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Melody Walton

@melodywalton

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Dedicated Ph.D. in Mathematics with a passion for research and teaching.

United States

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What I'm looking for

I seek a collaborative environment that fosters academic growth and innovative research opportunities.

I am Dr. Melody Walton, a passionate Ph.D. holder in Mathematics with a strong foundation in both theoretical and applied mathematics. My academic journey has equipped me with advanced problem-solving and analytical skills, which I am eager to leverage in a research-oriented or academic position. My dissertation focuses on the stability of nonlinear partial differential equations in high dimensions, showcasing my commitment to contributing innovative ideas to the field.

Throughout my time at the University of Texas at Austin, I have gained extensive teaching experience as a Graduate Teaching Assistant and Lecturer in Mathematics. I have developed and delivered lectures on various mathematical topics, provided individual tutoring, and collaborated with professors to enhance the learning experience for students. My research endeavors have led to publications in peer-reviewed journals, and I have presented my findings at international conferences, further solidifying my expertise in algebraic geometry and mathematical modeling.

Experience

Work history, roles, and key accomplishments

Current

Independent Research

Current

University of Texas at Austin

Jun 2023 - Present (2 years)

Conducted independent research in algebraic geometry, specifically on the classification of singularities in higher-dimensional varieties. Presented findings at several international conferences, including the International Conference on Mathematical Analysis, 2024.

Algebraic Geometry Singularity Classification Research Public Speaking

Lecturer in Mathematics

University of Texas at Austin

Jan 2024 - Present (1 year 5 months)

Developed and delivered lectures on topics including Real Analysis, Number Theory, and Mathematical Logic. Provided office hours and individual tutoring to students to improve their understanding of complex concepts. Designed and graded homework assignments and final exams.

Real Analysis Number Theory Mathematical Logic Curriculum Development

Research Assistant

University of Texas at Austin

Aug 2021 - Present (3 years 10 months)

Worked on a research project exploring nonlinear systems of partial differential equations, focusing on stability analysis and high-dimensional behavior. Published research papers in peer-reviewed journals related to stability analysis and mathematical modeling. Collaborated with multidisciplinary teams on projects involving computational methods and statistical modeling.

Statistical Modeling

Graduate Teaching Assistant

University of Texas at Austin

Aug 2021 - Present (3 years 10 months)

Assisted in teaching undergraduate courses in Calculus I, Linear Algebra, and Differential Equations. Led review sessions and graded assignments, quizzes, and exams. Collaborated with professors to develop teaching materials and curricula.

Linear Algebra Curriculum Development

Education

Degrees, certifications, and relevant coursework

University of Texas at Austin

Doctor of Philosophy (Ph.D.), Mathematics

Completed a Doctor of Philosophy degree with a focus on theoretical and applied mathematics. Dissertation research explored the stability of nonlinear partial differential equations in high dimensions, under the advisement of Dr. Johnathan Smith.