Do the Math

We are all victims of our childhood. My childhood started and ended with math. And yes, I was a victim. Math is first-order angst. Let us expand the math horizon, gently.

My earliest math memory was standing on my tiptoes peering over my father's desk as he worked. My father's work was triple integration (think dx, dy, dz) and spherical geometry (think not one, but two angles on different planes). He was gaming the volumes of spy satellite stuff as compared to the weight of the satellite. I pretended to be Dad by tracing french curves on MIT semi-log graph paper.

I am still pretending.

Rods

1962. I have the scars of half-degree burns on my face and left ear from my father ventilating over Rods. Rods, see photo above, was a con-job foisted on America post-I.G.Y. (see Donald Fagen). I won't bore you with the details but the Rods Debate was in the same set as the recent Core-Curriculum idiocy in New York State. (Do they understand, parents literally took their children out of New York schools because of this play-with-Gumby math? These two tragedies went in search of a substitute for the rigor, the struggle of basic math and then on to the continued struggle of first algebra. Their 'success' was to create a caste system of those that get math and those that do not. The math haves win and advance; the math have-nots, particularly those on in years, hide in silence and search for a path to math.

Concept, Geometry, Algebra, Diffy Qs

Understand at the margin, you have to get better at what you're good at while trying to strengthen what is weak. Start with the foundational path: concept first, then the geometry of whatever the topic is, then the algebra and then the dynamics of the thought, often expressed as a differential equation. My experience is out of 100 people, 40 are clueless, another 30 get the concept, 16 the geometry, 8 the algebra and 4-at-best the differential dynamics. Start with concept. Always start with concept. (Mathy types will note I can't count to 100 which is exactly what my father said.)

The above is not funny. Our math education is a travesty after guessing 7th grade. We crater on things Euclid, avoid the rigor of algebra and leave things static & dynamic to a LinkedIn set who are never out of a job and make factors more than the rest of us. Fact: the correlation of math ability to compensation-prospects is off the semi-log chart. Newtonian Moment: This is bound to get worse in the coming years. The 2020 math-gap second-derivative is accelerating.

Not Taking The Calculus

Call it T-Ball Math. We have grade-inflated our yout into believing they have math nailed. Everyone goes home with a trophy. We are drowning our offspring in an ocean of blue ribbons. On the nailing of math...most do not. This starts young. I have the clearest memories of the beyond-esteemed college advisor at the well-ivyed prep school explaining that they did not inflate grades. This precluded their chosen ones from too many colleges-of-their-choice. The 3-point-3 cherubs had to compete with sundry 4-point-0s from St. Inflated. Memo: Cash Flow turned out fine. Like Dad, and unlike his grandfather, he went down in flames on Brook Taylor's series. (The Taylor series for any polynomial is the polynomial itself.) 

Further, another offspring's headmaster punted the entire Advance Placement folly to infinity. I have lost count of select sainted interns who 'APed' math, did zero in college and are math-dumb as a wooden K & E slide rule. The immediate collegiate need for a better LinkedIn world is a required taking of one of three levels of the Calculus freshman year. If you took AP calc., take engineering calculus. You will think differently. Forever. 

If tangents did you in, by all means, take MATH 1050: Quantitative Reasoning (offered in the fall and the spring by the Director or Lecturer of the QR Program) for a general entry-point course with an emphasis on quantitative, statistical and financial literacies. Go Bowdoin Polar Bears!

Eli's Coming

You're beyond school. Obvs is to ramp up understanding of the basic math you forgot. Obvs deux is to read a calculus primer and nail basic differentiation and integration. Less obviously, ramp up your knowledge of the Cartesian space. Trigonometry is the great desert of American math ignorance. Depression: I just discovered that my beloved calculus text is in its 14th edition.

I go off on a tangent: Where is the fun? Where is the glory? Where is the, "Wow, that is so cool?"

Read Eli Maor. He has endless jewels, all wonderful. His coffee table book stops cocktail conversation cold. To keep things LinkedIn terse, his Trigonometric Delights resurrects the dead from the SOHCAHTOA of a distant adolescence. It is one part basic, one part stretching and one part difficult. Maor will take you to infinity and beyond. Trigonometric Delights is one example of what is missing in America's abject math failure. There must be a grace to math & science and Eli Maor is definitive in gifting us the grace of Math.

I can't help myself: Liberal Artists note, Jerry P. King's The Art of Mathematics is the single-best read on why we are so mathless. King was multiple decades ahead of any and all. It is a LinkedIn required read.

Learn the Log Y-axis

Jim Bianco is a required LinkedIn follow. His stream is deep and filled with logs. He does economics and finance and investment and outstanding charts on our 2020 virus, all with an odd vertical axis. That would be the y-axis. I won't take the space here, but a jump-condition to better math understanding is to understand that things exponential look and feel better with a logarithmic y-axis. If you don't understand the previous sentence, that is not good.

Learn a passing understanding of logarithms and how a semi-log chart shows proportional or percentage change. Go further, and strap the line, the series, to calculus where the slope of the line matters and the change in the slope matters evermore. Still pondering: ponder the wonderful Schaum's series on all things math. Wisdom is found in this Schaum's, all of chapter 9. Section 9.18 is about a boy tracing french curves. 

The Clarity of Chiang

Finally, and way more advanced, but as worthy as that time you finally figured out long division, is the quiet salvation of every graduate student. Say, you took anthropology with a double major in medieval french. Say, you applied to a group of schools knowing that if you were accepted, you would be the dumbest math-person in the class and/or zipcode. Say, you got an acceptance letter April 10th. You have 114 days to get smarter. In 1967 an economist by way of Shanghai then Colorado then Columbia published a book-for-the-century. (Consider the import of 'by-way-of Shanghai' within the middle 1960s.)

Alpha Chiang's Fundamental Methods of Mathematical Economics is near-800 pages of clarity. Chapter 10 is 35 pages of density on all things logarithmic. Chiang's magic and that of Kevin Wainwright, who has kept the torch burning, is the paragraph to next-paragraph clarity. The Chiang borders on religion. It begins on page one and never, not for one moment lets up. I can't find words for the value of struggling with any given chapter, sentence by sequential equation.

I see it each and every day. There are science majors that slipped by with minimal math understanding. There are liberal arts majors who just crush critical-thinking skills earned from mastering first-order difference equations (that's you Keiren!). The reality of 2030 America is we will be devoid of math confidence. Read Maor, read Bianco, daily. Keep the Schaum's out of reach of the children, keep the Chiang hidden under your bed. Just...

Do the Math.