Q. E. D.

Listen to the work here!
(Note: Extended techniques present in some etudes are not accurately reflected in the audio file linked above. If you'd like to produce a recording of the work, please reach out!)
 
Q. E. D. is a collection of etudes for solo snare drum. These etudes are rudimental in nature, although designed to be performed on a concert snare drum. The title of this collection is an abbreviation of the Latin phrase “quod erat demonstrandum”, meaning “that which was to be demonstrated”. This three letter abbreviation, or a black square indicating the same thing, is commonly used at the end of mathematical proofs, indicating that through logic and mathematical reasoning, that which the proof set out to demonstrate has been demonstrated.
 
Each etude in this collection is based on a math class that I took (or otherwise received credit for) toward earning my Bachelor of Science degree in Mathematics from the University of North Texas. These various mathematical topics are translated into music primarily through the idea of a character suite, putting this work in line with several others of mine which are character pieces based on math and science concepts. Some of the etudes also employ a certain degree of process-based or algorithmic composition, the algorithms themselves becoming the characters which connect each etude to its mathematical inspiration. The etudes are as follows:
Calculus I: A rudimental jam session that moves through several contrasting sections, which is inspired (punnily) by a specific rhythmic figure from JLin’s “Derivative”.
Calculus II: Using the Derivative Rhythm as a jumping off point, this etude builds up a single musical phrase one bit at a time, mimicking the partial sums of an infinite series.
Discrete Math: Inspired by the study of modular arithmetic, this etude in 19/16 takes a single musical phrase and permutates through all nineteen possible starting positions.
Linear Algebra: Short musical ideas expand outward, then fragment only to expand outward again, in a process like of a continuously expanding linear transformation.
Calculus III: Once again marked by the Derivative Rhythm, this etude in 9/8 time is inspired by multivariable calculus’s journey into the third dimension (9 = 3 * 3).
Real Analysis: This is a topic which rigorously builds the notions of real numbers through logic, and their continuity is given character here with a buzz-roll style etude.
Number Theory: Music with a metric structure of 22+7, referencing the 22/7 approximation for π which is used to introduce the idea of Diophantine approximations.
Differential Equations: This etude is modeled after a dramatic hunting song, based on the differential equation model of predator-prey relationships in an ecosystem.
Abstract Algebra: To complement the idea of doing algebra without numbers, this etude has no notes on the head of the drum and very little strict melodic development.
Applied Statistics: This etude is based on a random distribution of meters, which evenly fill out the range of 4 to 19 sixteenth notes, like responses to a musical survey.
Vector Calculus: As this is the most advanced purely computation based class here, the etude is quiet and skittering, like the rattling sounds of a calculator or pencil on paper.
Foundations of Geometry: This etude is a musical transliteration, step by step, of the geometric construction of a circle through two given points tangent to a given line.
Graph Theory: A companion to a longer work for snare drum, this minimalist etude uses complex rhythmic subdivisions to gradually morph short motifs into each other.
Functions of Complex Variables: As a musical finale and representation of the complex plane, this theme and variations uses each other etude to create each musical variation.