An Appreciation of Academic Material and A Review of The Art of Computer Programming

I’ve enjoyed reading textbooks for a while now. I first picked up the infamous Campbell Biology in the beginning of 10th grade after being encouraged by a friend to participate in USABO (to his disappointment, I forgot to take the exam despite registering). I had read nonfiction books suitable for the layperson, skimmed news articles, analyzed op-eds, and watched educational YouTube videos, but textbooks and academic publications were new to me. Admittedly, it was difficult to conceptualize Campbell Biology’s many complex concepts as I was unfamiliar with the style and rigor of academic writing. However, by persevering through half of the textbook (I couldn’t bring myself to finish it), I developed a proficiency in comprehending academic material that has continued to reward me. Unlike lay scientific material, academic material is intended for rigorous study. This rigor can only be appreciated as one endeavors to apply concepts delineated within academic material. Consider the way planes function.

Here is an overview of how planes work according to ChatGPT:

Planes, also known as aircraft, work based on the principles of aerodynamics and propulsion. The basic concept involves generating lift to counteract the force of gravity, allowing the plane to stay in the air, and using engines to provide forward thrust for movement.

Here's a simplified explanation of how planes work:

1. Lift: Lift is generated by the wings of the plane. The wings are curved on the top and flatter on the bottom, creating a shape called an airfoil. As the plane moves forward, air flows over the wings. The curved shape of the airfoil causes the air to move faster over the top, creating lower pressure, while the flatter bottom creates higher pressure. This pressure difference generates lift, pushing the plane upward.

2. Thrust: Thrust is produced by the engines of the plane. Most modern planes use jet engines, which work on the principle of jet propulsion. Jet engines draw in air, compress it, mix it with fuel, and ignite it. The resulting high-velocity exhaust gases are expelled backward, creating a forward thrust force that propels the plane through the air.

3. Control: To maneuver the plane, various control surfaces are used. The primary control surfaces are the ailerons, elevators, and rudder. Ailerons are located on the trailing edges of the wings and control the roll or banking motion of the aircraft. Elevators, typically found on the horizontal tail surface, control the pitch or up-and-down movement. The rudder, located on the vertical tail surface, controls the yaw or side-to-side movement of the aircraft.

4. Stability and Control: Planes are designed to be stable and controllable. The center of gravity (CG) must be properly balanced, and the wings and tail are designed to provide stability and control. The design incorporates various factors, such as the position of the wings and tail, to ensure the plane maintains stability during flight.

5. Navigation and Communication: Modern planes are equipped with navigation and communication systems that allow pilots to navigate accurately and communicate with air traffic control. These systems include instruments such as altimeters, airspeed indicators, navigation radios, GPS, and communication radios.

 

The accuracy of these facts is irrelevant to the point I’m trying to articulate. While an elementary understanding of concepts is beneficial, I can’t reasonably expect someone to design a plane with this information alone. This is where the rigor of academic material becomes essential. Being able to formally define all of these concepts and perform relevant calculations is necessary to design a plane. As much as some of us wish that courses could keep ideas simpler, simplification at the expense of comprehension holds potentially lethal repercussions. 

Reading textbooks and other academic material, such as research papers, can teach us to think more rigorously within a field outside our own. Research is a gradual process premised upon finder details; sudden epiphanies don’t magically solve large problems. With all of this said, I’d like to recommend this article , which contains the ‘best’ textbooks on every subject. 

I don’t believe that I’m knowledgeable enough to recommend any textbooks, but I would like to review one of the most famous textbooks of all time: The Art of Computer Programming by Donald Knuth. The Art of Computer Programming is a series of volumes and fascicles about theoretical computer science, specifically the analysis of algorithms. It is notorious for its unrelenting rigor and exercises, some of which are extremely challenging unsolved problems in computer science. I worked through roughly the first 100 pages of Volume I, which cover the mathematical fundamentals used in the rest of the series. Therefore, I can only critique this portion of the book, but I believe my criticism holds true for the entirety of Volume I. I re-emphasize that I am not a mathematician or computer scientist and this criticism is from the perspective of a high schooler who wants to learn more about theoretical computer science. 

Volume I begins with instructions for reading the rest of the series in the form of an algorithmic flowchart, setting the rigor of the series early on. The only prerequisites for the series are basic algebra, minimal experience programming, and a rudimentary understanding of computer architecture. Some of the optional concepts and exercises require higher math, ranging from vector calculus to linear algebra to real analysis. Don’t let the lack of prerequisites fool you—this book is the most challenging textbook I’ve ever read and demands an affinity for mathematical rigor. In his explanations, Knuth demonstrates a deep, infectious passion for his field that has encouraged me to consider academia as a career option. That’ s a level of praise I can’t give many books. Anyone who falls in love with the concepts in the book as I did will relish the challenge it provides and put it down more intellectually capable than before. I genuinely feel that this book opened a deeper level of thinking to me. 

I respect Knuth’s dedication to the series, which he drafts by hand on paper before committing it to LaTeX. He’s spent over 50 years on this series of books alone and I hope he may eventually complete it without compromising on quality. Notwithstanding, the book takes many liberties that not everyone will be fond of. Knuth regularly uses special notations and omits smaller algebraic steps in his proofs, making it unnecessarily difficult for readers to understand. Furthermore, his explanations expect the reader to automatically catch specific implications. This is most evident when he writes that part of a solution is trivial or that a proof suddenly becomes clear at a certain step. I’m no fan of didactic explanations, but rigor for the sake of rigor is pedagogically detrimental. I doubt it’s the result of ego; rather, it seems that Knuth has such a deep understanding of his field that he struggles to see a learner’s perspective. I did improve at identifying mathematical implications consequently, but I would have preferred if some of Knuth’s explanations were more thorough.

There are many exercises at the end of each chapter and all of them, save for the grand unsolved problems in computer science, have an answer and explanation. Math books are notorious for omitting answers and explanations to exercises, so this was greatly appreciated. The exercises cover a wide range of difficulties and some of them require higher math. I loved being able to set aside more difficult problems for later, although Knuth’s estimations of difficulty aren’t always accurate.

Overall, I enjoyed my time with The Art of Computer Programming. Its issues in explaining concepts aside, it gave me a deep appreciation for theoretical computer science and taught me to think at a greater level. I highly recommend anyone who is interested in math and computer science to at least check it out, though there are many more suitable books for learning data structures and algorithms.