Papers

• Bryce Christopehrson & Casia Steinhaus.  Bounds on the Critical Multiplicity of Ramsey Numbers with Many Colors.  10pp.  (Under Review).

• Bryce Christopherson & Jack Baretz.  When do the Kahn-Kalai Bounds Provide New Information?  Journal of Inequalities and Applications volume 23. 8 pp. (2025)

• Bryce Christopherson.  Ramsey-Theoretic Characterizations of Classically Non-Ramseyian Problems.  22 pp. (Under Review).

• Bryce Christopherson & Darian Colgrove.  A Conditional Extension of the Park-Pham Theorem.  9 pp. (Under Review)

• Bryce Christopherson, Boris Mordukhovich, Farhad Jafari. Continuous feedback stabilization of nonlinear control systems by composition operators. ESAIM: Control, Optimisation and Calculus of Variations, 22 pp. (2022).

• Bryce Christopherson & Dudo Salazar. Artificial Intelligence and Machine Learning Approaches for Enhanced SDA. Project West Wing Formal Report, The Aerospace Corporation, 49 pp. (2021).

• Robert Nelson & Bryce Christopherson.Digital Threat Model Verification & Validation. Technical Operating Report, The Aerospace Corporation, 7 pp. (2021).

• Bryce Christopherson, Farhad Jafari, Boris Mordukhovich.  A Variational Approach to Local Asymptotic and Exponential Stabilization of Nonlinear Systems. SN Operators Research Forum 1, 5, 28pp. (2020)

• Bryce Christopherson.  Stability in Common and Uncommon Places.   University of Wyoming, Ph.D. Dissertation, 264 pp. (2019).

Research

My research primarily focuses on stabilization phenomena, particularly in control theory, combinatorics (for example, Ramsey theory or thresholds for random objects), and in artificial intelligence (for example, lottery ticket emergence in sufficiently large neural networks).  In a nutshell, I am interested in understanding what is `really going on under the hood' when collections of objects suddenly stop `acting crazy' and start to `settle down' and become more structured--it seems like there should be a more unified way of understanding how this happens.  I am also interested in applied problems of all sorts--some recent and ongoing projects focus on optimal control topics in water purification plants, boosting the resiliency of electrical grids, describing malware propagation, and the coordinated operation of satellite swarms.

I enjoy advising graduate students and maintain an active research group of undergraduate student researchers.  I am always happy to take on new students to the extent that my schedule allows it, and I am always interested in hearing from anyone who may be interested in working on fun math problems with me.

Current Graduate Students

• Darian Colgrove (2026)

Past Graduate Students

• Ganesha Thondilege (2025)

• Alesinloye Tunde (2025)

• Daniel Kwakye (2025)

• Jonathan Wirkkala (2025)

Current Research Group Members

• Salah Dandan (2024-present)

• Jack Baretz (2023-present)

• Casia Steinhaus (2023-present)

Past Research Group Members

• Augustus Tandberg (2024)

• Gabrielle Wahl (2024)

• Martin Epstein (2024)

Teaching

Education for the sake of merely imparting information is all too common, and egregiously sells short the enduring, earnest dignity of real learning. Knowledge alone is paltry compensation in comparison to the truest and most precious gift an educator might offer: the courage to do and to think, to labor shamelessly towards understanding and to see the inevitable failures this endeavor brings with it as curiosities to be studied with joy, undeterred and persistent in the face of any setback.  Read my Statement of Teaching Philosophy here.

Courses Taught

• 2025 (Fall) Set Theory, University of North Dakota

• 2025 (Fall) Elementary Differential Equations, University of North Dakota

• 2025 (Spring) Linear Algebra, University of North Dakota

• 2025 (Spring) Elementary Differential Equations, University of North Dakota

• 2024 (Fall) Elementary Differential Equations, University of North Dakota

• 2024 (Spring) Linear Algebra, University of North Dakota

• 2023 (Fall) Numerical Analysis, University of North Dakota

• 2023 (Spring) Linear Algebra, University of North Dakota

• 2023 (Fall) Discrete Mathematics, University of North Dakota

• 2022 (Spring) Intro to Complex Analysis, University of Wyoming

• 2020 (Spring) Calculus I, University of Wyoming 

• 2019 (Fall) Algebra and Trigonometry, University of Wyoming

• 2019 (Fall) Calculus I, University of Wyoming 

• 2019 (Summer) Business Calculus, University of Wyoming

• 2019 (Spring) Elementary Linear Algebra, University of Wyoming

• 2018 (Fall) Calculus I, University of Wyoming 

• 2018 (Summer) Problem Solving, University of Wyoming

• 2018 (Summer) Business Calculus, University of Wyoming

• 2018 (Spring) Calculus III, University of Wyoming

• 2017 (Fall) Calculus II, University of Wyoming

• 2017 (Summer) Business Calculus, University of Wyoming

• 2017 (Spring) College Algebra, University of Wyoming

• 2016 (Fall) College Algebra, University of Wyoming

• 2016 (Summer) Problem Solving, University of Wyoming

• 2015 (Fall) Algebra and Trigonometry, University of Wyoming

University Service

• Student Academic Appeals Committee, University of North Dakota, (2025-2028)

• University Senate Essential Studies Committee, University of North Dakota (2025-present)

• Colloquium Committee Member, University of North Dakota Mathematics Department (2024-present)

