Personal Finance

Personal Finance- a subject which seems to be of increasing interest among high school students within the California Virtual Academies- is a case of an academic subject with the strong potential to integrate numerous key mathematical concepts to young people's everyday lives. Students who opt to take this class do so with a number of possible motives. Some students are college-bound, already firmly grounded in upper level math, and are taking this as an elective class to acquire exposure in economics, accounting, banking, investing, and the business world. Other students are not necessarily college-bound, seeking to complete their 3rd year of required math with classes such as this which do not involve upper level math that they are unlikely to ever use (from their perspective), and find that Personal Finance covers information that they will find useful immediately upon reaching their 18th birthday. The challenge "When am I going to ever use this?"- a rather cynical question expressed by students in many math classes- is one which is very rarely uttered by students in this particular class. Indeed, the material covered in personal finance is essential for high school students to acquire both to manage their own finances as they enter adulthood, and to avoid being scammed by people who actively endeavor to profit from people's lack of knowledge and awareness in this area. In the posts that follow, I provide a summary of what I hope students will derive from this course. This certainly does not effectively summarize or replace the course text, or provide any readers with an advantage in taking quizzes or completing the written assignments; rather, it might more accurately reflect what is in the back of my mind, as the key concepts I hope students will acquire and retain as a result of completing this course.

Psychohistory

This blog would be incomplete without some discussion of psychohistory. I should begin with a disclaimer; if you, dear reader, are unfamiliar with the science of "psychohistory", this is no surprise- unless you have read Isaac Asimov's Foundation series, and understand the reference. Psychohistory is a fictional science formulated about 22,000 years in our future, according to Isaac Asimov's fictional robot/empire/foundation historical universe, and incorporates the notion that human behavior can be reduced to mathematical equations. One of the primary principles involved is that while the behavior of an individual human being is extremely difficult to predict- with increasingly large numbers of humans being incorporated into the system, we have increasing ability to predict accurately. Those with basic knowledge of statistics should recall the law of large numbers; a similar principle applies here, with the average behavior of a large number of repetitions more accurately predictable than a single event. "Wait a minute," you might exclaim. "There is nothing new here!" In this you would be correct. Indeed, the basic principle of psychohistory is derived directly from economic theory, which in turn is largely the product of the Enlightenment (18th century). Economics does involve the representation of human behavior in the (now global) marketplace in mathematical form. A primary principle of economics is the notion that while an individual human being is essentially unpredictable, within a large system we have the "extremes" represented by different humans' personalities and the like cancelling each other, so that we can with increasing accuracy model the system based on the behavior of the "average" human being. Economics- and the areas of finance and accounting- are thus of particular interest to mathematicians, not merely because of the amount of math involved in these areas, but because of the ability to express the behavior of human beings in mathematical form, and potentially their future behavior.

Definitions and Mathematicians

Any mathematician will freely admit to our obsession with definitions. As an example of this, observe the result of asking any mathematician "Are you okay?" A normal individual would reply "Yes" or "No". Not so with a mathematician; you can fully expect a mathematician to reply, "How do you define 'okay'?" This is the main point I wanted to make; a mathematician will resist attempting any problem until he understands every word contained in the problem itself.
I should forewarn anyone reading this who might be either taking or planning to take any math courses at the university level and has the need to visit a professor during office hours: Please DO NOT ask for assistance with solving a problem without first understanding all relevant definitions. If you do this, you will at the very least annoy your professor, who will usually be unrestrained in expressing his annoyance at you. I should clarify: There is nothing wrong with being confused at definitions in material recently learned, and a math professor will have no problems if you say, "I am confused on problem 9. FIRST OFF, I AM CONFUSED BY THE DEFINITION OF...". In expressing your confusion while simultaneously admitting that you are unclear regarding one or more definitions, you are at least acknowledging that your confusion regarding definition(s) is obstructing your progress. If, however, you simply ask for help on a problem and- when the professor queries you regarding one of the definitions in the problem itself you reply that you do not know - then your professor will almost certainly become annoyed.
How does this notion apply in real world situations? We have seen several examples of this in terms of current events. For instance, what is the definition of an economic "depression" as compared to a "recession"? The lack of a clear quantitative definition raises the following question: Was the recent (and possibly still ongoing) economic crisis a recession or a depression? The term "Great
Recession" seems like an absurd attempt at sidestepping this issue.

MBA program overview

Having completed all but one course of the MBA program, I am now in a position to offer a better perspective concerning this program. Certainly the MBA can be considered a very useful professional degree, providing students with a wealth of knowledge applicable to the corporate world, particularly to intelligent and self-driven individuals aspiring to eventually rise to management and/or positions affecting the strategic direction of organization(s). Required courses include a combination of subjects involving a large amount of reading and synthesis- particularly in strategic planning, human behavior in organizations, operations management, leadership, information technology- as well as quantitatively based subjects including finance and accounting. The finance classes involve the most intense and advanced mathematical content. Mathematicians opting to complete the MBA program will likely derive the most enjoyment from these classes. Unsurprisingly, I opted for the finance emphasis in this program; as such, I completed classes in corporate valuation, investment and portfolio analysis, in addition to the required basic finance class. The strategic management class was also quite interesting, as it involved a business simulation game in which the class was broken down into 10 competing companies in the same industry. Over a 10-week period, we competed to optimize our own company's value and market share; each week, we made decisions regarding pricing, marketing, production, etc., with performance in the subsequent "year" dependent on the decisions made and entered into the simulation by each team. It was a fascinating illustration of game theory in practice.

