

How can you compare teaching Data Structures, Programming Logic II, Calculus III, Linear Algebra and Calculus I to teaching 3 sections of Arithmetic and 2 sections or Precalc?  You can't because remedial arithmetic consisted of sitting in the front while students worked through their books and occasionally took a test, which was graded in class using a right-or-wrong answer key.  The remedial teachers had lots of time to burn.  One at ECC had so much time to burn that he worked for various publishers while his remedial students did their work.  Remedial teachers could serve on multiple committees, and do all the political lobbying required to climb the ladder, and still be out the door by 3, and not taking any work home with them. 

I stepped down from teaching Computer Science. I might have continued but the math department had hired me to take over all the advanced courses as senior members retired, which I did, and doing that along with comp. sci. was exhausting, especially when management was largely disinterested of what I was doing. 

Other significant figures in computer science were John Baldwin, Bart Nigro and Mark Constantino. The story I was told about Bart Nigro was he was brilliant, but was chased away by a heavy-handed dean who foisted a banking computer upon us, and a few other colleges across New York.  That banking computer did not even have a FORTRAN compiler, which was needed for teaching a few classes at NCCC.  Art told me plenty of stories about that dean, who pretended to have knowledge that superseded  anyone on the faculty. 

In 38.5 years of teaching at NCCC I can't think of a single administrator who was well versed in the hard sciences.  By hard sciences, I mean math, physics, chemistry or engineering science. That was definitely true with academic affairs.  There was a benefit to this.  No one seemed to know what I was doing, and I managed to stay out of harm's way for 38.5 years.  Art told me when to duck, and what not to step in. I had a good mentor in Art Hadley.