• Applied Mathematics Committee Member, University of North Dakota Mathematics Department (2024-present)

• Executive Committee Chair, University of North Dakota Mathematics Department  (2024-present)

• Non-tenure-track Instructor Job Search Committee Member, University of North Dakota Mathematics Department (2023)

• Seminar Organizer, University of North Dakota Mathematics Department (2023-present)

• Tenure-track Assistant Professor Job Search Committee Member, University of North Dakota Mathematics Department (2023)

• Non-tenure-track Teaching Professor Job Search Committee Member, University of North Dakota Mathematics Department (2023)

• Non-tenure-track Math Active Learning Lab Assistant Director Job Search Committee Member, University of North Dakota Mathematics Department (2023)

• Executive Committee Member, University of North Dakota Mathematics Department  (2023-present)

• Curriculum Review Committee Member, University of North Dakota Mathematics Department (2023-present)

• Assessment Committee Member, University of North Dakota Mathematics Department  (2022-present)

• Tutoring Director, University of Wyoming Department of Mathematics & Statistics (2019-2020)

• CRLA Tutor Certification Training Workshop Coordinator, University of Wyoming Department of Mathematics & Statistics (2019-2020)

• Mathematics Tutor Subject Matter Competency Training Coordinator, University of Wyoming Department of Mathematics & Statistics (2019-2020)

• Professional Development Workshop Speaker (Talk: Job Searches, Building Your Professional Network, and CV/Resume Writing), University of Wyoming Department of Mathematics & Statistics (2020)

• Professional Development Workshop Speaker (Talk: Effective Grading for Large Enrollment Courses Workshop), University of Wyoming Department of Mathematics & Statistics (2019)

• Incoming Graduate Student Mentor, University of Wyoming Department of Mathematics & Statistics (2018)

Selected Presentations

• When do the Kahn-Kalai Bounds Provide New Information?,  Topics in Pure and Applied Mathematics Seminar, University of North Dakota  (2024)

• An Introduction to Comma Categories and Slice Categories with Examples,  Topics in Pure and Applied Mathematics Seminar, University of North Dakota  (2023)

•  A Primer on Lyapunov Theory,  Topics in Pure and Applied Mathematics Seminar, University of North Dakota  (2023)

• An Extension of the Kahn-Kalai Bounds,  Topics in Pure and Applied Mathematics Seminar, University of North Dakota  (2023)

• Some Algebraic Techniques for Ramsey Theory,  Mathematical Association of America North Central Section Fall Meeting, University of Minnesota Duluth (2023)

• Some Algebraic Techniques for Ramsey Theory,  Topics in Pure and Applied Mathematics Seminar, University of North Dakota  (2023)

• The Feedback Stabilization Problem and Local Sections,  Topics in Pure and Applied Mathematics Seminar, University of North Dakota  (2023)

• Expectation Thresholds and the Lottery Ticket Hypothesis,  Physics Colloquium, University of North Dakota  (2022)

• Expectation Thresholds and the Lottery Ticket Hypothesis,  Mathematical Association of America North Central Section Fall Meeting, University of North Dakota (2022)

• Understanding Upside-Down Reinforcement Learning, Reinforcement Learning Colloquium, Data Science & Artificial Intelligence Group, The Aerospace Corporation (2021)

• Integrated Digital Engineering Prototyping Testbed Hub:  Markovian Techniques for Mission Thread Analysis in Support of Acquisitions Decisions, Systems Engineering Forum, Computer Applications & Assurance Subdivision, The Aerospace Corporation (2020)

• An Introduction to Extremal Graph Theory in Intelligence Applications, Space Launch and Intelligence Colloquium, Strategic & Global Awareness Directorate, The Aerospace Corporation (2020)

• Variational Characterizations of Local Asymptotic and Exponential Stabilizability, Von Neumann Seminar in Analysis, University of Wyoming (2018)

• A K-Theory for Combinatorial Games, Graduate Presentations in K-Theory, University of Wyoming (2018)

• Local Asymptotic Stabilizability and the Smoothness of Stabilizing Controls, Von Neumann Seminar in Analysis, University of Wyoming (2017)

• Regularity of Linear Elliptic and Parabolic Solutions: A Weakening of the Lipschitz Condition, Graduate Presentations in Partial Differential Equations, University of Wyoming (2017)

• Trace Parameterization of Nonnegative Hermitian Trigonometric Polynomials: A Control Theory Perspective, Graduate Presentations in Harmonic Analysis, University of Wyoming (2017)

• The Combinatorial Game of Nim on Graphs, Graduate Research Seminar, University of Wyoming (2016)

• The Combinatorial Game of Nim on Trees, Mathematical Association of America, Mathfest, Washington DC (2015)

• The Combinatorial Game of Nim on Trees, Arthur Olsen Student Research Symposium, Augustana College (2015)

• Geometric Connections between Graphical and Integer Ramsey Theory: What can Van der Waerden Numbers tell us about congressional infighting?, Mathematics on the Northern Plains Regional Undergraduate Conference, Dordt College (2015)

• The Combinatorial Game of Nim on Trees, Mathematics on the Northern Plains Regional Undergraduate Conference, Dordt College (2015)

• The Combinatorial Game of Nim on Trees, Mathematical Association of America North Central Section Fall Meeting, North Dakota State University (2014)