MBA Program- Prerequisites and Admission

In previous postings, I discussed post-college educational paths for mathematicians seeking to improve their knowledge and career options. A large degree of self-evaluation, perhaps through a degree of trial and error, would be in order.
After considerable reflection, I am beginning an online MBA (Master's in Business Administration) program, with an emphasis on finance. This seems to be the wisest program for me at present. The online format allows me to continue working during the day, and allows the flexibility of possibly completing the program in less than 2 years, or- if necessary- slowing down the course of study and taking up to 5 years to complete.
I shall relay experiences concerning the MBA program as I have them to relate. Thus far, my suitability for the program is confirmed statistically. As a prerequisite for admission, candidates are required to take the GMAT, a computer-administered exam with a math section, English section, and section with 2 essays. The score used by universities in admitting students is based on the math and English section, with an average score around 500, and most scores between 400 and 600. The GMAT's statisticians claim there is a .51 correlation between GMAT score and GPA among first year MBA students. The GMAT is comparatively expensive- costing $250. To forewarn testtakers in advance, the math section is designed such that problems will become harder upon answering questions correctly, and less challenging after problems are answered incorrectly. This unusual method of testing- which is not utilized in the English section- seems to cause regression to the mean. In my case, my percentile in the math section was lower (yes, lower!) than that in the English section. Mathematicians, or other testtakers with a strong quantitative background, should not be shocked if they have this same experience.

Versatility of Mathematicians to Employers

I have just learned that I passed the CSET exam in earth science. Having previously passed the CSETs in foundational science, physics, chemistry, and biology, I shall soon (after completing the necessary paperwork) be considered highly qualified to teach any of the major sciences- in addition to math- through 12th grade.
I am posting this online not to brag of my accomplishment, but rather to point out our versatility to employers. My background was in applied math- not science- yet despite being over 12 years out of college, was able to successfully prepare myself for college-level exams demonstrating my mastery in all of the major sciences! Many employers seem rather short-sighted, focused on testing what skills potential employees have on that same day. Foolish! Has not this past recession and ongoing slump demonstrated the consequences of pursuing short-term gain at the expense of society's long-term prosperity? We mathematicians are a wise investment for a company. A wise employer would see the benefit of hiring us if our skills are "deficient" in certain technical areas, as we are easily and quickly trainable. We can quickly surpass the performance of a non-mathematician who, though initially more "skilled", is more specialized in his studies and mental processes, and thus more difficult to train for his and the company's future good.

Mathematician's Guide to the Public Schools

My perspective concerning the situation in the public schools displays a measure of cynicism. The reasons for this are numerous, and run far deeper than budget cuts and limited teacher openings. School systems have for over 10 years complained of shortages of qualified math (and science) teachers. This phenomenon is in fact not the problem, but rather a symptom of the problems in today's public schools.
A mathematician such as myself, with a long family history of scholars and educators, may initially find the prospect of working in the public schools to be attractive. He expects that his innate mathematical talent will be appreciated by many of the students, and that the kids will respect his consistent enforcement of his behavioral standards in the classroom. Given that school systems complain of shortages of math teachers, he expects school principals will be highly motivated to support him as a teacher, and certainly will want to award him tenure at the end of his second or third year in the district. He naturally intends to grow as a teacher over the years, and- being tenured- will be able to provide for his family from that point on.
When he finally completes the credential program and enters the classroom, he faces the reality of today's public schools. Many students appreciate his mathematical knowledge and talent, but others would prefer not only to avoid learning, but also to disrupt the class and prevent all of the others from learning. The mathematician is initially patient, but soon needs to discipline the non-compliant students. Now the mathematician's personality becomes a liability. In most cases, the administrators do not support the mathematician's actions, but rather blame him for some of the students' disruptive behavior! It is not the kids' fault for misbehaving; rather, the teacher is responsible for not being able to relate well to these kids and- by establishing rapport with all of them- inspire them to not misbehave. The new student-centered learning environment requires the teacher to mould his expectations to the kids' wishes. Many kids are rude and discourteous, seeing nothing wrong in blatantly talking to classmates when the teacher is talking. Teachers who actually follow school policy prohibiting use of cell phones, headphones, and the like in class are considered "uncool" and overly strict by kids, who respond by being even more disruptive. Consequences for repeated disruption or even severe misbehaviors are usually light, and the kids are well aware of this. The inmates are now running the asylum! Only a master in the area of social interactions can manage these kids, and the mathematician- who as I indicated previously is typically deficient in this area- will find this a struggle. Even as he exerts his maximum available energy into running his classes, and several off-duty hours per day preparing for classes, grading, contacting parents, meeting parents, tutoring students and/or holding after-school detention, he finds his efforts are unappreciated by many students, their parents, and many administrators. He now knows the reason that 50% of teachers leave this stressful profession- often after such stress affects their health- within 5 years. (From personal experience, nearly everyone in the teaching credential program is initially energetic, altruistic, and optimistic as they prepare to enter the field of education). It is also evident why school districts face a shortage of qualified math teachers. Mathematicians and scientists are not desired in the classroom. Instead, administrators seek teachers who can relate well to and be accepted by their kids, including the difficult kids who have no desire to learn. Oh, by the way, we cannot use the term "bad kids"; rather, those who are a challenge are classified as "good kids who make bad choices." This follows even though the presidential and vice-presidential candidates in 2008 freely made reference to "bad teachers" who should not be in the classroom. What administrators seek are not masters of the subject matter, but rather masters of socialization and interaction with their students. Subject matter mastery is far less important, leading to mediocre quality of education. Future innovation in this country- which would greatly help our economy in the long term- is impeded, as both administrators and politicians are focused on the short-term at the expense of the long-term.