Teaching philosophy

Relevant links

In practice

I adopt two separate views of mathematics; the first is that when practicing mathematics, I implicitly regard mathematical objects as existing in their own right. However, when teaching mathematics, I regard math almost entirely as a cultural activity, wherein people communicate observations about patterns with one another. I believe this is an important distinction to hold while teaching, because teaching is fundamentally enabled by effective communication.

I also regard math as an incredibly creative and artistic activity. The sentiments expressed in A Mathematician's Lament capture this view in better words than I can write, by comparing the art of mathematical reasoning to the arts of music and painting.

Expository publications

I have been a part of writing a couple textbook chapters, both for graduate and undergraduate students. Writing expository work is as important to me as writing original research work, beacuse expository work is what enables others to follow in your footsteps.

  • G. Micheli and A.W. Murphy. Locally recoverable codes and finding good polynomials. Springer Publishing, expected 2024.

  • G.L. Matthews and A.W. Murphy. Cryptography, in Mathematics in Cyber Research. CRC Publishing, February 2022. Link here

Course instruction

Virginia Tech

Visiting Assistant Professor

  • Math 1225: Calculus of a Single Variable
    Semesters: Fall 2022 (x2)
    Modalities: 2 in-person

Graduate Teacher of Record

  • Math 1225: Calculus of a Single Variable
    Semesters: Spring 2020, Fall 2020, Summer II 2021, Fall 2021, Spring 2022.
    Modalities: 2 in-person, 2 online, 1 transitioned mid-semester (COVID)
    Notes: 2 ESL sections, as part of the AdvantageVT Program

  • Math 1226: Calculus of a Single Variable
    Semesters: Spring 2021.
    Modalities: 1 online.

Other teaching

Virginia Tech

  • Tutor, Math GRE Tutor, VT PREP Program, Fall 2021

  • Grader, Math 2204: Introduction to Multivariable Calculus, Summer I 2020

  • Lab Instructor, Math 1026: Elementary Calculus, Spring 2019

Clemson University

  • Grader, Math 4120: Algebra I, Spring 2018

  • Grader, Math 3190: Introduction to Proof, Spring 2018

  • Teaching Assistant, Math 1080: Business Calculus II

S.U.N.Y. Geneseo

  • Lab Instructor, Physics 116: General Physics II Lab, Spring 2017

  • Lab Instructor, Physics 114: General Physics I Lab, Fall 2016

Expository talks

High-school level

  • Error-correcting codes, ASPIRE Program Brown-bag series, Johns Hopkins Applied Physics Laboratory (August 2023).

  • Computational complexity, ASPIRE Program Brown-bag series, Johns Hopkins Applied Physics Laboratory (July 2023).

  • Error-correcting codes, ASPIRE Program Brown-bag series, Johns Hopkins Applied Physics Laboratory (July 2023).

Undergraduate level

  • Code-based cryptography, Part III: McEliece's cryptosystem, Resilient Military Systems (QCM) Brown-bag series, Johns Hopkins Applied Physics Laboratory (July 2023).

  • Code-based cryptography, Part II: Computational hardness, Resilient Military Systems (QCM) Brown-bag series, Johns Hopkins Applied Physics Laboratory (May 2023).

  • Code-based cryptography, Part I: Error-correcting codes, Resilient Military Systems (QCM) Brown-bag series, Johns Hopkins Applied Physics Laboratory (April 2023).

  • How to Prove (in fewer pages than Bertrand Russell) that 1 + 1 = 2, Math Club, Clemson University (September 2017).

Graduate level

  • Locally recoverable codes, Virginia Tech Research Day, Virginia Tech (November 2022).

  • Codes from the Hermitian curve (guest lecture), Mathematics 5114 (Topics in Algebra: Applied Algebra), Virginia Tech (April 2022).

  • Algebraic geometry codes (guest lecture), Mathematics 5114 (Topics in Algebra: Applied Algebra), Virginia Tech (April 2022).

  • Welch-Berlekamp decoding of Reed-Solomon codes, Mathematics 5114 (Topics in Algebra: Applied Algebra), Virginia Tech (February 2022).

  • Reed-Solomon codes, Mathematics 5114 (Topics in Algebra: Applied Algebra), Virginia Tech (January 2022).

Other

  • Making progress on your dissertation, Mathematics Senior Graduate Teaching Assistant (SGTA) Seminar, Virginia Tech (February 2022).

  • Workshop: Creating your own website, Mathematics Senior Graduate Teaching Assistant (SGTA) Seminar, Virginia Tech (August 2021).