Julianne Barnhart

About Julianne

I am currently a PhD Candidate and Graduate Teacher of Record in the School of Mathematical and Statistical Sciences at Clemson University in South Carolina. I work under the supervision of Michael Burr studying computational and numerical algebraic geometry.

I am originally from the beautiful state of Washington. I completed my undergraduate studies at Gordon College in Wenham, Massachusetts with a double major in Mathematics and History. In my free time I enjoy getting outside, reading, playing board games, and solving crossword puzzles.

Julianne Headshot here

Teaching

Teaching Philosophy

Courses Taught

Clemson University

  • MATH 1080, Calculus of One Variable II: Fall 2025
  • MATH 1070, Differential and Integral Calculus: Spring 2025
  • MATH 1060, Calculus of One Variable I: Fall 2023
  • MATH 1040, Precalculus and Introductory Calculus: Fall 2024, Spring 2023, Fall 2022, Spring 2021, Fall 2021

    • Courses TA'd

    Clemson University

  • MATH 1030, Elementary Functions: Summer 2024, Summer 2021
  • MATH 9000, Introduction to Teaching College Mathematics: Spring 2024
  • MATH 1080, Calculus of One Variable II: Spring 2024
  • MATH 1980, College Algebra: Summer 2022
  • MATH 1060, Calculus of One Variable I: Summer 2021
  • MATH 3110, Linear Algebra: Spring 2021
  • MATH 2060, Calculus of Several Variables: Fall 2020

    • Gordon College

  • MAT 231, Transitions to Higher Mathematics: Fall 2017

    • Research

    Interests

      My research focuses on the behavior of polynomial systems. Broadly speaking, I am interested in questions within algebraic geometry, also called non-linear algebra, and I approach them using computational methods. Current questions include:
  • Monodromy groups of restricted sparse polynomial systems
  • Applications of monodromy to real polynomial systems solving
  • Machine learning real solutions to polynomial systems
  • Computing algebraic objects with Macaulay2

    • Publications

    • Restricted Monodromy and the Sparse Trace Test J. Barnhart, T. Brysiewicz, M. Burr, T. Yahl Preprint forthcoming, 2025
    • Identifying Trace Affine Linear Sets Using Homotopy Continuation J. Barnhart (née McKay) MS Thesis, 2022 PDF
    Research Statement

    Curriculum Vitae

    Education

    • 2020-2026 PhD Candidate in Mathematics, Clemson University
    • 2015-2019 BA in Mathematics and History, Gordon College

    Academic Positions

    • 2020-present Graduate Teacher of Record, Clemson University
    • 2020-2025 Private Tutor
    Download Full CV

    Contact

    mckay6@clemson.edu